diff --git a/crates/ld-engine/src/compose.rs b/crates/ld-engine/src/compose.rs
index a97c89b..6f640e7 100644
--- a/crates/ld-engine/src/compose.rs
+++ b/crates/ld-engine/src/compose.rs
@@ -18,9 +18,11 @@
 //! - which proposals enter into force now (`adoptions`);
 //! - what the document would read if the well-rated, or all, proposals passed
 //!   (`preview`);
-//! - which formula a proposal is judged by (`params_for`).
+//! - which formula a proposal is judged by (`params_for`): the level of
+//!   inertia of its unit, on the scale of its group (`inertia::Scale`).
 
-use crate::threshold::{FormulaParams, InertiaPreset, Tally, ThresholdError, evaluate};
+use crate::inertia::{InertiaLevel, Scale};
+use crate::threshold::{FormulaParams, Tally, ThresholdError, evaluate};
 use serde::{Deserialize, Serialize};
 
 #[derive(Clone, Debug, PartialEq, Serialize, Deserialize)]
@@ -37,7 +39,7 @@ pub struct VersionText {
 pub struct UnitState {
     pub id: String,
     pub position: f64,
-    pub inertia: InertiaPreset,
+    pub inertia: InertiaLevel,
     pub in_force: Option<VersionText>,
 }
 
@@ -49,7 +51,7 @@ pub enum ProposalKind {
     /// Remove the unit from the text in force.
     Remove,
     /// Change the inertia of the unit.
-    Inertia(InertiaPreset),
+    Inertia(InertiaLevel),
 }
 
 impl ProposalKind {
@@ -72,13 +74,18 @@ pub struct ProposalState {
     pub blocked: bool,
 }
 
-/// A change of inertia is voted one level above the unit (« inertie + »).
-pub fn params_for(unit: &UnitState, kind: ProposalKind, floor: f64) -> FormulaParams {
-    let preset = match kind {
-        ProposalKind::Inertia(_) => unit.inertia.raised(),
-        ProposalKind::Text | ProposalKind::Remove => unit.inertia,
-    };
-    FormulaParams::for_inertia(preset, floor)
+/// The level a proposal is voted at. A change of inertia inherits the level of
+/// its unit, as its text does (Yvv, 2026-10-30: « par défaut l'inertie de
+/// l'indice d'inertie lui-même hérite de l'inertie de l'article ») — this
+/// replaces « inertie + », one level above (2026-10-21).
+pub fn voting_level(unit: &UnitState, kind: ProposalKind) -> InertiaLevel {
+    match kind {
+        ProposalKind::Text | ProposalKind::Remove | ProposalKind::Inertia(_) => unit.inertia,
+    }
+}
+
+pub fn params_for(unit: &UnitState, kind: ProposalKind, scale: &Scale) -> FormulaParams {
+    scale.params(voting_level(unit, kind))
 }
 
 /// A proposal that changes nothing cannot enter into force.
@@ -98,13 +105,8 @@ struct Scored<'a> {
     well_rated: bool,
 }
 
-fn score<'a>(
-    unit: &UnitState,
-    p: &'a ProposalState,
-    electorate: u32,
-    floor: f64,
-) -> Result<Scored<'a>, ThresholdError> {
-    let e = evaluate(p.tally, electorate, &params_for(unit, p.kind, floor))?;
+fn score<'a>(unit: &UnitState, p: &'a ProposalState, scale: &Scale) -> Result<Scored<'a>, ThresholdError> {
+    let e = evaluate(p.tally, scale.electorate, &params_for(unit, p.kind, scale))?;
     Ok(Scored {
         proposal: p,
         margin: i64::from(p.tally.for_votes) - i64::from(e.required),
@@ -126,9 +128,9 @@ fn best<'a>(mut rivals: Vec<Scored<'a>>) -> Option<&'a ProposalState> {
 }
 
 /// Margin of the version in force, judged like a text proposal on its unit.
-fn in_force_margin(unit: &UnitState, electorate: u32, floor: f64) -> Result<Option<i64>, ThresholdError> {
+fn in_force_margin(unit: &UnitState, scale: &Scale) -> Result<Option<i64>, ThresholdError> {
     let Some(v) = &unit.in_force else { return Ok(None) };
-    let e = evaluate(v.tally, electorate, &params_for(unit, ProposalKind::Text, floor))?;
+    let e = evaluate(v.tally, scale.electorate, &params_for(unit, ProposalKind::Text, scale))?;
     Ok(Some(i64::from(v.tally.for_votes) - i64::from(e.required)))
 }
 
@@ -138,19 +140,18 @@ fn in_force_margin(unit: &UnitState, electorate: u32, floor: f64) -> Result<Opti
 pub fn adoptions(
     units: &[UnitState],
     proposals: &[ProposalState],
-    electorate: u32,
-    floor: f64,
+    scale: &Scale,
 ) -> Result<Vec<String>, ThresholdError> {
     let mut out = Vec::new();
     for unit in units {
-        let incumbent = in_force_margin(unit, electorate, floor)?;
+        let incumbent = in_force_margin(unit, scale)?;
         for content in [true, false] {
             let mut rivals = Vec::new();
             for p in proposals.iter().filter(|p| p.unit_id == unit.id && p.kind.is_content() == content) {
                 if p.blocked || !is_effective(unit, p) {
                     continue;
                 }
-                let s = score(unit, p, electorate, floor)?;
+                let s = score(unit, p, scale)?;
                 let beats_incumbent = !content || incumbent.is_none_or(|m| s.margin > m);
                 if s.reached && beats_incumbent {
                     rivals.push(s);
@@ -200,8 +201,7 @@ pub struct PreviewUnit {
 pub fn preview(
     units: &[UnitState],
     proposals: &[ProposalState],
-    electorate: u32,
-    floor: f64,
+    scale: &Scale,
     mode: PreviewMode,
 ) -> Result<Vec<PreviewUnit>, ThresholdError> {
     let mut ordered: Vec<&UnitState> = units.iter().collect();
@@ -216,7 +216,7 @@ pub fn preview(
                 if !is_effective(unit, p) {
                     continue;
                 }
-                let s = score(unit, p, electorate, floor)?;
+                let s = score(unit, p, scale)?;
                 if mode == PreviewMode::All || s.well_rated {
                     rivals.push(s);
                 }
@@ -263,7 +263,7 @@ mod tests {
         UnitState {
             id: id.into(),
             position,
-            inertia: InertiaPreset::Standard,
+            inertia: InertiaLevel::DEFAULT,
             in_force: in_force.map(|b| VersionText {
                 id: format!("{id}-v"),
                 title: id.into(),
@@ -286,23 +286,27 @@ mod tests {
         }
     }
 
-    const W: u32 = 5745;
-    const C: f64 = 50.0;
+    /// Monnaie libre before any median: W 5745, C 50, the reference p0 = 2C/W.
+    const SCALE: Scale = Scale { electorate: 5745, floor: 50.0, participation: 100.0 / 5745.0 };
+
+    fn level(k: u8) -> InertiaLevel {
+        InertiaLevel::new(k).expect("1 to 5")
+    }
 
     #[test]
     fn nothing_passes_at_zero_votes() {
         let units = [unit("I1", 1.0, Some("préambule")), unit("E3", 7.0, None)];
         let props = [prop("p1", "E3", ProposalKind::Text, "connaître", 0, 0)];
-        assert!(adoptions(&units, &props, W, C).expect("valid").is_empty());
+        assert!(adoptions(&units, &props, &SCALE).expect("valid").is_empty());
     }
 
     #[test]
     fn the_floor_holds_then_releases() {
         let units = [unit("E3", 7.0, None)];
         let few = [prop("p1", "E3", ProposalKind::Text, "connaître", 49, 0)];
-        assert!(adoptions(&units, &few, W, C).expect("valid").is_empty());
+        assert!(adoptions(&units, &few, &SCALE).expect("valid").is_empty());
         let enough = [prop("p1", "E3", ProposalKind::Text, "connaître", 50, 0)];
-        assert_eq!(adoptions(&units, &enough, W, C).expect("valid"), vec!["p1".to_string()]);
+        assert_eq!(adoptions(&units, &enough, &SCALE).expect("valid"), vec!["p1".to_string()]);
     }
 
     #[test]
@@ -312,7 +316,7 @@ mod tests {
             prop("a", "E3", ProposalKind::Text, "variante a", 60, 0),
             prop("bb", "E3", ProposalKind::Text, "variante b", 70, 0),
         ];
-        assert_eq!(adoptions(&units, &props, W, C).expect("valid"), vec!["bb".to_string()]);
+        assert_eq!(adoptions(&units, &props, &SCALE).expect("valid"), vec!["bb".to_string()]);
     }
 
     #[test]
@@ -320,19 +324,22 @@ mod tests {
         let units = [unit("E1", 4.0, Some("unicité"))];
         let props = [
             prop("t", "E1", ProposalKind::Text, "unicité reformulée", 60, 0),
-            prop("i", "E1", ProposalKind::Inertia(InertiaPreset::High), "", 60, 0),
+            prop("i", "E1", ProposalKind::Inertia(level(4)), "", 60, 0),
         ];
-        let won = adoptions(&units, &props, W, C).expect("valid");
+        let won = adoptions(&units, &props, &SCALE).expect("valid");
         assert_eq!(won, vec!["t".to_string(), "i".to_string()]);
     }
 
     #[test]
-    fn inertia_change_is_voted_one_level_up() {
-        let u = unit("E1", 4.0, Some("x"));
-        let p = params_for(&u, ProposalKind::Inertia(InertiaPreset::Low), C);
-        assert_eq!(p.majority_pct, InertiaPreset::High.majority_pct());
-        assert_eq!(p.gradient, InertiaPreset::High.gradient());
-        assert_eq!(params_for(&u, ProposalKind::Text, C).gradient, InertiaPreset::Standard.gradient());
+    fn inertia_change_is_voted_at_the_level_of_the_unit() {
+        let mut u = unit("E1", 4.0, Some("x"));
+        u.inertia = level(4);
+        for target in [1, 3, 5] {
+            let kind = ProposalKind::Inertia(level(target));
+            assert_eq!(voting_level(&u, kind), level(4), "inherits the level of the article");
+            assert_eq!(params_for(&u, kind, &SCALE), params_for(&u, ProposalKind::Text, &SCALE));
+        }
+        assert_eq!(params_for(&u, ProposalKind::Text, &SCALE).majority_pct, 60.0);
     }
 
     #[test]
@@ -341,8 +348,8 @@ mod tests {
         let mut blocked = prop("t", "E1", ProposalKind::Text, "autre", 80, 0);
         blocked.blocked = true;
         let same = prop("s", "E1", ProposalKind::Text, "unicité", 80, 0);
-        let same_inertia = prop("i", "E1", ProposalKind::Inertia(InertiaPreset::Standard), "", 80, 0);
-        assert!(adoptions(&units, &[blocked, same, same_inertia], W, C).expect("valid").is_empty());
+        let same_inertia = prop("i", "E1", ProposalKind::Inertia(level(3)), "", 80, 0);
+        assert!(adoptions(&units, &[blocked, same, same_inertia], &SCALE).expect("valid").is_empty());
     }
 
     #[test]
@@ -350,20 +357,20 @@ mod tests {
         let mut units = [unit("E1", 4.0, Some("unicité"))];
         // The seed a minima has no vote: the first rival that reaches its threshold wins.
         let rival = [prop("r", "E1", ProposalKind::Text, "unicité reformulée", 50, 0)];
-        assert_eq!(adoptions(&units, &rival, W, C).expect("valid"), vec!["r".to_string()]);
-        // A version in force by vote, margin 60 − 50 = 10: a rival at margin 5 waits.
+        assert_eq!(adoptions(&units, &rival, &SCALE).expect("valid"), vec!["r".to_string()]);
+        // A version in force by vote, margin 60 − 58 = 2: a rival at 55 (margin 55 − 54 = 1) waits.
         if let Some(v) = units[0].in_force.as_mut() {
             v.tally = Tally { for_votes: 60, against: 0 };
         }
         let weaker = [prop("w", "E1", ProposalKind::Text, "autre", 55, 0)];
-        assert!(adoptions(&units, &weaker, W, C).expect("valid").is_empty());
+        assert!(adoptions(&units, &weaker, &SCALE).expect("valid").is_empty());
         let stronger = [prop("s", "E1", ProposalKind::Text, "autre", 70, 0)];
-        assert_eq!(adoptions(&units, &stronger, W, C).expect("valid"), vec!["s".to_string()]);
+        assert_eq!(adoptions(&units, &stronger, &SCALE).expect("valid"), vec!["s".to_string()]);
         // The same rule holds for a removal; inertia does not compete with the text.
         let removal = [prop("x", "E1", ProposalKind::Remove, "", 55, 0)];
-        assert!(adoptions(&units, &removal, W, C).expect("valid").is_empty());
-        let inertia = [prop("i", "E1", ProposalKind::Inertia(InertiaPreset::High), "", 55, 0)];
-        assert_eq!(adoptions(&units, &inertia, W, C).expect("valid"), vec!["i".to_string()]);
+        assert!(adoptions(&units, &removal, &SCALE).expect("valid").is_empty());
+        let inertia = [prop("i", "E1", ProposalKind::Inertia(level(4)), "", 55, 0)];
+        assert_eq!(adoptions(&units, &inertia, &SCALE).expect("valid"), vec!["i".to_string()]);
     }
 
     #[test]
@@ -373,16 +380,16 @@ mod tests {
             prop("well", "E3", ProposalKind::Text, "connaître", 3, 0),
             prop("weak", "E1", ProposalKind::Remove, "", 1, 5),
         ];
-        let in_force = preview(&units, &props, W, C, PreviewMode::InForce).expect("valid");
+        let in_force = preview(&units, &props, &SCALE, PreviewMode::InForce).expect("valid");
         assert_eq!(in_force.iter().map(|u| u.unit_id.as_str()).collect::<Vec<_>>(), ["I1", "E1"]);
 
-        let likely = preview(&units, &props, W, C, PreviewMode::WellRated).expect("valid");
+        let likely = preview(&units, &props, &SCALE, PreviewMode::WellRated).expect("valid");
         assert_eq!(
             likely.iter().map(|u| (u.unit_id.as_str(), u.mark)).collect::<Vec<_>>(),
             [("I1", PreviewMark::Unchanged), ("E1", PreviewMark::Unchanged), ("E3", PreviewMark::Added),]
         );
 
-        let all = preview(&units, &props, W, C, PreviewMode::All).expect("valid");
+        let all = preview(&units, &props, &SCALE, PreviewMode::All).expect("valid");
         assert_eq!(
             all.iter().map(|u| (u.unit_id.as_str(), u.mark)).collect::<Vec<_>>(),
             [("I1", PreviewMark::Unchanged), ("E1", PreviewMark::Removed), ("E3", PreviewMark::Added),]
@@ -396,7 +403,7 @@ mod tests {
             prop("a", "E3", ProposalKind::Text, "variante a", 0, 0),
             prop("bb", "E3", ProposalKind::Text, "variante b", 1, 3),
         ];
-        let all = preview(&units, &props, W, C, PreviewMode::All).expect("valid");
+        let all = preview(&units, &props, &SCALE, PreviewMode::All).expect("valid");
         assert_eq!(all[0].proposal_id.as_deref(), Some("bb"));
     }
 }
diff --git a/crates/ld-engine/src/inertia.rs b/crates/ld-engine/src/inertia.rs
new file mode 100644
index 0000000..0025cb9
--- /dev/null
+++ b/crates/ld-engine/src/inertia.rs
@@ -0,0 +1,438 @@
+//! Inertia in five levels, on a scale that follows the group (ADR 0007).
+//!
+//! Yvv, 2026-10-30: « L'indice d'inertie doit avoir 5 niveaux » ; « une échelle
+//! cohérente qui s'adapte aux nombres de certifiés et à la participation
+//! médiane aux votes du groupe » — the scale chosen is « calée sur la
+//! participation ».
+//!
+//! The formula stays the Ğ1 one (`threshold`); only M and G depend on the
+//! level k:
+//!
+//! - M_k, the majority at full participation: 50, 50, 55, 60, 66 %;
+//! - s_k, the share of *for* votes asked **beyond C** at the group's usual
+//!   participation p̃: 60, 67, 75, 83, 90 %;
+//! - G_k follows from `s_k = M_k + (1 − M_k)(1 − p̃^G_k)`:
+//!   `G_k = ln(1 − (s_k − M_k)/(1 − M_k)) / ln(p̃)`.
+//!
+//! p̃ is the median number of voters on the group's proposals, over W
+//! (`Participation`). Until the group has voted on enough proposals, a
+//! reference `p0 = 2C/W` stands in. Both are kept within [1 %, 50 %]: ln(p̃)
+//! stays negative and finite, so G is finite and positive, and the threshold
+//! rises with the level and relaxes toward M as participation grows.
+
+use crate::threshold::{Evaluation, FormulaParams, Tally, ThresholdError, evaluate};
+use serde::de::Error as _;
+use serde::{Deserialize, Deserializer, Serialize, Serializer};
+
+/// One of the five levels of inertia, 1 (lightest) to 5 (heaviest).
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash, PartialOrd, Ord)]
+pub struct InertiaLevel(u8);
+
+/// M_k, in percent.
+const MAJORITY_PCT: [f64; 5] = [50.0, 50.0, 55.0, 60.0, 66.0];
+/// s_k, in percent.
+const SHARE_PCT: [f64; 5] = [60.0, 67.0, 75.0, 83.0, 90.0];
+
+impl InertiaLevel {
+    pub const LOWEST: Self = Self(1);
+    pub const HIGHEST: Self = Self(5);
+    /// The middle level: every proposal starts there (Yvv, 2026-10-30).
+    pub const DEFAULT: Self = Self(3);
+    pub const ALL: [Self; 5] = [Self(1), Self(2), Self(3), Self(4), Self(5)];
+
+    pub fn new(k: u8) -> Option<Self> {
+        (1..=5).contains(&k).then_some(Self(k))
+    }
+
+    pub fn get(self) -> u8 {
+        self.0
+    }
+
+    fn index(self) -> usize {
+        usize::from(self.0 - 1)
+    }
+
+    /// M_k, in percent.
+    pub fn majority_pct(self) -> f64 {
+        MAJORITY_PCT[self.index()]
+    }
+
+    /// s_k, in percent: the share of *for* asked beyond C at the usual participation.
+    pub fn share_pct(self) -> f64 {
+        SHARE_PCT[self.index()]
+    }
+
+    /// How a level is kept in the database: its digit.
+    pub fn as_db(self) -> String {
+        self.0.to_string()
+    }
+
+    /// A digit from 1 to 5, or a word of the four levels before 2026-10-30, read
+    /// as the level it became: low → 2, standard → 3, high → 4, max → 5.
+    pub fn parse(raw: &str) -> Option<Self> {
+        match raw.trim() {
+            "low" => Some(Self(2)),
+            "standard" => Some(Self(3)),
+            "high" => Some(Self(4)),
+            "max" => Some(Self(5)),
+            digits => digits.parse::<u8>().ok().and_then(Self::new),
+        }
+    }
+}
+
+impl Default for InertiaLevel {
+    fn default() -> Self {
+        Self::DEFAULT
+    }
+}
+
+impl Serialize for InertiaLevel {
+    fn serialize<S: Serializer>(&self, s: S) -> Result<S::Ok, S::Error> {
+        s.serialize_u8(self.0)
+    }
+}
+
+impl<'de> Deserialize<'de> for InertiaLevel {
+    /// A number from 1 to 5, or a string `parse` reads (a seed or a client of before).
+    fn deserialize<D: Deserializer<'de>>(d: D) -> Result<Self, D::Error> {
+        #[derive(Deserialize)]
+        #[serde(untagged)]
+        enum Raw {
+            Number(u64),
+            Text(String),
+        }
+        let level = match Raw::deserialize(d)? {
+            Raw::Number(n) => u8::try_from(n).ok().and_then(Self::new),
+            Raw::Text(s) => Self::parse(&s),
+        };
+        level.ok_or_else(|| D::Error::custom("an inertia level is 1 to 5"))
+    }
+}
+
+/// Where p̃ comes from.
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Serialize, Deserialize)]
+#[serde(rename_all = "lowercase")]
+pub enum ParticipationSource {
+    /// The median of the group's voted proposals.
+    Median,
+    /// Too few voted proposals yet: `p0 = 2C/W`.
+    Reference,
+}
+
+/// p̃ — the usual participation of a group, as a share of its electorate.
+#[derive(Clone, Copy, Debug, PartialEq, Serialize, Deserialize)]
+#[serde(rename_all = "camelCase")]
+pub struct Participation {
+    /// p̃, within [`Participation::LOWEST`, `Participation::HIGHEST`].
+    pub ratio: f64,
+    pub source: ParticipationSource,
+    /// Voted proposals the median rests on (counted even when too few).
+    pub sample: u32,
+    /// The median number of voters measured, when at least one proposal was voted on.
+    pub median: Option<f64>,
+    /// The measured (or reference) share fell outside the bounds and was brought back.
+    pub bounded: bool,
+}
+
+impl Participation {
+    /// Fewer voted proposals than this, and the reference stands in.
+    pub const MIN_SAMPLE: u32 = 5;
+    pub const LOWEST: f64 = 0.01;
+    pub const HIGHEST: f64 = 0.5;
+
+    /// `2C/W`, before the bounds: the floor twice over, a participation the
+    /// group must reach anyway for C to leave room to the majority.
+    pub fn reference_ratio(electorate: u32, floor: f64) -> f64 {
+        2.0 * floor.max(0.0) / f64::from(electorate.max(1))
+    }
+
+    /// p̃ from what was measured: the median when it rests on enough proposals,
+    /// the reference otherwise; brought back within the bounds.
+    pub fn of(electorate: u32, floor: f64, median: Option<f64>, sample: u32) -> Self {
+        let (raw, source) = match median {
+            Some(m) if sample >= Self::MIN_SAMPLE => (m / f64::from(electorate.max(1)), ParticipationSource::Median),
+            _ => (Self::reference_ratio(electorate, floor), ParticipationSource::Reference),
+        };
+        let ratio = bounded(raw);
+        Self { ratio, source, sample, median, bounded: ratio != raw }
+    }
+
+    /// p̃ · W — the number of voters p̃ stands for.
+    pub fn voters(&self, electorate: u32) -> f64 {
+        self.ratio * f64::from(electorate.max(1))
+    }
+}
+
+/// The median of the numbers of voters, `None` for none.
+pub fn median(values: &[u32]) -> Option<f64> {
+    let mut sorted = values.to_vec();
+    sorted.sort_unstable();
+    let n = sorted.len();
+    let mid = n / 2;
+    match n {
+        0 => None,
+        _ if n % 2 == 1 => Some(f64::from(sorted[mid])),
+        _ => Some((f64::from(sorted[mid - 1]) + f64::from(sorted[mid])) / 2.0),
+    }
+}
+
+/// Within [1 %, 50 %]; anything that is not a number goes to the lowest bound.
+fn bounded(ratio: f64) -> f64 {
+    if ratio.is_nan() { Participation::LOWEST } else { ratio.clamp(Participation::LOWEST, Participation::HIGHEST) }
+}
+
+/// G_k at the usual participation p̃ (brought back within the bounds).
+pub fn gradient(level: InertiaLevel, participation: f64) -> f64 {
+    let m = level.majority_pct() / 100.0;
+    let s = level.share_pct() / 100.0;
+    // Both logarithms are negative: 0 < 1 − (s − M)/(1 − M) < 1 since M < s < 1,
+    // and 0 < p̃ < 1 within the bounds.
+    (1.0 - (s - m) / (1.0 - m)).ln() / bounded(participation).ln()
+}
+
+/// What the votes of a group are judged by: its electorate W, its floor C and
+/// its usual participation p̃.
+#[derive(Clone, Copy, Debug, PartialEq, Serialize, Deserialize)]
+#[serde(rename_all = "camelCase")]
+pub struct Scale {
+    pub electorate: u32,
+    pub floor: f64,
+    /// p̃.
+    pub participation: f64,
+}
+
+impl Scale {
+    /// The letters of the formula for a level.
+    pub fn params(&self, level: InertiaLevel) -> FormulaParams {
+        FormulaParams {
+            majority_pct: level.majority_pct(),
+            gradient: gradient(level, self.participation),
+            base: FormulaParams::DEFAULT_BASE,
+            constant: self.floor,
+        }
+    }
+
+    pub fn evaluate(&self, tally: Tally, level: InertiaLevel) -> Result<Evaluation, ThresholdError> {
+        evaluate(tally, self.electorate, &self.params(level))
+    }
+
+    /// ⌈R⌉ for a level at `cast` votes.
+    pub fn required(&self, cast: u32, level: InertiaLevel) -> Result<u32, ThresholdError> {
+        crate::threshold::wot_threshold(self.electorate, cast, &self.params(level))
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use crate::threshold::required_ratio;
+
+    const W: u32 = 7224;
+    const C: f64 = 50.0;
+
+    fn at_median(voters: u32) -> Scale {
+        Scale { electorate: W, floor: C, participation: f64::from(voters) / f64::from(W) }
+    }
+
+    fn row(scale: &Scale, cast: u32) -> Vec<u32> {
+        InertiaLevel::ALL.iter().map(|k| scale.required(cast, *k).expect("valid")).collect()
+    }
+
+    #[test]
+    fn five_levels_three_in_the_middle() {
+        let m: Vec<f64> = InertiaLevel::ALL.iter().map(|k| k.majority_pct()).collect();
+        let s: Vec<f64> = InertiaLevel::ALL.iter().map(|k| k.share_pct()).collect();
+        assert_eq!(m, [50.0, 50.0, 55.0, 60.0, 66.0]);
+        assert_eq!(s, [60.0, 67.0, 75.0, 83.0, 90.0]);
+        for k in InertiaLevel::ALL {
+            assert!(k.share_pct() > k.majority_pct(), "s_k above M_k keeps G positive");
+            assert_eq!(InertiaLevel::parse(&k.as_db()), Some(k));
+        }
+        assert_eq!(InertiaLevel::default().get(), 3);
+        assert_eq!(InertiaLevel::new(0), None);
+        assert_eq!(InertiaLevel::new(6), None);
+    }
+
+    #[test]
+    fn the_four_words_of_before_read_as_levels() {
+        let read = |w: &str| InertiaLevel::parse(w).map(InertiaLevel::get);
+        assert_eq!([read("low"), read("standard"), read("high"), read("max")], [Some(2), Some(3), Some(4), Some(5)]);
+        assert_eq!(read("maximale"), None);
+        let from_json = |v: &str| serde_json::from_str::<InertiaLevel>(v).ok().map(InertiaLevel::get);
+        assert_eq!([from_json("4"), from_json("\"standard\""), from_json("\"5\"")], [Some(4), Some(3), Some(5)]);
+        assert_eq!(from_json("0"), None);
+        assert_eq!(from_json("\"6\""), None);
+        assert_eq!(serde_json::to_string(&InertiaLevel::HIGHEST).expect("json"), "5");
+    }
+
+    #[test]
+    fn the_values_shown_to_yvv() {
+        // W 7224, C 50, a median of 120 voters (the smith vote of 2024).
+        let scale = at_median(120);
+        assert_eq!(row(&scale, 120), [92, 97, 103, 109, 113]);
+        assert_eq!(row(&scale, 500), [306, 329, 362, 397, 432]);
+        assert_eq!(row(&scale, 2000), [1091, 1145, 1271, 1404, 1549]);
+    }
+
+    #[test]
+    fn a_median_of_360_voters() {
+        let scale = at_median(360);
+        assert_eq!(row(&scale, 120), [95, 101, 106, 112, 116]);
+        assert_eq!(row(&scale, 360), [236, 258, 283, 308, 329]);
+        assert_eq!(row(&scale, 500), [316, 345, 381, 416, 449]);
+        assert_eq!(row(&scale, 2000), [1114, 1184, 1318, 1460, 1608]);
+    }
+
+    #[test]
+    fn at_the_usual_participation_the_share_beyond_c_is_s_k() {
+        for (w, c, voters) in [(7224, 50.0, 120), (7224, 50.0, 360), (5745, 50.0, 300), (40, 1.0, 9), (2, 1.0, 1)] {
+            let scale = Scale { electorate: w, floor: c, participation: f64::from(voters) / f64::from(w) };
+            for k in InertiaLevel::ALL {
+                let ratio = required_ratio(w, voters, &scale.params(k));
+                assert!((ratio - k.share_pct() / 100.0).abs() < 1e-12, "W {w}, k {}: {ratio}", k.get());
+            }
+        }
+    }
+
+    #[test]
+    fn a_threshold_landing_on_a_whole_number_stays_on_it() {
+        // Level 5 at the median: 90 % of the 70 votes beyond C is exactly 63.
+        assert_eq!(at_median(120).required(120, InertiaLevel::HIGHEST), Ok(113));
+        // Level 1: 60 % of 70 is exactly 42.
+        assert_eq!(at_median(120).required(120, InertiaLevel::LOWEST), Ok(92));
+    }
+
+    #[test]
+    fn the_threshold_rises_with_the_level() {
+        for (w, c) in [(7224, 50.0), (5745, 50.0), (40, 1.0), (2, 1.0), (1, 1.0)] {
+            for voters in [1, 2, 9, 60, 120, 360, 3000] {
+                let scale = Scale {
+                    electorate: w,
+                    floor: c,
+                    participation: Participation::of(w, c, Some(f64::from(voters)), 9).ratio,
+                };
+                for cast in (0..=w.min(4000)).step_by(7).chain([w]) {
+                    let r = row(&scale, cast);
+                    assert!(r.windows(2).all(|p| p[0] <= p[1]), "W {w}, p̃ {voters}, T {cast}: {r:?}");
+                    let ratios: Vec<f64> =
+                        InertiaLevel::ALL.iter().map(|k| required_ratio(w, cast, &scale.params(*k))).collect();
+                    if cast > 0 && cast < w {
+                        assert!(
+                            ratios.windows(2).all(|p| p[0] < p[1]),
+                            "strictly below full participation: {ratios:?}"
+                        );
+                    }
+                }
+            }
+        }
+    }
+
+    #[test]
+    fn the_share_relaxes_toward_m_as_participation_rises() {
+        for voters in [120, 360] {
+            let scale = at_median(voters);
+            for k in InertiaLevel::ALL {
+                let p = scale.params(k);
+                let mut last = 1.0;
+                for cast in (1..=W).step_by(13).chain([W]) {
+                    let ratio = required_ratio(W, cast, &p);
+                    assert!(ratio <= last, "k {}: the share never rises with participation", k.get());
+                    assert!(ratio >= k.majority_pct() / 100.0 - 1e-12);
+                    last = ratio;
+                }
+                assert!((required_ratio(W, W, &p) - k.majority_pct() / 100.0).abs() < 1e-12, "M at full participation");
+            }
+        }
+    }
+
+    #[test]
+    fn c_stays_a_floor_one_vote_never_passes_in_monnaie_libre() {
+        for voters in [1, 72, 120, 360, 3612] {
+            let scale = Scale {
+                electorate: W,
+                floor: C,
+                participation: Participation::of(W, C, Some(f64::from(voters)), 9).ratio,
+            };
+            for k in InertiaLevel::ALL {
+                let lone = scale.evaluate(Tally { for_votes: 1, against: 0 }, k).expect("valid");
+                assert!(!lone.reached, "k {}", k.get());
+                assert_eq!(lone.required, 50);
+                for cast in 1..=50 {
+                    assert!(scale.required(cast, k).expect("valid") >= 50, "nothing passes under C for");
+                }
+                assert!(!scale.evaluate(Tally { for_votes: 49, against: 0 }, k).expect("valid").reached);
+                assert!(scale.evaluate(Tally { for_votes: 50, against: 0 }, k).expect("valid").reached);
+            }
+        }
+    }
+
+    #[test]
+    fn the_median() {
+        assert_eq!(median(&[]), None);
+        assert_eq!(median(&[7]), Some(7.0));
+        assert_eq!(median(&[3, 1, 2]), Some(2.0));
+        assert_eq!(median(&[4, 1, 3, 2]), Some(2.5));
+        assert_eq!(median(&[1, 1, 1, 200, 300]), Some(1.0), "one big vote does not move it");
+    }
+
+    #[test]
+    fn the_reference_stands_in_until_five_proposals_are_voted_on() {
+        // Monnaie libre: 2 × 50 / 7224 = 1.38 %, a hundred voters.
+        assert!((Participation::reference_ratio(W, C) - 100.0 / 7224.0).abs() < 1e-15);
+        let early = Participation::of(W, C, Some(120.0), 4);
+        assert_eq!(early.source, ParticipationSource::Reference);
+        assert!((early.voters(W) - 100.0).abs() < 1e-9);
+        assert_eq!((early.sample, early.median, early.bounded), (4, Some(120.0), false));
+        let none = Participation::of(W, C, None, 0);
+        assert_eq!(none.source, ParticipationSource::Reference);
+        let measured = Participation::of(W, C, Some(120.0), 5);
+        assert_eq!(measured.source, ParticipationSource::Median);
+        assert!((measured.voters(W) - 120.0).abs() < 1e-9);
+        assert!(!measured.bounded);
+    }
+
+    #[test]
+    fn participation_is_kept_within_one_and_fifty_percent() {
+        // Two voters on 7224: brought up to 1 %.
+        let low = Participation::of(W, C, Some(2.0), 9);
+        assert_eq!((low.ratio, low.bounded), (0.01, true));
+        // A group where everyone votes: brought down to half.
+        let all = Participation::of(12, 1.0, Some(12.0), 9);
+        assert_eq!((all.ratio, all.bounded), (0.5, true));
+        // The test group, W = 2, C = 1: the reference is 100 %, kept at half.
+        let essai = Participation::of(2, 1.0, None, 0);
+        assert_eq!((essai.ratio, essai.source, essai.bounded), (0.5, ParticipationSource::Reference, true));
+        // A tiny electorate never breaks G.
+        for w in [1, 2, 3] {
+            let p = Participation::of(w, 1.0, Some(1.0), 9);
+            for k in InertiaLevel::ALL {
+                let g = gradient(k, p.ratio);
+                assert!(g.is_finite() && g > 0.0, "W {w}, k {}: {g}", k.get());
+            }
+        }
+        // Whatever reaches it, G stays finite and positive.
+        for bad in [0.0, 1.0, -3.0, 7.0, f64::NAN, f64::INFINITY] {
+            let g = gradient(InertiaLevel::DEFAULT, bad);
+            assert!(g.is_finite() && g > 0.0, "{bad}: {g}");
+        }
+    }
+
+    #[test]
+    fn the_test_group_needs_everyone() {
+        // W = 2, C = 1: both must vote for, at every level.
+        let scale = Scale { electorate: 2, floor: 1.0, participation: Participation::of(2, 1.0, None, 0).ratio };
+        for k in InertiaLevel::ALL {
+            assert!(!scale.evaluate(Tally { for_votes: 1, against: 0 }, k).expect("valid").reached);
+            assert!(scale.evaluate(Tally { for_votes: 2, against: 0 }, k).expect("valid").reached);
+        }
+    }
+
+    #[test]
+    fn gradients_at_a_median_of_120() {
+        let g: Vec<f64> = InertiaLevel::ALL.iter().map(|k| gradient(*k, 120.0 / 7224.0)).collect();
+        let expected = [0.054_455, 0.101_404, 0.143_442, 0.208_818, 0.298_651];
+        for (got, want) in g.iter().zip(expected) {
+            assert!((got - want).abs() < 1e-5, "{g:?}");
+        }
+    }
+}
diff --git a/crates/ld-engine/src/lib.rs b/crates/ld-engine/src/lib.rs
index 616a534..a41ac17 100644
--- a/crates/ld-engine/src/lib.rs
+++ b/crates/ld-engine/src/lib.rs
@@ -9,8 +9,10 @@
 pub mod assist;
 pub mod compose;
 pub mod edit;
+pub mod inertia;
 pub mod names;
 pub mod pending;
 pub mod threshold;
 
-pub use threshold::{FormulaParams, InertiaPreset, Tally};
+pub use inertia::{InertiaLevel, Participation, Scale};
+pub use threshold::{FormulaParams, Tally};
diff --git a/crates/ld-engine/src/threshold.rs b/crates/ld-engine/src/threshold.rs
index 95f0bbe..52dfe97 100644
--- a/crates/ld-engine/src/threshold.rs
+++ b/crates/ld-engine/src/threshold.rs
@@ -12,66 +12,13 @@
 //! (Yvv, 2026-10-21: « Nombre minimal de votants »).
 //!
 //! Parity: identical to `maquette/frontend/app/engine/threshold.ts` and the
-//! Python reference, with one deliberate guard — the participation ratio is
-//! capped at 1, so a stale W can never lower the bar below M.
+//! Python reference, with two deliberate guards — the participation ratio is
+//! capped at 1, so a stale W can never lower the bar below M; and a count that
+//! lands on a whole number stays on it (`settle`), so a rounding error never
+//! adds a vote. Which M and G a text is judged by: `inertia` (five levels).
 
 use serde::{Deserialize, Serialize};
 
-/// The four inertia levels of a modular text. Wiring of the v2 maquette:
-/// low = M50 G0.1, standard = M50 G0.2, high = M60 G0.4, max = M66 G0.6 (B = 0.1).
-#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash, PartialOrd, Ord, Serialize, Deserialize)]
-#[serde(rename_all = "lowercase")]
-pub enum InertiaPreset {
-    Low,
-    Standard,
-    High,
-    Max,
-}
-
-impl InertiaPreset {
-    pub const ALL: [Self; 4] = [Self::Low, Self::Standard, Self::High, Self::Max];
-
-    pub fn majority_pct(self) -> f64 {
-        match self {
-            Self::Low | Self::Standard => 50.0,
-            Self::High => 60.0,
-            Self::Max => 66.0,
-        }
-    }
-
-    pub fn gradient(self) -> f64 {
-        match self {
-            Self::Low => 0.1,
-            Self::Standard => 0.2,
-            Self::High => 0.4,
-            Self::Max => 0.6,
-        }
-    }
-
-    /// « Inertie + » : one level up, capped at max. A change of inertia is
-    /// itself voted at the raised level of the unit it touches.
-    pub fn raised(self) -> Self {
-        match self {
-            Self::Low => Self::Standard,
-            Self::Standard => Self::High,
-            Self::High | Self::Max => Self::Max,
-        }
-    }
-
-    pub fn as_str(self) -> &'static str {
-        match self {
-            Self::Low => "low",
-            Self::Standard => "standard",
-            Self::High => "high",
-            Self::Max => "max",
-        }
-    }
-
-    pub fn parse(raw: &str) -> Option<Self> {
-        Self::ALL.into_iter().find(|p| p.as_str() == raw)
-    }
-}
-
 /// The letters of the formula, named.
 #[derive(Clone, Copy, Debug, PartialEq, Serialize, Deserialize)]
 pub struct FormulaParams {
@@ -87,10 +34,6 @@ pub struct FormulaParams {
 
 impl FormulaParams {
     pub const DEFAULT_BASE: f64 = 0.1;
-
-    pub fn for_inertia(preset: InertiaPreset, constant: f64) -> Self {
-        Self { majority_pct: preset.majority_pct(), gradient: preset.gradient(), base: Self::DEFAULT_BASE, constant }
-    }
 }
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq)]
@@ -119,12 +62,20 @@ pub fn wot_threshold(electorate: u32, cast: u32, params: &FormulaParams) -> Resu
     let raw = if cast == 0 {
         c + offset
     } else {
-        c + offset + required_ratio(electorate, cast, params) * (f64::from(cast) - c).max(0.0)
+        c + offset + settle(required_ratio(electorate, cast, params) * (f64::from(cast) - c).max(0.0))
     };
     // `raw` is finite and non-negative for any valid input; saturate rather than wrap.
     Ok(clamp_ceil(raw))
 }
 
+/// A count of votes that lands on a whole number stays on it: a rounding error
+/// of the logarithms (a billionth of a vote) must never raise a threshold by
+/// one. At the usual participation, 90 % of the 70 votes beyond C is exactly 63.
+fn settle(votes: f64) -> f64 {
+    let whole = votes.round();
+    if (votes - whole).abs() < 1e-9 { whole } else { votes }
+}
+
 fn clamp_ceil(raw: f64) -> u32 {
     let ceiled = raw.ceil();
     if ceiled <= 0.0 {
@@ -193,9 +144,16 @@ mod tests {
         FormulaParams { majority_pct: m, gradient: g, base: 0.1, constant: 0.0 }
     }
 
+    /// The letters of the « standard » inertia before the five levels: M 50 %, G 0.2.
+    fn standard(constant: f64) -> FormulaParams {
+        FormulaParams { constant, ..g1vote(50.0, 0.2) }
+    }
+
     #[test]
     fn reference_case_of_the_smith_vote() {
         // Engagement forgeron v2.0.0: W 7224, 97 for, 23 against, M50 B.1 G.2 → 94.
+        // The formula's own reference, letters given: the five levels (ADR 0007)
+        // choose M and G, the formula that turns them into a threshold is this one.
         let p = g1vote(50.0, 0.2);
         assert_eq!(wot_threshold(7224, 120, &p), Ok(94));
         let e = evaluate(Tally { for_votes: 97, against: 23 }, 7224, &p).expect("valid");
@@ -218,9 +176,9 @@ mod tests {
     #[test]
     fn one_vote_passes_without_floor_and_never_with_it() {
         // The trap of a permanent vote: a lone "for" meets the inertial bar.
-        let bare = FormulaParams::for_inertia(InertiaPreset::Standard, 0.0);
+        let bare = standard(0.0);
         assert!(evaluate(Tally { for_votes: 1, against: 0 }, 5745, &bare).expect("valid").reached);
-        let guarded = FormulaParams::for_inertia(InertiaPreset::Standard, 50.0);
+        let guarded = standard(50.0);
         let e = evaluate(Tally { for_votes: 1, against: 0 }, 5745, &guarded).expect("valid");
         assert!(!e.reached);
         assert_eq!(e.required, 50);
@@ -230,7 +188,7 @@ mod tests {
 
     #[test]
     fn floor_is_a_minimum_of_for_votes() {
-        let p = FormulaParams::for_inertia(InertiaPreset::Standard, 50.0);
+        let p = standard(50.0);
         // 50 unanimous votes reach it, 49 do not.
         assert!(evaluate(Tally { for_votes: 50, against: 0 }, 5745, &p).expect("valid").reached);
         assert!(!evaluate(Tally { for_votes: 49, against: 0 }, 5745, &p).expect("valid").reached);
@@ -241,7 +199,7 @@ mod tests {
 
     #[test]
     fn no_vote_is_never_reached() {
-        let p = FormulaParams::for_inertia(InertiaPreset::Low, 0.0);
+        let p = g1vote(50.0, 0.1);
         let e = evaluate(Tally::default(), 3, &p).expect("valid");
         assert!(!e.reached);
         assert!(!e.well_rated);
@@ -250,7 +208,7 @@ mod tests {
     #[test]
     fn small_group_needs_everyone() {
         // Test group of two people, C = 1: both must vote for.
-        let p = FormulaParams::for_inertia(InertiaPreset::Standard, 1.0);
+        let p = standard(1.0);
         assert!(!evaluate(Tally { for_votes: 1, against: 0 }, 2, &p).expect("valid").reached);
         assert!(evaluate(Tally { for_votes: 2, against: 0 }, 2, &p).expect("valid").reached);
     }
@@ -266,13 +224,13 @@ mod tests {
     }
 
     #[test]
-    fn inertia_levels_rise_and_cap() {
-        assert_eq!(InertiaPreset::Low.raised(), InertiaPreset::Standard);
-        assert_eq!(InertiaPreset::Standard.raised(), InertiaPreset::High);
-        assert_eq!(InertiaPreset::Max.raised(), InertiaPreset::Max);
-        for p in InertiaPreset::ALL {
-            assert_eq!(InertiaPreset::parse(p.as_str()), Some(p));
-        }
+    fn a_whole_number_of_votes_never_gains_one_by_rounding() {
+        // 101 members, everyone votes, M 55 %: 1 + 55 % of 100 = 56. In floating
+        // point 0.55 × 100 is 55.000000000000007, which would ask for 57.
+        let p = FormulaParams { majority_pct: 55.0, gradient: 0.3, base: 0.1, constant: 1.0 };
+        assert_eq!(wot_threshold(101, 101, &p), Ok(56));
+        // A genuine fraction still rounds up.
+        assert_eq!(wot_threshold(101, 100, &FormulaParams { constant: 0.0, ..p }), Ok(56));
     }
 
     #[test]
diff --git a/crates/ld-server/migrations/0005_inertia_levels.sql b/crates/ld-server/migrations/0005_inertia_levels.sql
new file mode 100644
index 0000000..43122f4
--- /dev/null
+++ b/crates/ld-server/migrations/0005_inertia_levels.sql
@@ -0,0 +1,50 @@
+-- Inertia in five levels (2026-10-30, ADR 0007). Additive: nothing is lost.
+--
+-- The four words of before become levels: low → 2, standard → 3, high → 4,
+-- max → 5 (level 1 is new, below them). Each word is first kept as it was, in a
+-- column of its own, then its level is written in its place. The adoptions are
+-- left as they are: their `params` hold the M and G each was judged by. The
+-- server still reads the four words (a row written by an older image).
+
+ALTER TABLE units ADD COLUMN inertia_legacy TEXT;            -- the word before 2026-10-30, as it was
+UPDATE units SET inertia_legacy = inertia WHERE inertia IN ('low', 'standard', 'high', 'max');
+UPDATE units SET inertia = CASE inertia
+    WHEN 'low' THEN '2' WHEN 'standard' THEN '3' WHEN 'high' THEN '4' WHEN 'max' THEN '5' END
+  WHERE inertia IN ('low', 'standard', 'high', 'max');
+
+ALTER TABLE proposals ADD COLUMN inertia_target_legacy TEXT; -- the word before 2026-10-30, as it was
+UPDATE proposals SET inertia_target_legacy = inertia_target WHERE inertia_target IN ('low', 'standard', 'high', 'max');
+UPDATE proposals SET inertia_target = CASE inertia_target
+    WHEN 'low' THEN '2' WHEN 'standard' THEN '3' WHEN 'high' THEN '4' WHEN 'max' THEN '5' END
+  WHERE inertia_target IN ('low', 'standard', 'high', 'max');
+
+-- Every change of the inertia of an article from now on, by a vote or by an
+-- amendment of the seed: what the article says of its own inertia.
+CREATE TABLE inertia_changes (
+    id            INTEGER PRIMARY KEY AUTOINCREMENT,
+    unit_id       TEXT NOT NULL REFERENCES units(id),
+    doc_id        TEXT NOT NULL REFERENCES documents(id),
+    from_level    TEXT NOT NULL,
+    to_level      TEXT NOT NULL,
+    cause         TEXT NOT NULL,             -- vote | amendment
+    proposal_id   TEXT,                      -- the change of inertia voted
+    amendment_id  TEXT,                      -- the amendment applied
+    at            TEXT NOT NULL
+);
+CREATE INDEX inertia_changes_unit ON inertia_changes(unit_id);
+
+-- Inertia amendments (src/inertia_amend.rs): a starting level of the seed raised
+-- in an existing base, decided once per document and only on an article whose
+-- inertia no vote ever changed. Each decision is kept here: applied, refused
+-- (and why), or already present.
+CREATE TABLE inertia_amendments (
+    amendment_id  TEXT NOT NULL,
+    doc_id        TEXT NOT NULL REFERENCES documents(id),
+    unit_code     TEXT NOT NULL,
+    from_level    TEXT,                      -- the level found
+    to_level      TEXT NOT NULL,
+    outcome       TEXT NOT NULL,             -- applied | refused | present
+    reason        TEXT,                      -- why it was refused
+    at            TEXT NOT NULL,
+    PRIMARY KEY (amendment_id, doc_id)
+);
diff --git a/crates/ld-server/src/adoption.rs b/crates/ld-server/src/adoption.rs
index 4e4eebc..951a11a 100644
--- a/crates/ld-server/src/adoption.rs
+++ b/crates/ld-server/src/adoption.rs
@@ -1,8 +1,9 @@
 //! Entering into force — automatic, as soon as a proposal reaches its
 //! threshold (Yvv, 2026-10-21: « Dès qu'une proposition atteint le score, elle
 //! remonte en vigueur »). The human gesture is the vote itself; the engine
-//! only counts. Every entry is recorded with its numbers and queued for
-//! publication to the texts repository.
+//! only counts. Every entry is recorded with its numbers — the level of
+//! inertia, M, G, s_k and the usual participation it was judged by — and
+//! queued for publication to the texts repository.
 
 use crate::AppState;
 use crate::docs::{self, DocRow, DocState};
@@ -66,16 +67,16 @@ pub async fn run(state: &AppState, doc_id: &str) -> AppResult<Vec<Entered>> {
     let st = docs::load_state(state, doc_id).await?;
     confirm_seeds(state, &st).await?;
     let units = st.unit_states();
-    let winners = compose::adoptions(&units, &st.proposal_states(), st.electorate, st.doc.vote_floor)
+    let scale = st.scale();
+    let winners = compose::adoptions(&units, &st.proposal_states(), &scale)
         .map_err(|_| crate::error::AppError::Invalid("electorate"))?;
     let mut entered = Vec::new();
     for id in winners {
         let Some(p) = st.proposals.iter().find(|p| p.id == id) else { continue };
         let Some(unit) = st.units.iter().find(|u| u.id == p.unit_id) else { continue };
-        let us = units.iter().find(|u| u.id == unit.id);
         let tally = st.tally(&p.id);
         let eval = st.evaluation(unit, p);
-        let params = us.map(|u| compose::params_for(u, p.kind(), st.doc.vote_floor));
+        let params = kept_params(&st, unit, p);
         let now = util::now();
         let mut tx = state.db.begin().await?;
         // The text that enters is the text that was counted: a revision that landed
@@ -140,10 +141,22 @@ pub async fn run(state: &AppState, doc_id: &str) -> AppResult<Vec<Entered>> {
                     .execute(&mut *tx)
                     .await?;
                 sqlx::query("UPDATE units SET inertia = ? WHERE id = ?")
-                    .bind(target.as_str())
+                    .bind(target.as_db())
                     .bind(&unit.id)
                     .execute(&mut *tx)
                     .await?;
+                sqlx::query(
+                    "INSERT INTO inertia_changes (unit_id, doc_id, from_level, to_level, cause, proposal_id, at)
+                     VALUES (?, ?, ?, ?, 'vote', ?, ?)",
+                )
+                .bind(&unit.id)
+                .bind(&st.doc.id)
+                .bind(docs::inertia_of(unit).as_db())
+                .bind(target.as_db())
+                .bind(&p.id)
+                .bind(&now)
+                .execute(&mut *tx)
+                .await?;
                 "inertia"
             }
         };
@@ -159,7 +172,7 @@ pub async fn run(state: &AppState, doc_id: &str) -> AppResult<Vec<Entered>> {
         .bind(i64::from(tally.against))
         .bind(i64::from(st.electorate))
         .bind(eval.map_or(0, |e| i64::from(e.required)))
-        .bind(serde_json::to_string(&params).unwrap_or_default())
+        .bind(params.to_string())
         .bind(&now)
         .execute(&mut *tx)
         .await?;
@@ -174,12 +187,30 @@ pub async fn run(state: &AppState, doc_id: &str) -> AppResult<Vec<Entered>> {
     Ok(entered)
 }
 
+/// What an adoption keeps of the formula it was judged by. The four letters
+/// stay where the rows of before have them (`majority_pct`, `gradient`, `base`,
+/// `constant`: read as they were written); the level and the scale join them.
+fn kept_params(st: &DocState, unit: &docs::UnitRow, p: &docs::ProposalRow) -> serde_json::Value {
+    let level = st.voting_level(unit, p);
+    let f = st.scale().params(level);
+    serde_json::json!({
+        "majority_pct": f.majority_pct, "gradient": f.gradient, "base": f.base, "constant": f.constant,
+        "level": level, "share_pct": level.share_pct(),
+        "participation": st.participation.ratio, "participation_source": st.participation.source,
+        "participation_sample": st.participation.sample, "participation_median": st.participation.median,
+    })
+}
+
 /// The electorate changes (the web of trust grows or shrinks): every few
-/// minutes, every document is passed through the engine again.
+/// minutes, every document is passed through the engine again — after the
+/// usual participation of each group is measured again, once a day.
 pub async fn sweeper(state: AppState) {
     let mut tick = tokio::time::interval(Duration::from_secs(300));
     loop {
         tick.tick().await;
+        if let Err(e) = crate::participation::refresh(&state, false).await {
+            tracing::warn!(error = %e, "usual participation");
+        }
         let ids: Vec<String> = match sqlx::query_scalar("SELECT id FROM documents").fetch_all(&state.db).await {
             Ok(ids) => ids,
             Err(e) => {
diff --git a/crates/ld-server/src/docs.rs b/crates/ld-server/src/docs.rs
index 8776901..2c147b4 100644
--- a/crates/ld-server/src/docs.rs
+++ b/crates/ld-server/src/docs.rs
@@ -6,11 +6,13 @@
 use crate::AppState;
 use crate::auth::{IdentityRow, User};
 use crate::error::{AppError, AppResult};
+use crate::participation;
 use crate::util::{self, LangMap};
 use axum::Json;
 use axum::extract::{Path, Query, State};
 use ld_engine::compose::{self, PreviewMode, ProposalKind, ProposalState, UnitState, VersionText};
-use ld_engine::threshold::{Evaluation, InertiaPreset, Tally, evaluate};
+use ld_engine::inertia::{InertiaLevel, Participation, Scale};
+use ld_engine::threshold::{Evaluation, Tally};
 use serde::{Deserialize, Serialize};
 use serde_json::json;
 use std::collections::{BTreeMap, HashMap, HashSet};
@@ -231,16 +233,17 @@ impl ProposalRow {
     pub fn kind(&self) -> ProposalKind {
         match self.kind.as_str() {
             "remove" => ProposalKind::Remove,
-            "inertia" => ProposalKind::Inertia(
-                self.inertia_target.as_deref().and_then(InertiaPreset::parse).unwrap_or(InertiaPreset::Standard),
-            ),
+            "inertia" => {
+                ProposalKind::Inertia(self.inertia_target.as_deref().and_then(InertiaLevel::parse).unwrap_or_default())
+            }
             _ => ProposalKind::Text,
         }
     }
 }
 
-pub fn inertia_of(unit: &UnitRow) -> InertiaPreset {
-    InertiaPreset::parse(&unit.inertia).unwrap_or(InertiaPreset::Standard)
+/// The level of a unit: a digit, or one of the four words of before.
+pub fn inertia_of(unit: &UnitRow) -> InertiaLevel {
+    InertiaLevel::parse(&unit.inertia).unwrap_or_default()
 }
 
 pub struct DocState {
@@ -253,6 +256,9 @@ pub struct DocState {
     pub signal_counts: HashMap<String, i64>,
     pub electorate: u32,
     pub electorate_source: &'static str,
+    /// p̃, from the group's last measure (or the reference).
+    pub participation: Participation,
+    pub measured_at: Option<String>,
 }
 
 pub async fn load_doc(state: &AppState, doc_id: &str) -> AppResult<DocRow> {
@@ -351,10 +357,40 @@ pub async fn load_state(state: &AppState, doc_id: &str) -> AppResult<DocState> {
         }
     }
     let (electorate, electorate_source) = electorate(state, &group).await?;
-    Ok(DocState { doc, group, units, proposals, tallies, blocked, signal_counts, electorate, electorate_source })
+    let measure = participation::stored(state, &group.slug).await?;
+    let participation = Participation::of(
+        electorate,
+        doc.vote_floor,
+        measure.as_ref().and_then(|m| m.median),
+        measure.as_ref().map_or(0, |m| m.sample),
+    );
+    let measured_at = measure.map(|m| m.measured_at);
+    Ok(DocState {
+        doc,
+        group,
+        units,
+        proposals,
+        tallies,
+        blocked,
+        signal_counts,
+        electorate,
+        electorate_source,
+        participation,
+        measured_at,
+    })
 }
 
 impl DocState {
+    /// What this document's votes are judged by: W, C and p̃.
+    pub fn scale(&self) -> Scale {
+        Scale { electorate: self.electorate, floor: self.doc.vote_floor, participation: self.participation.ratio }
+    }
+
+    /// p̃ · W, as a whole number of voters.
+    pub fn usual_voters(&self) -> u32 {
+        whole(self.participation.voters(self.electorate))
+    }
+
     pub fn tally(&self, id: &str) -> Tally {
         self.tallies.get(id).copied().unwrap_or_default()
     }
@@ -396,9 +432,45 @@ impl DocState {
     }
 
     pub fn evaluation(&self, unit: &UnitRow, p: &ProposalRow) -> Option<Evaluation> {
-        let us = UnitState { id: unit.id.clone(), position: unit.position, inertia: inertia_of(unit), in_force: None };
-        evaluate(self.tally(&p.id), self.electorate, &compose::params_for(&us, p.kind(), self.doc.vote_floor)).ok()
+        self.scale().evaluate(self.tally(&p.id), self.voting_level(unit, p)).ok()
     }
+
+    /// The level a proposal is voted at — a change of inertia inherits its article's.
+    pub fn voting_level(&self, unit: &UnitRow, p: &ProposalRow) -> InertiaLevel {
+        let us = UnitState { id: unit.id.clone(), position: unit.position, inertia: inertia_of(unit), in_force: None };
+        compose::voting_level(&us, p.kind())
+    }
+
+    /// The usual participation, as the screen tells it.
+    pub fn participation_json(&self) -> serde_json::Value {
+        let p = &self.participation;
+        json!({
+            "ratio": p.ratio, "source": p.source, "sample": p.sample, "median": p.median, "bounded": p.bounded,
+            "voters": self.usual_voters(), "minSample": Participation::MIN_SAMPLE,
+            "windowDays": participation::WINDOW_DAYS, "everyHours": participation::EVERY_HOURS,
+            "bounds": [Participation::LOWEST, Participation::HIGHEST], "measuredAt": self.measured_at,
+        })
+    }
+
+    /// The five levels on this scale: M, G, s_k, and the *for* votes asked at `cast` votes.
+    pub fn levels_json(&self, cast: u32) -> Vec<serde_json::Value> {
+        let scale = self.scale();
+        InertiaLevel::ALL
+            .iter()
+            .map(|k| {
+                let params = scale.params(*k);
+                json!({
+                    "level": k, "majorityPct": params.majority_pct, "gradient": params.gradient,
+                    "sharePct": k.share_pct(), "cast": cast, "required": scale.required(cast, *k).ok(),
+                })
+            })
+            .collect()
+    }
+}
+
+/// A non-negative count, rounded to the nearest whole.
+fn whole(x: f64) -> u32 {
+    if x.is_finite() && x > 0.0 { x.round().min(f64::from(u32::MAX)) as u32 } else { 0 }
 }
 
 // ---------------------------------------------------------------------------
@@ -462,12 +534,9 @@ fn proposal_json(
     let (kind, target) = match p.kind() {
         ProposalKind::Text => ("text", None),
         ProposalKind::Remove => ("remove", None),
-        ProposalKind::Inertia(t) => ("inertia", Some(t.as_str())),
-    };
-    let voted_at = match p.kind() {
-        ProposalKind::Inertia(_) => inertia_of(unit).raised(),
-        _ => inertia_of(unit),
+        ProposalKind::Inertia(t) => ("inertia", Some(t)),
     };
+    let voted_at = st.voting_level(unit, p);
     json!({
         "id": p.id, "unitId": p.unit_id, "kind": kind, "inertiaTarget": target,
         "title": p.title, "body": p.body, "status": p.status, "origin": p.origin, "label": p.label,
@@ -480,7 +549,7 @@ fn proposal_json(
         "seedMinimal": p.status == "in_force" && p.entered_at.is_none() && p.confirmed_at.is_none() && p.origin == "seed",
         "tally": st.tally(&p.id),
         "evaluation": eval,
-        "votedAtInertia": voted_at.as_str(),
+        "votedAtInertia": voted_at,
         "blocked": st.blocked.contains(&p.id),
         "signals": st.signal_counts.get(&p.id).copied().unwrap_or(0),
         "myVote": mine.map(|v| v.choice.as_str()),
@@ -514,6 +583,7 @@ pub async fn document(
     .map(|v| (v.proposal_id.clone(), v))
     .collect();
 
+    let changes = inertia_changes(&state, &id).await?;
     let units: Vec<_> = st
         .units
         .iter()
@@ -529,7 +599,8 @@ pub async fn document(
                 .and_then(|fid| of_unit.iter().find(|p| p["id"].as_str() == Some(fid.as_str())).cloned());
             let proposals: Vec<_> = of_unit.into_iter().filter(|p| p["status"] != "in_force").collect();
             json!({
-                "id": u.id, "code": u.code, "section": u.section, "position": u.position, "inertia": u.inertia,
+                "id": u.id, "code": u.code, "section": u.section, "position": u.position, "inertia": inertia_of(u),
+                "inertiaChanges": changes.get(&u.id).cloned().unwrap_or_default(),
                 "inForce": in_force, "proposals": proposals,
             })
         })
@@ -545,15 +616,41 @@ pub async fn document(
             "sourceLang": st.doc.source_lang, "voteFloor": st.doc.vote_floor,
             "electorate": st.electorate, "electorateSource": st.electorate_source,
             "formula": { "base": ld_engine::FormulaParams::DEFAULT_BASE },
+            "participation": st.participation_json(),
             "publication": publication,
         },
         "units": units,
-        "inertia": InertiaPreset::ALL.iter().map(|p| json!({
-            "key": p.as_str(), "majorityPct": p.majority_pct(), "gradient": p.gradient(),
-        })).collect::<Vec<_>>(),
+        // The five levels, with the *for* votes asked at the usual participation.
+        "levels": st.levels_json(st.usual_voters()),
     })))
 }
 
+/// The past of each article's inertia (unit id → changes, oldest first).
+async fn inertia_changes(state: &AppState, doc_id: &str) -> AppResult<HashMap<String, Vec<serde_json::Value>>> {
+    #[derive(sqlx::FromRow)]
+    struct Row {
+        unit_id: String,
+        from_level: String,
+        to_level: String,
+        cause: String,
+        at: String,
+    }
+    let rows = sqlx::query_as::<_, Row>(
+        "SELECT unit_id, from_level, to_level, cause, at FROM inertia_changes WHERE doc_id = ? ORDER BY id",
+    )
+    .bind(doc_id)
+    .fetch_all(&state.db)
+    .await?;
+    let mut out: HashMap<String, Vec<serde_json::Value>> = HashMap::new();
+    for r in rows {
+        out.entry(r.unit_id).or_default().push(json!({
+            "from": InertiaLevel::parse(&r.from_level), "to": InertiaLevel::parse(&r.to_level),
+            "cause": r.cause, "at": r.at,
+        }));
+    }
+    Ok(out)
+}
+
 pub async fn publication_status(state: &AppState, doc_id: &str) -> AppResult<serde_json::Value> {
     #[derive(sqlx::FromRow)]
     struct Row {
@@ -598,7 +695,7 @@ pub async fn preview(
         Some("wellrated") => PreviewMode::WellRated,
         _ => PreviewMode::InForce,
     };
-    let units = compose::preview(&st.unit_states(), &st.proposal_states(), st.electorate, st.doc.vote_floor, mode)
+    let units = compose::preview(&st.unit_states(), &st.proposal_states(), &st.scale(), mode)
         .map_err(|_| AppError::Invalid("electorate"))?;
     // Translations of the versions shown.
     let shown: HashSet<String> = units
diff --git a/crates/ld-server/src/inertia_amend.rs b/crates/ld-server/src/inertia_amend.rs
new file mode 100644
index 0000000..3af65c6
--- /dev/null
+++ b/crates/ld-server/src/inertia_amend.rs
@@ -0,0 +1,309 @@
+//! Inertia amendments — a starting level of the seed raised in an existing base.
+//!
+//! Yvv, 2026-10-30: « Tu mets par défaut au milieu (3) pour toutes les
+//! propositions, (4) pour les 2 engagements structurels » — Unicité du compte
+//! (E1) and Réciprocité (E2). New bases get level 4 from the seed. An existing
+//! base, where both are in force at the starting level (`standard`, now 3),
+//! gets it through an amendment listed here, and **only if no vote ever
+//! changed the article's inertia**:
+//!
+//! - no adoption of a change of inertia on the article (`adoptions`, and the
+//!   journal `inertia_changes`);
+//! - its level is still the one the amendment raises (the seed's 3).
+//!
+//! An open proposal to change the inertia does not stop it (orch, 2026-10-30:
+//! two such proposals exist in production, I1 → 5 and E1 → 5, at zero votes):
+//! it stays open, with its target, and is voted at the article's new level,
+//! since a change of inertia inherits it (ADR 0007).
+//!
+//! Like the seed amendments (`seed_amend`), each document is decided once, at
+//! the first start that knows the amendment; the decision is kept in
+//! `inertia_amendments` (applied, refused and why, or present) and in the
+//! logs. Applied, the level is written in one transaction with a line in
+//! `inertia_changes` (the article says so) and, where the document publishes,
+//! a row in the publication queue (`document.json` carries the levels).
+
+use crate::AppState;
+use crate::seed::SeedDoc;
+use crate::util;
+use ld_engine::inertia::InertiaLevel;
+use sqlx::SqliteConnection;
+
+/// One starting level to raise, in every document instantiated from a seed.
+pub struct InertiaAmendment {
+    /// Stable identifier: each document's decision is kept under it.
+    pub id: &'static str,
+    /// Slug of the seed document.
+    pub doc: &'static str,
+    /// Code of the article.
+    pub unit: &'static str,
+    /// The level it must still hold.
+    pub from: u8,
+    /// The level it gets: the seed's today, which must say so.
+    pub to: u8,
+    /// Reason given to the publication queue, and so to the commit of the texts.
+    pub reason: &'static str,
+}
+
+pub const AMENDMENTS: &[InertiaAmendment] = &[
+    InertiaAmendment {
+        id: "2026-10-30-e1-inertie-4",
+        doc: "acte-engagement-certification",
+        unit: "E1",
+        from: 3,
+        to: 4,
+        reason: "inertie de départ relevée : E1, 3 → 4",
+    },
+    InertiaAmendment {
+        id: "2026-10-30-e2-inertie-4",
+        doc: "acte-engagement-certification",
+        unit: "E2",
+        from: 3,
+        to: 4,
+        reason: "inertie de départ relevée : E2, 3 → 4",
+    },
+];
+
+/// What the database says of the article.
+#[derive(Debug, Clone, Default, PartialEq, Eq)]
+pub struct Facts {
+    /// `units.inertia` as written.
+    pub raw: String,
+    /// Changes of its inertia that a vote brought into force.
+    pub voted_changes: i64,
+    /// Open proposals to change its inertia (they stay open; told in the logs).
+    pub open_proposals: i64,
+}
+
+#[derive(Debug, Clone, Copy, PartialEq, Eq)]
+pub enum Verdict {
+    Apply,
+    /// The level is already there: nothing to do.
+    Present,
+    Refuse(&'static str),
+}
+
+/// The rule, apart from the database: a vote on the inertia keeps it.
+pub fn verdict(facts: Option<&Facts>, a: &InertiaAmendment) -> Verdict {
+    let Some(f) = facts else { return Verdict::Refuse("no_article") };
+    let Some(level) = InertiaLevel::parse(&f.raw) else { return Verdict::Refuse("level_unreadable") };
+    if level.get() == a.to {
+        return Verdict::Present;
+    }
+    if f.voted_changes > 0 {
+        Verdict::Refuse("changed_by_vote")
+    } else if level.get() != a.from {
+        Verdict::Refuse("level_differs")
+    } else {
+        Verdict::Apply
+    }
+}
+
+/// A decision taken at this start.
+#[derive(Debug, Clone, PartialEq, Eq)]
+pub struct Outcome {
+    pub amendment: &'static str,
+    pub group: String,
+    pub verdict: Verdict,
+}
+
+/// Decides every amendment not yet decided, document by document.
+pub async fn apply(state: &AppState, seeds: &[SeedDoc], list: &[InertiaAmendment]) -> anyhow::Result<Vec<Outcome>> {
+    let mut out = Vec::new();
+    for a in list {
+        if !seed_says(seeds, a) {
+            continue;
+        }
+        let docs: Vec<(String, String, Option<String>)> =
+            sqlx::query_as("SELECT id, group_slug, publish_path FROM documents WHERE slug = ? ORDER BY group_slug")
+                .bind(a.doc)
+                .fetch_all(&state.db)
+                .await?;
+        for (doc_id, group, publish_path) in docs {
+            let Some((v, open)) = decide(state, a, &doc_id, publish_path.is_some()).await? else { continue };
+            match v {
+                Verdict::Apply => tracing::info!(
+                    amendment = a.id, %group, unit = a.unit, from = a.from, to = a.to, open_inertia_proposals = open,
+                    "inertia amendment applied"
+                ),
+                Verdict::Present => {
+                    tracing::info!(amendment = a.id, %group, unit = a.unit, "inertia amendment: level already there")
+                }
+                Verdict::Refuse(why) => tracing::warn!(
+                    amendment = a.id, %group, unit = a.unit, reason = why,
+                    "inertia amendment refused: the article keeps its inertia"
+                ),
+            }
+            if v == Verdict::Apply && publish_path.is_some() {
+                state.publish_wake.notify_one();
+            }
+            out.push(Outcome { amendment: a.id, group, verdict: v });
+        }
+    }
+    Ok(out)
+}
+
+/// The seed must hold the level the amendment gives: a seed edited later never
+/// reaches a base by this way.
+fn seed_says(seeds: &[SeedDoc], a: &InertiaAmendment) -> bool {
+    let level = seeds.iter().find(|s| s.slug == a.doc).and_then(|s| s.units.iter().find(|u| u.code == a.unit));
+    match level {
+        Some(u) if u.inertia.get() == a.to => true,
+        _ => {
+            tracing::error!(
+                amendment = a.id,
+                doc = a.doc,
+                unit = a.unit,
+                "inertia amendment: the seed does not give this level, nothing decided"
+            );
+            false
+        }
+    }
+}
+
+async fn facts(conn: &mut SqliteConnection, unit_id: &str, raw: String) -> anyhow::Result<Facts> {
+    let voted_changes: i64 = sqlx::query_scalar(
+        "SELECT (SELECT COUNT(*) FROM adoptions WHERE unit_id = ?1 AND kind = 'inertia')
+              + (SELECT COUNT(*) FROM inertia_changes WHERE unit_id = ?1 AND cause = 'vote')",
+    )
+    .bind(unit_id)
+    .fetch_one(&mut *conn)
+    .await?;
+    let open_proposals: i64 =
+        sqlx::query_scalar("SELECT COUNT(*) FROM proposals WHERE unit_id = ? AND kind = 'inertia' AND status = 'open'")
+            .bind(unit_id)
+            .fetch_one(&mut *conn)
+            .await?;
+    Ok(Facts { raw, voted_changes, open_proposals })
+}
+
+/// One document, in one transaction: `None` when it was decided at an earlier start.
+async fn decide(
+    state: &AppState,
+    a: &InertiaAmendment,
+    doc_id: &str,
+    publishes: bool,
+) -> anyhow::Result<Option<(Verdict, i64)>> {
+    let mut tx = state.db.begin().await?;
+    let decided: i64 =
+        sqlx::query_scalar("SELECT COUNT(*) FROM inertia_amendments WHERE amendment_id = ? AND doc_id = ?")
+            .bind(a.id)
+            .bind(doc_id)
+            .fetch_one(&mut *tx)
+            .await?;
+    if decided > 0 {
+        return Ok(None);
+    }
+    let unit: Option<(String, String)> = sqlx::query_as("SELECT id, inertia FROM units WHERE doc_id = ? AND code = ?")
+        .bind(doc_id)
+        .bind(a.unit)
+        .fetch_optional(&mut *tx)
+        .await?;
+    let found = match &unit {
+        Some((id, raw)) => Some(facts(&mut tx, id, raw.clone()).await?),
+        None => None,
+    };
+    let mut v = verdict(found.as_ref(), a);
+    let now = util::now();
+    let to = InertiaLevel::new(a.to).map(InertiaLevel::as_db).unwrap_or_default();
+    if let (Verdict::Apply, Some((unit_id, raw))) = (v, &unit) {
+        // Written only over the level that was judged.
+        let done = sqlx::query("UPDATE units SET inertia = ? WHERE id = ? AND inertia = ?")
+            .bind(&to)
+            .bind(unit_id)
+            .bind(raw)
+            .execute(&mut *tx)
+            .await?;
+        if done.rows_affected() == 1 {
+            sqlx::query(
+                "INSERT INTO inertia_changes (unit_id, doc_id, from_level, to_level, cause, amendment_id, at)
+                 VALUES (?, ?, ?, ?, 'amendment', ?, ?)",
+            )
+            .bind(unit_id)
+            .bind(doc_id)
+            .bind(a.from.to_string())
+            .bind(&to)
+            .bind(a.id)
+            .bind(&now)
+            .execute(&mut *tx)
+            .await?;
+            if publishes {
+                sqlx::query("INSERT INTO outbox (doc_id, reason, created_at, next_at) VALUES (?, ?, ?, ?)")
+                    .bind(doc_id)
+                    .bind(a.reason)
+                    .bind(&now)
+                    .bind(&now)
+                    .execute(&mut *tx)
+                    .await?;
+            }
+        } else {
+            v = Verdict::Refuse("changed");
+        }
+    }
+    let (outcome, reason) = match v {
+        Verdict::Apply => ("applied", None),
+        Verdict::Present => ("present", None),
+        Verdict::Refuse(why) => ("refused", Some(why)),
+    };
+    sqlx::query(
+        "INSERT INTO inertia_amendments (amendment_id, doc_id, unit_code, from_level, to_level, outcome, reason, at)
+         VALUES (?, ?, ?, ?, ?, ?, ?, ?)",
+    )
+    .bind(a.id)
+    .bind(doc_id)
+    .bind(a.unit)
+    .bind(unit.as_ref().map(|(_, raw)| raw.clone()))
+    .bind(&to)
+    .bind(outcome)
+    .bind(reason)
+    .bind(&now)
+    .execute(&mut *tx)
+    .await?;
+    tx.commit().await?;
+    Ok(Some((v, found.map_or(0, |f| f.open_proposals))))
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    const A: InertiaAmendment =
+        InertiaAmendment { id: "test", doc: "doc", unit: "E1", from: 3, to: 4, reason: "inertie de départ relevée" };
+
+    fn at(raw: &str) -> Facts {
+        Facts { raw: raw.into(), ..Facts::default() }
+    }
+
+    #[test]
+    fn the_starting_level_is_raised() {
+        assert_eq!(verdict(Some(&at("3")), &A), Verdict::Apply);
+        // The word of before, if an older image wrote it.
+        assert_eq!(verdict(Some(&at("standard")), &A), Verdict::Apply);
+    }
+
+    #[test]
+    fn an_open_change_of_inertia_does_not_stop_it() {
+        let f = Facts { open_proposals: 1, ..at("3") };
+        assert_eq!(verdict(Some(&f), &A), Verdict::Apply);
+    }
+
+    #[test]
+    fn the_level_already_there_is_left_as_it_is() {
+        assert_eq!(verdict(Some(&at("4")), &A), Verdict::Present);
+        assert_eq!(verdict(Some(&at("high")), &A), Verdict::Present);
+    }
+
+    #[test]
+    fn a_vote_on_the_inertia_keeps_it() {
+        let cases = [
+            (None, "no_article"),
+            (Some(Facts { voted_changes: 1, ..at("3") }), "changed_by_vote"),
+            (Some(at("5")), "level_differs"),
+            (Some(at("2")), "level_differs"),
+            (Some(at("haute")), "level_unreadable"),
+        ];
+        for (facts, reason) in cases {
+            assert_eq!(verdict(facts.as_ref(), &A), Verdict::Refuse(reason), "{facts:?}");
+        }
+    }
+}
diff --git a/crates/ld-server/src/lib.rs b/crates/ld-server/src/lib.rs
index 187c161..102e59a 100644
--- a/crates/ld-server/src/lib.rs
+++ b/crates/ld-server/src/lib.rs
@@ -11,7 +11,9 @@ pub mod auth;
 pub mod config;
 pub mod docs;
 pub mod error;
+pub mod inertia_amend;
 pub mod overview;
+pub mod participation;
 pub mod proposals;
 pub mod publish;
 pub mod seed;
@@ -197,6 +199,7 @@ pub async fn run() -> anyhow::Result<()> {
     let state = AppState::new(cfg, db).await?;
 
     seed::ensure(&state).await?;
+    participation::refresh(&state, false).await?;
     auth::bootstrap(&state).await?;
     if let Err(e) = publish::ensure_key(&state).await {
         tracing::warn!(error = %e, "publication key");
diff --git a/crates/ld-server/src/participation.rs b/crates/ld-server/src/participation.rs
new file mode 100644
index 0000000..36b631f
--- /dev/null
+++ b/crates/ld-server/src/participation.rs
@@ -0,0 +1,132 @@
+//! p̃ — the usual participation of each group, the anchor of the five levels
+//! of inertia (ADR 0007, `ld_engine::inertia`).
+//!
+//! What is measured: the proposals of the group (every document, every kind,
+//! drafts aside) that hold at least one vote on their current revision, the
+//! last one cast within the past year. For each, T is the number of those
+//! votes **at the time of measuring** — the same T the formula sees, since the
+//! vote is permanent. The median of these T, and how many proposals it rests
+//! on, are kept in `settings` under `participation:<group>`.
+//!
+//! When: once a day (at start, then by the sweeper), never at each vote — a
+//! threshold that moved with every vote cast elsewhere could not be read. W
+//! moves on its own (the web of trust, every six hours): p̃ = T̃ / W follows it
+//! at once, so the scale still asks s_k of the same usual number of voters.
+
+use crate::AppState;
+use crate::util;
+use serde::{Deserialize, Serialize};
+use time::OffsetDateTime;
+use time::format_description::well_known::Rfc3339;
+
+/// Only proposals voted on within this many days count.
+pub const WINDOW_DAYS: i64 = 365;
+/// A measure older than this is taken again.
+pub const EVERY_HOURS: i64 = 24;
+
+const KEY: &str = "participation:";
+
+/// What was measured for a group.
+#[derive(Clone, Debug, Default, PartialEq, Serialize, Deserialize)]
+#[serde(rename_all = "camelCase")]
+pub struct Measure {
+    /// The median number of voters, when at least one proposal was voted on.
+    pub median: Option<f64>,
+    /// Proposals it rests on.
+    pub sample: u32,
+    pub measured_at: String,
+}
+
+/// The numbers of voters of the group's proposals voted on since `since`.
+pub async fn sample(state: &AppState, group: &str, since: &str) -> sqlx::Result<Vec<u32>> {
+    let rows: Vec<i64> = sqlx::query_scalar(
+        "SELECT COUNT(*) FROM votes v
+           JOIN proposals p ON p.id = v.proposal_id
+           JOIN units u ON u.id = p.unit_id
+           JOIN documents d ON d.id = u.doc_id
+          WHERE d.group_slug = ? AND p.status <> 'draft' AND v.revision = p.revision
+          GROUP BY v.proposal_id
+         HAVING MAX(v.cast_at) >= ?",
+    )
+    .bind(group)
+    .bind(since)
+    .fetch_all(&state.db)
+    .await?;
+    Ok(rows.into_iter().map(|n| u32::try_from(n).unwrap_or(u32::MAX)).collect())
+}
+
+/// Measures the group now.
+pub async fn measure(state: &AppState, group: &str) -> sqlx::Result<Measure> {
+    let now = OffsetDateTime::now_utc();
+    let since = util::stamp(now - time::Duration::days(WINDOW_DAYS));
+    let votes = sample(state, group, &since).await?;
+    Ok(Measure {
+        median: ld_engine::inertia::median(&votes),
+        sample: u32::try_from(votes.len()).unwrap_or(u32::MAX),
+        measured_at: util::stamp(now),
+    })
+}
+
+/// The last measure kept for the group, if any.
+pub async fn stored(state: &AppState, group: &str) -> sqlx::Result<Option<Measure>> {
+    let raw: Option<String> = sqlx::query_scalar("SELECT value FROM settings WHERE key = ?")
+        .bind(format!("{KEY}{group}"))
+        .fetch_optional(&state.db)
+        .await?;
+    Ok(raw.and_then(|v| serde_json::from_str(&v).ok()))
+}
+
+async fn keep(state: &AppState, group: &str, m: &Measure) -> anyhow::Result<()> {
+    sqlx::query(
+        "INSERT INTO settings (key, value, updated_at) VALUES (?, ?, ?)
+         ON CONFLICT(key) DO UPDATE SET value = excluded.value, updated_at = excluded.updated_at",
+    )
+    .bind(format!("{KEY}{group}"))
+    .bind(serde_json::to_string(m)?)
+    .bind(&m.measured_at)
+    .execute(&state.db)
+    .await?;
+    Ok(())
+}
+
+fn is_stale(m: &Measure, now: OffsetDateTime) -> bool {
+    OffsetDateTime::parse(&m.measured_at, &Rfc3339)
+        .map_or(true, |at| now - at >= time::Duration::hours(EVERY_HOURS) || at > now)
+}
+
+/// Measures again every group whose measure is missing or a day old (all of
+/// them with `force`). Returns the groups measured.
+pub async fn refresh(state: &AppState, force: bool) -> anyhow::Result<Vec<String>> {
+    let groups: Vec<String> =
+        sqlx::query_scalar("SELECT slug FROM groups ORDER BY position").fetch_all(&state.db).await?;
+    let now = OffsetDateTime::now_utc();
+    let mut done = Vec::new();
+    for group in groups {
+        let due = force || stored(state, &group).await?.is_none_or(|m| is_stale(&m, now));
+        if !due {
+            continue;
+        }
+        let m = measure(state, &group).await?;
+        keep(state, &group, &m).await?;
+        tracing::info!(%group, median = ?m.median, sample = m.sample, "usual participation measured");
+        done.push(group);
+    }
+    Ok(done)
+}
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn a_measure_is_taken_again_after_a_day() {
+        let now = OffsetDateTime::now_utc();
+        let at =
+            |hours: i64| Measure { measured_at: util::stamp(now - time::Duration::hours(hours)), ..Measure::default() };
+        assert!(!is_stale(&at(1), now));
+        assert!(!is_stale(&at(23), now));
+        assert!(is_stale(&at(24), now));
+        assert!(is_stale(&at(-2), now), "a measure from the future is taken again");
+        assert!(is_stale(&Measure::default(), now), "unreadable");
+    }
+}
diff --git a/crates/ld-server/src/proposals.rs b/crates/ld-server/src/proposals.rs
index 0cfb385..1081296 100644
--- a/crates/ld-server/src/proposals.rs
+++ b/crates/ld-server/src/proposals.rs
@@ -21,7 +21,7 @@ use axum::Json;
 use axum::extract::{Path, State};
 use ld_engine::assist::{self, Hint};
 use ld_engine::edit::{self, EditKind};
-use ld_engine::threshold::InertiaPreset;
+use ld_engine::inertia::InertiaLevel;
 use serde::Deserialize;
 use serde_json::json;
 
@@ -191,13 +191,14 @@ async fn new_unit(state: &AppState, st: &DocState, after: Option<&str>) -> AppRe
     let section = after.and_then(|a| st.units.iter().find(|u| u.id == a)).and_then(|u| u.section.clone());
     sqlx::query(
         "INSERT INTO units (id, doc_id, code, section, position, inertia, in_force_id, created_at)
-         VALUES (?, ?, ?, ?, ?, 'standard', NULL, ?)",
+         VALUES (?, ?, ?, ?, ?, ?, NULL, ?)",
     )
     .bind(&id)
     .bind(&st.doc.id)
     .bind(format!("N{}", n + 1))
     .bind(section)
     .bind(position_after(&st.units, after))
+    .bind(InertiaLevel::DEFAULT.as_db())
     .bind(util::now())
     .execute(&state.db)
     .await?;
@@ -626,28 +627,33 @@ pub async fn detail(
         _ => None,
     };
     let eval = st.evaluation(unit, &p);
-    let voted_at = if p.kind == "inertia" { docs::inertia_of(unit).raised() } else { docs::inertia_of(unit) };
+    let voted_at = st.voting_level(unit, &p);
+    let target = p.inertia_target.as_deref().and_then(InertiaLevel::parse);
     let tr = docs::translations_for(&state, &[&p]).await?;
     Ok(Json(json!({
         "proposal": {
-            "id": p.id, "kind": p.kind, "inertiaTarget": p.inertia_target, "title": p.title, "body": p.body,
+            "id": p.id, "kind": p.kind, "inertiaTarget": target, "title": p.title, "body": p.body,
             "status": p.status, "origin": p.origin, "label": p.label, "revision": p.revision,
             "author": p.author_name, "authorInvited": p.author_invited.unwrap_or(false),
             "mine": p.author_id.as_deref() == Some(user.id.as_str()),
             "submittedAt": p.submitted_at, "enteredAt": p.entered_at, "confirmedAt": p.confirmed_at,
             "seedMinimal": p.status == "in_force" && p.entered_at.is_none() && p.confirmed_at.is_none() && p.origin == "seed",
-            "tally": st.tally(&p.id), "evaluation": eval, "votedAtInertia": voted_at.as_str(),
+            "tally": st.tally(&p.id), "evaluation": eval, "votedAtInertia": voted_at,
             "blocked": st.blocked.contains(&p.id),
             "myVote": my_vote.as_ref().map(|v| &v.0), "myVoteStale": my_vote.as_ref().is_some_and(|v| v.1 != p.revision),
             "translations": tr.get(&p.id).cloned().unwrap_or_default(),
         },
-        "unit": { "id": unit.id, "code": unit.code, "inertia": unit.inertia },
+        "unit": { "id": unit.id, "code": unit.code, "inertia": docs::inertia_of(unit) },
         "inForce": in_force.map(|v| json!({ "id": v.id, "title": v.title, "body": v.body })),
         "diff": diff,
         "history": history,
         "signals": signals,
         "electorate": st.electorate,
+        "electorateSource": st.electorate_source,
         "voteFloor": st.doc.vote_floor,
+        "participation": st.participation_json(),
+        // The five levels, with the *for* votes each would ask at this version's participation.
+        "levels": st.levels_json(st.tally(&p.id).cast()),
     })))
 }
 
@@ -783,18 +789,20 @@ pub async fn lift_signal(
 
 #[derive(Deserialize)]
 pub struct InertiaBody {
-    target: String,
+    /// A level, 1 to 5 (a word of before is read as its level).
+    target: serde_json::Value,
 }
 
-/// Propose a change of inertia; it is voted one level above the unit. An open
-/// proposal for the same target is reused rather than duplicated.
+/// Propose a change of inertia; it is voted at the level of the unit (it
+/// inherits it, ADR 0007). An open proposal for the same target is reused
+/// rather than duplicated.
 pub async fn propose_inertia(
     State(state): State<AppState>,
     User(user): User,
     Path(unit_id): Path<String>,
     Json(b): Json<InertiaBody>,
 ) -> AppResult<Json<serde_json::Value>> {
-    let target = InertiaPreset::parse(&b.target).ok_or(AppError::Invalid("inertia"))?;
+    let target = serde_json::from_value::<InertiaLevel>(b.target).map_err(|_| AppError::Invalid("inertia"))?;
     let doc_id = doc_of_unit(&state, &unit_id).await?;
     let st = docs::load_state(&state, &doc_id).await?;
     docs::require_open(&state, &user, &st.group).await?;
@@ -806,17 +814,18 @@ pub async fn propose_inertia(
         p.unit_id == unit_id
             && p.kind == "inertia"
             && p.status == "open"
-            && p.inertia_target.as_deref() == Some(target.as_str())
+            && p.inertia_target.as_deref().and_then(InertiaLevel::parse) == Some(target)
     }) {
         return Ok(Json(json!({ "id": existing.id, "existing": true })));
     }
-    let title = format!("inertia:{}", target.as_str());
+    let title = format!("inertia:{}", target.get());
+    let level = target.as_db();
     let id = insert_proposal(
         &state,
         NewProposal {
             unit_id: &unit_id,
             kind: "inertia",
-            inertia_target: Some(target.as_str()),
+            inertia_target: Some(&level),
             title: &title,
             body: "",
             author: &user.id,
@@ -869,14 +878,7 @@ mod tests {
     use super::*;
 
     fn unit(id: &str, position: f64) -> UnitRow {
-        UnitRow {
-            id: id.into(),
-            code: id.into(),
-            section: None,
-            position,
-            inertia: "standard".into(),
-            in_force_id: None,
-        }
+        UnitRow { id: id.into(), code: id.into(), section: None, position, inertia: "3".into(), in_force_id: None }
     }
 
     #[test]
diff --git a/crates/ld-server/src/publish.rs b/crates/ld-server/src/publish.rs
index b9ad765..873d45d 100644
--- a/crates/ld-server/src/publish.rs
+++ b/crates/ld-server/src/publish.rs
@@ -347,7 +347,7 @@ pub async fn render(state: &AppState, st: &DocState) -> anyhow::Result<Vec<(Stri
             }
             let tally = st.tally(&p.id);
             json!({
-                "code": u.code, "title": title, "body": body, "inertia": u.inertia,
+                "code": u.code, "title": title, "body": body, "inertia": crate::docs::inertia_of(u),
                 "status": if p.entered_at.is_some() { "adopted" } else if p.confirmed_at.is_some() { "confirmed" } else { "seed-minimal" },
                 "enteredAt": p.entered_at, "votes": { "for": tally.for_votes, "against": tally.against },
             })
diff --git a/crates/ld-server/src/seed.rs b/crates/ld-server/src/seed.rs
index 9337c84..ef1cd07 100644
--- a/crates/ld-server/src/seed.rs
+++ b/crates/ld-server/src/seed.rs
@@ -5,11 +5,15 @@
 //! yet**. An existing document is never instantiated again: from its first
 //! vote on, it is runtime data. The one way a newer seed text reaches an
 //! existing document is a seed amendment (`seed_amend`): listed, decided once,
-//! and applied only to an article nobody has touched.
+//! and applied only to an article nobody has touched; a newer starting level of
+//! inertia, an inertia amendment (`inertia_amend`), on an article whose inertia
+//! no vote changed.
 
 use crate::AppState;
+use crate::inertia_amend;
 use crate::seed_amend;
 use crate::util::{self, LangMap};
+use ld_engine::inertia::InertiaLevel;
 use serde::Deserialize;
 use std::path::Path;
 
@@ -37,7 +41,8 @@ pub struct SeedUnit {
     pub code: String,
     pub section: Option<String>,
     pub position: f64,
-    pub inertia: String,
+    /// A level, 1 to 5 (a word of before is read as its level).
+    pub inertia: InertiaLevel,
     pub versions: Vec<SeedVersion>,
 }
 
@@ -67,11 +72,12 @@ pub async fn ensure_groups(state: &AppState) -> anyhow::Result<()> {
     Ok(())
 }
 
-/// On start: the groups, the documents missing from them, then the seed
-/// amendments (each decided once per document).
+/// On start: the groups, the documents missing from them, then the seed and
+/// inertia amendments (each decided once per document).
 pub async fn ensure(state: &AppState) -> anyhow::Result<()> {
     let seeds = documents(state).await?;
     seed_amend::apply(state, &seeds, seed_amend::AMENDMENTS).await?;
+    inertia_amend::apply(state, &seeds, inertia_amend::AMENDMENTS).await?;
     Ok(())
 }
 
@@ -159,7 +165,7 @@ async fn instantiate(state: &AppState, seed: &SeedDoc, inst: &SeedInstance) -> a
         .bind(&unit.code)
         .bind(&unit.section)
         .bind(unit.position)
-        .bind(&unit.inertia)
+        .bind(unit.inertia.as_db())
         .bind(&now)
         .execute(&mut *tx)
         .await?;
diff --git a/crates/ld-server/tests/api.rs b/crates/ld-server/tests/api.rs
index fd0263d..426a17f 100644
--- a/crates/ld-server/tests/api.rs
+++ b/crates/ld-server/tests/api.rs
@@ -112,13 +112,15 @@ async fn the_seed_a_minima_and_the_open_proposals() {
     assert_eq!(e1["tally"]["for"], 0);
     assert_eq!(doc["doc"]["voteFloor"], 50.0);
     assert_eq!(doc["doc"]["electorate"], 5745);
-    // Every other article is an open proposal at zero votes, standard inertia.
+    // Every other article is an open proposal at zero votes, at the middle level of inertia.
     let e3 = unit(&doc, "E3");
     assert!(e3["inForce"].is_null());
     // In the order of the seed, whatever their random identifiers.
     let labels: Vec<&str> = e3["proposals"].as_array().expect("p").iter().filter_map(|p| p["label"].as_str()).collect();
     assert_eq!(labels, ["1.0.0", "0.4.0-draft"], "E3 and its 0.4.0 variant");
-    assert_eq!(e3["inertia"], "standard");
+    assert_eq!(e3["inertia"], 3);
+    // The two structural commitments start one level up (Yvv, 2026-10-30).
+    assert_eq!((unit(&doc, "E1")["inertia"].as_u64(), unit(&doc, "E2")["inertia"].as_u64()), (Some(4), Some(4)));
     // Translations seeded.
     assert!(e1["translations"]["en"]["body"].as_str().expect("en").contains("commit"));
 }
@@ -375,20 +377,23 @@ async fn a_contradiction_signal_blocks_entering_into_force() {
     assert_eq!(v["entered"][0]["code"], "K1");
 }
 
+/// Replaces « inertia change is voted one level up » (2026-10-21): since
+/// 2026-10-30 a change of inertia inherits the level of its article (ADR 0007).
 #[tokio::test]
-async fn inertia_change_is_voted_one_level_up() {
+async fn inertia_change_is_voted_at_the_level_of_the_article() {
     let (mut a, _) = Client::new().await;
     a.login("Yvv", false).await;
     let id = doc_id(&mut a, "monnaie-libre").await;
     let (_, doc) = a.call("GET", &format!("/api/docs/{id}"), None).await;
     let uid = unit(&doc, "E1")["id"].as_str().expect("u").to_owned();
-    let (s, v) = a.call("POST", &format!("/api/units/{uid}/inertia"), Some(json!({ "target": "high" }))).await;
+    let (s, v) = a.call("POST", &format!("/api/units/{uid}/inertia"), Some(json!({ "target": 5 }))).await;
     assert_eq!(s, StatusCode::OK, "{v}");
     let p = v["id"].as_str().expect("id").to_owned();
-    let (_, again) = a.call("POST", &format!("/api/units/{uid}/inertia"), Some(json!({ "target": "high" }))).await;
+    // The word of before reads as its level: the same proposal, not a second one.
+    let (_, again) = a.call("POST", &format!("/api/units/{uid}/inertia"), Some(json!({ "target": "max" }))).await;
     assert_eq!(again["id"], p.as_str());
     let (_, d) = a.call("GET", &format!("/api/proposals/{p}"), None).await;
-    assert_eq!(d["proposal"]["votedAtInertia"], "high");
+    assert_eq!((d["proposal"]["inertiaTarget"].as_u64(), d["proposal"]["votedAtInertia"].as_u64()), (Some(5), Some(4)));
 }
 
 #[tokio::test]
@@ -769,6 +774,10 @@ async fn publication_writes_the_texts_in_force_to_the_repository() {
         serde_json::from_str(&show("monnaie-libre/acte-engagement-certification/document.json")).expect("json");
     assert_eq!(json["units"].as_array().expect("units").len(), 3);
     assert_eq!(json["units"][0]["status"], "seed-minimal");
+    // Levels of inertia are published as numbers, 1 to 5.
+    let levels: Vec<Option<u64>> =
+        json["units"].as_array().expect("units").iter().map(|u| u["inertia"].as_u64()).collect();
+    assert_eq!(levels, [Some(3), Some(4), Some(4)]);
     assert!(show("README.md").contains("libreDecision"));
     let done: i64 = sqlx::query_scalar("SELECT COUNT(*) FROM outbox WHERE done_at IS NULL")
         .fetch_one(&state.db)
diff --git a/crates/ld-server/tests/inertia.rs b/crates/ld-server/tests/inertia.rs
new file mode 100644
index 0000000..3904c68
--- /dev/null
+++ b/crates/ld-server/tests/inertia.rs
@@ -0,0 +1,549 @@
+//! Inertia in five levels (ADR 0007): the levels and the scale served, the
+//! usual participation of a group, the change of inertia voted at the level
+//! of its article, the migration of the four words of before, and the
+//! amendment that raises E1 and E2 to level 4 in an existing base.
+
+use axum::body::Body;
+use axum::http::{Request, StatusCode, header};
+use http_body_util::BodyExt;
+use ld_engine::inertia::{InertiaLevel, Scale, gradient};
+use ld_engine::threshold::required_ratio;
+use ld_server::{AppState, CSRF_HEADER, CSRF_VALUE, Config, app, open_db, seed};
+use serde_json::{Value, json};
+use sqlx::SqlitePool;
+use std::borrow::Cow;
+use tower::ServiceExt;
+
+struct Client {
+    router: axum::Router,
+    cookie: Option<String>,
+}
+
+impl Client {
+    fn of(state: &AppState) -> Self {
+        Self { router: app(state.clone()), cookie: None }
+    }
+
+    async fn new() -> (Self, AppState) {
+        let db = open_db("sqlite::memory:").await.expect("db");
+        let state = AppState::new(Config::for_tests(), db).await.expect("state");
+        seed::ensure(&state).await.expect("seed");
+        (Self::of(&state), state)
+    }
+
+    fn other(&self) -> Self {
+        Self { router: self.router.clone(), cookie: None }
+    }
+
+    async fn call(&mut self, method: &str, uri: &str, body: Option<Value>) -> (StatusCode, Value) {
+        let mut req = Request::builder().method(method).uri(uri).header(CSRF_HEADER, CSRF_VALUE);
+        if let Some(c) = &self.cookie {
+            req = req.header(header::COOKIE, c);
+        }
+        let req = match body {
+            Some(b) => req.header(header::CONTENT_TYPE, "application/json").body(Body::from(b.to_string())),
+            None => req.body(Body::empty()),
+        }
+        .expect("request");
+        let res = self.router.clone().oneshot(req).await.expect("response");
+        let status = res.status();
+        if let Some(set) = res.headers().get(header::SET_COOKIE) {
+            let raw = set.to_str().expect("cookie").split(';').next().unwrap_or_default().to_owned();
+            if raw.starts_with("ld_session=") {
+                self.cookie = Some(raw);
+            }
+        }
+        let bytes = res.into_body().collect().await.expect("body").to_bytes();
+        (status, serde_json::from_slice(&bytes).unwrap_or(Value::Null))
+    }
+
+    async fn get(&mut self, uri: &str) -> Value {
+        let (s, v) = self.call("GET", uri, None).await;
+        assert_eq!(s, StatusCode::OK, "{uri}: {v}");
+        v
+    }
+
+    async fn login(&mut self, name: &str) {
+        let (s, v) = self.call("POST", "/api/auth/dev", Some(json!({ "name": name, "admin": false }))).await;
+        assert_eq!(s, StatusCode::OK, "{v}");
+    }
+
+    async fn vote(&mut self, proposal: &str, choice: &str) -> Value {
+        let (s, v) =
+            self.call("POST", &format!("/api/proposals/{proposal}/vote"), Some(json!({ "choice": choice }))).await;
+        assert_eq!(s, StatusCode::OK, "{v}");
+        v
+    }
+
+    async fn doc(&mut self, group: &str) -> Value {
+        let g = self.get(&format!("/api/groups/{group}")).await;
+        let id = g["docs"][0]["id"].as_str().expect("doc").to_owned();
+        self.get(&format!("/api/docs/{id}")).await
+    }
+}
+
+fn unit<'a>(doc: &'a Value, code: &str) -> &'a Value {
+    doc["units"].as_array().expect("units").iter().find(|u| u["code"] == code).expect("unit")
+}
+
+fn level(k: u8) -> InertiaLevel {
+    InertiaLevel::new(k).expect("1 to 5")
+}
+
+fn numbers(levels: &Value, key: &str) -> Vec<f64> {
+    levels.as_array().expect("levels").iter().map(|l| l[key].as_f64().expect(key)).collect()
+}
+
+#[tokio::test]
+async fn the_five_levels_and_the_scale_are_served() {
+    let (mut c, _) = Client::new().await;
+    c.login("Chiara").await;
+    let doc = c.doc("monnaie-libre").await;
+    // 3 everywhere, 4 for the two structural commitments.
+    let raised: Vec<&str> = doc["units"]
+        .as_array()
+        .expect("units")
+        .iter()
+        .filter(|u| u["inertia"] != 3)
+        .map(|u| u["code"].as_str().expect("code"))
+        .collect();
+    assert_eq!(raised, ["E1", "E2"]);
+    assert!(unit(&doc, "E1")["inertia"] == 4 && unit(&doc, "E2")["inertia"] == 4);
+
+    // No vote yet: the reference, 2C/W = 100 voters out of 5745.
+    let p = &doc["doc"]["participation"];
+    assert_eq!(
+        (p["source"].as_str(), p["sample"].as_u64(), p["voters"].as_u64()),
+        (Some("reference"), Some(0), Some(100))
+    );
+    assert_eq!(
+        (p["minSample"].as_u64(), p["windowDays"].as_u64(), p["everyHours"].as_u64()),
+        (Some(5), Some(365), Some(24))
+    );
+    let ratio = p["ratio"].as_f64().expect("ratio");
+    assert!((ratio - 100.0 / 5745.0).abs() < 1e-12);
+
+    let levels = &doc["levels"];
+    assert_eq!(numbers(levels, "level"), [1.0, 2.0, 3.0, 4.0, 5.0]);
+    assert_eq!(numbers(levels, "majorityPct"), [50.0, 50.0, 55.0, 60.0, 66.0]);
+    assert_eq!(numbers(levels, "sharePct"), [60.0, 67.0, 75.0, 83.0, 90.0]);
+    let scale = Scale { electorate: 5745, floor: 50.0, participation: ratio };
+    for (l, k) in levels.as_array().expect("levels").iter().zip(InertiaLevel::ALL) {
+        assert!((l["gradient"].as_f64().expect("G") - gradient(k, ratio)).abs() < 1e-12);
+        // At the usual participation, C plus s_k of the votes beyond C.
+        assert_eq!(l["cast"], 100);
+        assert_eq!(l["required"].as_u64(), Some(u64::from(scale.required(100, k).expect("valid"))));
+        let at_usual = 50.0 + k.share_pct() / 100.0 * 50.0;
+        assert_eq!(l["required"].as_f64(), Some(at_usual.ceil()));
+    }
+
+    // A version: the five levels at its own participation, and the level it is voted at.
+    let e1 = unit(&doc, "E1")["inForce"]["id"].as_str().expect("e1").to_owned();
+    let d = c.get(&format!("/api/proposals/{e1}")).await;
+    assert_eq!(d["proposal"]["votedAtInertia"], 4);
+    assert_eq!(numbers(&d["levels"], "cast"), [0.0; 5]);
+    assert_eq!(numbers(&d["levels"], "required"), [50.0; 5], "nothing passes under C");
+    assert_eq!(d["participation"]["source"], "reference");
+    assert_eq!(d["electorateSource"], "wot");
+}
+
+#[tokio::test]
+async fn a_change_of_inertia_is_voted_at_the_level_of_its_article_and_journaled() {
+    let (mut a, state) = Client::new().await;
+    a.login("Yvv").await;
+    let mut b = a.other();
+    b.login("Chiara").await;
+    let doc = a.doc("essai").await;
+    let e2 = unit(&doc, "E2")["id"].as_str().expect("e2").to_owned();
+    let to = |t: Value| json!({ "target": t });
+    for bad in [json!(0), json!(6), json!("haute"), json!(null)] {
+        let (s, v) = a.call("POST", &format!("/api/units/{e2}/inertia"), Some(to(bad.clone()))).await;
+        assert_eq!((s, v["error"].as_str()), (StatusCode::BAD_REQUEST, Some("inertia")), "{bad}");
+    }
+    let (s, v) = a.call("POST", &format!("/api/units/{e2}/inertia"), Some(to(json!(4)))).await;
+    assert_eq!((s, v["error"].as_str()), (StatusCode::BAD_REQUEST, Some("same_inertia")));
+    let (s, v) = a.call("POST", &format!("/api/units/{e2}/inertia"), Some(to(json!(1)))).await;
+    assert_eq!(s, StatusCode::OK, "{v}");
+    let p = v["id"].as_str().expect("id").to_owned();
+    let d = a.get(&format!("/api/proposals/{p}")).await;
+    assert_eq!((d["proposal"]["inertiaTarget"].as_u64(), d["proposal"]["votedAtInertia"].as_u64()), (Some(1), Some(4)));
+    // W(essai) = 2: both vote for, the article goes to level 1.
+    a.vote(&p, "for").await;
+    let v = b.vote(&p, "for").await;
+    assert_eq!(v["entered"][0]["kind"], "inertia");
+    let doc = a.doc("essai").await;
+    let e2u = unit(&doc, "E2");
+    assert_eq!(e2u["inertia"], 1);
+    let changes = e2u["inertiaChanges"].as_array().expect("changes");
+    assert_eq!(changes.len(), 1);
+    assert_eq!(
+        (changes[0]["from"].as_u64(), changes[0]["to"].as_u64(), changes[0]["cause"].as_str()),
+        (Some(4), Some(1), Some("vote"))
+    );
+    // The adoption keeps the level it was judged at, and the scale.
+    let params: String = sqlx::query_scalar("SELECT params FROM adoptions WHERE proposal_id = ?")
+        .bind(&p)
+        .fetch_one(&state.db)
+        .await
+        .expect("adoption");
+    let params: Value = serde_json::from_str(&params).expect("json");
+    assert_eq!(
+        (params["level"].as_u64(), params["majority_pct"].as_f64(), params["share_pct"].as_f64()),
+        (Some(4), Some(60.0), Some(83.0))
+    );
+    assert_eq!(
+        (params["participation"].as_f64(), params["participation_source"].as_str()),
+        (Some(0.5), Some("reference"))
+    );
+    assert!(params["gradient"].as_f64().is_some_and(|g| (g - gradient(level(4), 0.5)).abs() < 1e-12));
+}
+
+#[tokio::test]
+async fn the_usual_participation_is_the_median_of_five_voted_proposals() {
+    let (mut first, state) = Client::new().await;
+    // Ten people, all members of the test group: W = 10, C = 1.
+    let mut people = Vec::new();
+    for name in ["P1", "P2", "P3", "P4", "P5", "P6", "P7", "P8", "P9", "P10"] {
+        let mut c = first.other();
+        c.login(name).await;
+        people.push(c);
+    }
+    first.login("P1").await;
+    let doc = first.doc("essai").await;
+    let open: Vec<String> = ["I2", "T1", "E4", "E5", "E6"]
+        .iter()
+        .map(|code| unit(&doc, code)["proposals"][0]["id"].as_str().expect("open").to_owned())
+        .collect();
+    // 1, 2, 3, 3 and 4 voters (against: nothing enters into force, the count is what matters).
+    for (p, n) in open.iter().zip([1, 2, 3, 3, 4]) {
+        for c in people.iter_mut().take(n) {
+            c.vote(p, "against").await;
+        }
+    }
+    // Measured once a day, not at each vote: until then, the reference.
+    let doc = first.doc("essai").await;
+    assert_eq!(doc["doc"]["participation"]["source"], "reference");
+    assert_eq!(doc["doc"]["electorate"], 10);
+
+    let measured = ld_server::participation::refresh(&state, false).await.expect("refresh");
+    assert!(measured.contains(&"essai".to_owned()));
+    let doc = first.doc("essai").await;
+    let p = &doc["doc"]["participation"];
+    assert_eq!(
+        (p["source"].as_str(), p["sample"].as_u64(), p["median"].as_f64()),
+        (Some("median"), Some(5), Some(3.0))
+    );
+    assert_eq!((p["ratio"].as_f64(), p["voters"].as_u64(), p["bounded"].as_bool()), (Some(0.3), Some(3), Some(false)));
+    assert!(p["measuredAt"].is_string());
+    for (l, k) in doc["levels"].as_array().expect("levels").iter().zip(InertiaLevel::ALL) {
+        assert!((l["gradient"].as_f64().expect("G") - gradient(k, 0.3)).abs() < 1e-12);
+    }
+    // Thresholds follow: the proposal with 4 voters is judged on this scale.
+    let d = first.get(&format!("/api/proposals/{}", open[4])).await;
+    let scale = Scale { electorate: 10, floor: 1.0, participation: 0.3 };
+    let ratio = d["proposal"]["evaluation"]["requiredRatio"].as_f64().expect("ratio");
+    assert!((ratio - required_ratio(10, 4, &scale.params(level(3)))).abs() < 1e-12);
+
+    // A new vote does not move it within the day…
+    people[4].vote(&open[0], "against").await;
+    assert!(ld_server::participation::refresh(&state, false).await.expect("refresh").is_empty());
+    assert_eq!(first.doc("essai").await["doc"]["participation"]["median"], 3.0);
+    // …the next measure sees it: 2, 2, 3, 3, 4.
+    ld_server::participation::refresh(&state, true).await.expect("refresh");
+    assert_eq!(first.doc("essai").await["doc"]["participation"]["median"], 3.0);
+
+    // A proposal last voted on more than a year ago leaves the sample: four are too few.
+    sqlx::query("UPDATE votes SET cast_at = '2025-01-01T00:00:00Z' WHERE proposal_id = ?")
+        .bind(&open[2])
+        .execute(&state.db)
+        .await
+        .expect("age");
+    ld_server::participation::refresh(&state, true).await.expect("refresh");
+    let p = first.doc("essai").await["doc"]["participation"].clone();
+    assert_eq!(
+        (p["source"].as_str(), p["sample"].as_u64(), p["median"].as_f64()),
+        (Some("reference"), Some(4), Some(2.5))
+    );
+    // The reference of the test group: 2C/W = 20 %.
+    assert_eq!(p["ratio"].as_f64(), Some(0.2));
+    // Monnaie libre is measured apart, from its own votes (none).
+    let ml = first.doc("monnaie-libre").await;
+    assert_eq!(
+        (ml["doc"]["participation"]["sample"].as_u64(), ml["doc"]["participation"]["source"].as_str()),
+        (Some(0), Some("reference"))
+    );
+}
+
+// ---------------------------------------------------------------------------
+// The base as production holds it on 2026-10-30, then the new version
+// ---------------------------------------------------------------------------
+
+/// Migrations up to 0004: the schema production runs before this version.
+async fn base_before_levels(tag: &str) -> (SqlitePool, AppState) {
+    use sqlx::sqlite::{SqliteConnectOptions, SqlitePoolOptions};
+    use std::str::FromStr;
+    let options = SqliteConnectOptions::from_str("sqlite::memory:").expect("url").foreign_keys(true);
+    let pool = SqlitePoolOptions::new().max_connections(1).connect_with(options).await.expect("db");
+    let mut before = sqlx::migrate!("./migrations");
+    before.migrations = Cow::Owned(before.migrations.iter().filter(|m| m.version <= 4).cloned().collect());
+    before.run(&pool).await.expect("migrations 1 to 4");
+    let mut cfg = Config::for_tests();
+    cfg.data_dir = std::env::temp_dir().join(format!("ld-levels-{tag}-{}", std::process::id()));
+    let state = AppState::new(cfg, pool.clone()).await.expect("state");
+    seed::documents(&state).await.expect("documents");
+    // The words of the time: every article `standard`.
+    sqlx::query("UPDATE units SET inertia = 'standard'").execute(&pool).await.expect("words");
+    (pool, state)
+}
+
+/// The new version starts: migration 0005, then the seed and its amendments.
+async fn start_new_version(pool: &SqlitePool) -> AppState {
+    let mut all = sqlx::migrate!("./migrations");
+    all.set_ignore_missing(true);
+    all.run(pool).await.expect("migrations");
+    restart(pool).await
+}
+
+async fn restart(pool: &SqlitePool) -> AppState {
+    let state = AppState::new(Config::for_tests(), pool.clone()).await.expect("state");
+    seed::ensure(&state).await.expect("seed");
+    state
+}
+
+async fn unit_id(pool: &SqlitePool, group: &str, code: &str) -> String {
+    sqlx::query_scalar(
+        "SELECT u.id FROM units u JOIN documents d ON d.id = u.doc_id WHERE d.group_slug = ? AND u.code = ?",
+    )
+    .bind(group)
+    .bind(code)
+    .fetch_one(pool)
+    .await
+    .expect("unit")
+}
+
+/// An open change of inertia written as production holds it (a word, no vote).
+async fn legacy_inertia_proposal(pool: &SqlitePool, unit: &str, word: &str) -> String {
+    let id = format!("legacy-{unit}-{word}");
+    sqlx::query(
+        "INSERT INTO proposals (id, unit_id, kind, inertia_target, title, body, status, origin, author_id, revision,
+           created_at, updated_at, submitted_at)
+         VALUES (?, ?, 'inertia', ?, ?, '', 'open', 'member', NULL, 1, '2026-10-29T21:54:00Z', '2026-10-29T21:54:00Z',
+           '2026-10-29T21:54:00Z')",
+    )
+    .bind(&id)
+    .bind(unit)
+    .bind(word)
+    .bind(format!("inertia:{word}"))
+    .execute(pool)
+    .await
+    .expect("proposal");
+    id
+}
+
+type Decision = (String, String, String, Option<String>);
+
+async fn inertia_decisions(pool: &SqlitePool) -> Vec<Decision> {
+    sqlx::query_as(
+        "SELECT d.group_slug, a.unit_code, a.outcome, a.reason FROM inertia_amendments a
+           JOIN documents d ON d.id = a.doc_id ORDER BY d.group_slug, a.unit_code",
+    )
+    .fetch_all(pool)
+    .await
+    .expect("decisions")
+}
+
+fn decided(rows: &[Decision]) -> Vec<(&str, &str, &str, Option<&str>)> {
+    rows.iter().map(|(g, u, o, r)| (g.as_str(), u.as_str(), o.as_str(), r.as_deref())).collect()
+}
+
+#[tokio::test]
+async fn a_new_base_starts_with_e1_and_e2_at_level_4() {
+    let (_, state) = Client::new().await;
+    assert_eq!(
+        decided(&inertia_decisions(&state.db).await),
+        [
+            ("essai", "E1", "present", None),
+            ("essai", "E2", "present", None),
+            ("monnaie-libre", "E1", "present", None),
+            ("monnaie-libre", "E2", "present", None),
+        ]
+    );
+    let changes: i64 =
+        sqlx::query_scalar("SELECT COUNT(*) FROM inertia_changes").fetch_one(&state.db).await.expect("n");
+    assert_eq!(changes, 0, "born at 4: nothing changed");
+}
+
+#[tokio::test]
+async fn the_migration_turns_the_four_words_into_levels_and_keeps_them() {
+    let (pool, _) = base_before_levels("migration").await;
+    let i1 = unit_id(&pool, "monnaie-libre", "I1").await;
+    let e3 = unit_id(&pool, "monnaie-libre", "E3").await;
+    for (unit, word) in [(&i1, "low"), (&e3, "high")] {
+        sqlx::query("UPDATE units SET inertia = ? WHERE id = ?")
+            .bind(word)
+            .bind(unit)
+            .execute(&pool)
+            .await
+            .expect("word");
+    }
+    let p = legacy_inertia_proposal(&pool, &e3, "max").await;
+    // An adoption of before: its params are the letters it was judged by.
+    let old_params = r#"{"majority_pct":50.0,"gradient":0.2,"base":0.1,"constant":50.0}"#;
+    sqlx::query(
+        "INSERT INTO adoptions (proposal_id, unit_id, doc_id, kind, votes_for, votes_against, electorate, required, params, at)
+         SELECT 'past', ?, doc_id, 'text', 60, 0, 7224, 58, ?, '2026-10-25T00:00:00Z' FROM units WHERE id = ?",
+    )
+    .bind(&e3)
+    .bind(old_params)
+    .bind(&e3)
+    .execute(&pool)
+    .await
+    .expect("adoption");
+
+    let mut all = sqlx::migrate!("./migrations");
+    all.set_ignore_missing(true);
+    all.run(&pool).await.expect("migration 0005");
+
+    let words: Vec<(String, String, Option<String>)> =
+        sqlx::query_as("SELECT code, inertia, inertia_legacy FROM units WHERE doc_id = (SELECT doc_id FROM units WHERE id = ?) AND code IN ('I1', 'E1', 'E3') ORDER BY code")
+            .bind(&i1)
+            .fetch_all(&pool)
+            .await
+            .expect("units");
+    assert_eq!(
+        words,
+        [
+            ("E1".into(), "3".into(), Some("standard".into())),
+            ("E3".into(), "4".into(), Some("high".into())),
+            ("I1".into(), "2".into(), Some("low".into())),
+        ]
+    );
+    let target: (Option<String>, Option<String>) =
+        sqlx::query_as("SELECT inertia_target, inertia_target_legacy FROM proposals WHERE id = ?")
+            .bind(&p)
+            .fetch_one(&pool)
+            .await
+            .expect("proposal");
+    assert_eq!(target, (Some("5".into()), Some("max".into())));
+    let kept: String = sqlx::query_scalar("SELECT params FROM adoptions WHERE proposal_id = 'past'")
+        .fetch_one(&pool)
+        .await
+        .expect("params");
+    assert_eq!(kept, old_params, "the history is never rewritten");
+}
+
+/// Production on 2026-10-30 (orch): every article `standard`, no vote, and two open
+/// changes of inertia at zero votes, I1 → max and E1 → max.
+#[tokio::test]
+async fn e1_and_e2_go_to_level_4_once_and_an_open_change_stays_open_voted_at_4() {
+    let (pool, _) = base_before_levels("production").await;
+    let mut proposals = Vec::new();
+    for group in ["monnaie-libre", "essai"] {
+        for code in ["I1", "E1"] {
+            let u = unit_id(&pool, group, code).await;
+            proposals.push((group, code, legacy_inertia_proposal(&pool, &u, "max").await));
+        }
+    }
+    let state = start_new_version(&pool).await;
+    let first = inertia_decisions(&pool).await;
+    assert_eq!(
+        decided(&first),
+        [
+            ("essai", "E1", "applied", None),
+            ("essai", "E2", "applied", None),
+            ("monnaie-libre", "E1", "applied", None),
+            ("monnaie-libre", "E2", "applied", None),
+        ]
+    );
+    let mut c = Client::of(&state);
+    c.login("Yvv").await;
+    for group in ["monnaie-libre", "essai"] {
+        let doc = c.doc(group).await;
+        let levels: Vec<(&str, u64)> = ["I1", "E1", "E2", "E3"]
+            .iter()
+            .map(|code| (*code, unit(&doc, code)["inertia"].as_u64().expect("level")))
+            .collect();
+        assert_eq!(levels, [("I1", 3), ("E1", 4), ("E2", 4), ("E3", 3)], "{group}");
+        // The article says so.
+        let changes = unit(&doc, "E1")["inertiaChanges"].as_array().expect("changes").clone();
+        assert_eq!(changes.len(), 1);
+        assert_eq!(
+            (changes[0]["from"].as_u64(), changes[0]["to"].as_u64(), changes[0]["cause"].as_str()),
+            (Some(3), Some(4), Some("amendment"))
+        );
+    }
+    // The open changes stay open, their target read as 5, voted at the article's level.
+    for (group, code, id) in &proposals {
+        let d = c.get(&format!("/api/proposals/{id}")).await;
+        assert_eq!(d["proposal"]["status"], "open", "{group} {code}");
+        assert_eq!(d["proposal"]["inertiaTarget"], 5, "{group} {code}");
+        let at = if *code == "E1" { 4 } else { 3 };
+        assert_eq!(d["proposal"]["votedAtInertia"], at, "{group} {code}");
+    }
+    // And votable: in Monnaie libre, judged at level 4.
+    let (_, _, e1_ml) = &proposals[1];
+    c.vote(e1_ml, "for").await;
+    let d = c.get(&format!("/api/proposals/{e1_ml}")).await;
+    let ratio = d["proposal"]["evaluation"]["requiredRatio"].as_f64().expect("ratio");
+    let p = d["participation"]["ratio"].as_f64().expect("p");
+    let scale = Scale { electorate: 5745, floor: 50.0, participation: p };
+    assert!((ratio - required_ratio(5745, 1, &scale.params(level(4)))).abs() < 1e-12);
+    assert!((ratio - required_ratio(5745, 1, &scale.params(level(3)))).abs() > 1e-6, "not at the old level");
+    assert_eq!(d["proposal"]["evaluation"]["required"], 50);
+    // Republished where the document publishes; never from the test group.
+    let queued: Vec<(String, String)> = sqlx::query_as(
+        "SELECT d.group_slug, o.reason FROM outbox o JOIN documents d ON d.id = o.doc_id
+          WHERE o.reason LIKE 'inertie%' ORDER BY o.id",
+    )
+    .fetch_all(&pool)
+    .await
+    .expect("outbox");
+    assert_eq!(
+        queued,
+        [
+            ("monnaie-libre".to_owned(), "inertie de départ relevée : E1, 3 → 4".to_owned()),
+            ("monnaie-libre".to_owned(), "inertie de départ relevée : E2, 3 → 4".to_owned()),
+        ]
+    );
+    // Once only: the next start changes nothing.
+    let again = restart(&pool).await;
+    assert_eq!(inertia_decisions(&again.db).await, first);
+    let changes: i64 = sqlx::query_scalar("SELECT COUNT(*) FROM inertia_changes").fetch_one(&pool).await.expect("n");
+    assert_eq!(changes, 4);
+}
+
+#[tokio::test]
+async fn an_inertia_changed_by_a_vote_keeps_its_level() {
+    let (pool, _) = base_before_levels("voted").await;
+    // The migration runs; a vote changes E2's inertia in the test group, before the
+    // version that knows the amendment starts.
+    let mut all = sqlx::migrate!("./migrations");
+    all.set_ignore_missing(true);
+    all.run(&pool).await.expect("migrations");
+    let between = AppState::new(Config::for_tests(), pool.clone()).await.expect("state");
+    let mut a = Client::of(&between);
+    a.login("Yvv").await;
+    let mut b = a.other();
+    b.login("Chiara").await;
+    let e2 = unit_id(&pool, "essai", "E2").await;
+    let (s, v) = a.call("POST", &format!("/api/units/{e2}/inertia"), Some(json!({ "target": 5 }))).await;
+    assert_eq!(s, StatusCode::OK, "{v}");
+    let p = v["id"].as_str().expect("id").to_owned();
+    a.vote(&p, "for").await;
+    assert_eq!(b.vote(&p, "for").await["entered"][0]["kind"], "inertia");
+
+    let state = restart(&pool).await;
+    assert_eq!(
+        decided(&inertia_decisions(&state.db).await),
+        [
+            ("essai", "E1", "applied", None),
+            ("essai", "E2", "refused", Some("changed_by_vote")),
+            ("monnaie-libre", "E1", "applied", None),
+            ("monnaie-libre", "E2", "applied", None),
+        ]
+    );
+    let mut c = Client::of(&state);
+    c.login("Yvv").await;
+    let doc = c.doc("essai").await;
+    assert_eq!(unit(&doc, "E2")["inertia"], 5, "the vote holds");
+}
diff --git a/seeds/acte-engagement-certification.json b/seeds/acte-engagement-certification.json
index 59b1a1d..ac0f7b2 100644
--- a/seeds/acte-engagement-certification.json
+++ b/seeds/acte-engagement-certification.json
@@ -29,7 +29,7 @@
       "code": "I1",
       "section": "introduction",
       "position": 1,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -51,7 +51,7 @@
       "code": "I2",
       "section": "introduction",
       "position": 2,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -73,7 +73,7 @@
       "code": "T1",
       "section": "fondamental",
       "position": 3,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -95,7 +95,7 @@
       "code": "E1",
       "section": "fondamental",
       "position": 4,
-      "inertia": "standard",
+      "inertia": 4,
       "versions": [
         {
           "label": "1.0.0",
@@ -117,7 +117,7 @@
       "code": "E2",
       "section": "fondamental",
       "position": 5,
-      "inertia": "standard",
+      "inertia": 4,
       "versions": [
         {
           "label": "1.0.0",
@@ -139,7 +139,7 @@
       "code": "T2",
       "section": "technique",
       "position": 6,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -161,7 +161,7 @@
       "code": "E3",
       "section": "technique",
       "position": 7,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -197,7 +197,7 @@
       "code": "E4",
       "section": "technique",
       "position": 8,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -219,7 +219,7 @@
       "code": "E5",
       "section": "technique",
       "position": 9,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -241,7 +241,7 @@
       "code": "E6",
       "section": "technique",
       "position": 10,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -263,7 +263,7 @@
       "code": "E7",
       "section": "technique",
       "position": 11,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -299,7 +299,7 @@
       "code": "T3",
       "section": "technique",
       "position": 12,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -321,7 +321,7 @@
       "code": "E8",
       "section": "technique",
       "position": 13,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -343,7 +343,7 @@
       "code": "E9",
       "section": "technique",
       "position": 14,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -365,7 +365,7 @@
       "code": "E10",
       "section": "technique",
       "position": 15,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -387,7 +387,7 @@
       "code": "E11",
       "section": "technique",
       "position": 16,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -409,7 +409,7 @@
       "code": "K1",
       "section": "conclusion",
       "position": 17,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -431,7 +431,7 @@
       "code": "K2",
       "section": "conclusion",
       "position": 18,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -453,7 +453,7 @@
       "code": "X1",
       "section": "annexe",
       "position": 19,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -475,7 +475,7 @@
       "code": "X1.1",
       "section": "annexe",
       "position": 20,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -497,7 +497,7 @@
       "code": "X1.2",
       "section": "annexe",
       "position": 21,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -519,7 +519,7 @@
       "code": "X1.3",
       "section": "annexe",
       "position": 22,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -541,7 +541,7 @@
       "code": "X2",
       "section": "annexe",
       "position": 23,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -563,7 +563,7 @@
       "code": "X2.1",
       "section": "annexe",
       "position": 24,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -585,7 +585,7 @@
       "code": "X2.2",
       "section": "annexe",
       "position": 25,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -607,7 +607,7 @@
       "code": "X2.3",
       "section": "annexe",
       "position": 26,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -629,7 +629,7 @@
       "code": "F1",
       "section": "formule",
       "position": 27,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -651,7 +651,7 @@
       "code": "F1.1",
       "section": "formule",
       "position": 28,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -673,7 +673,7 @@
       "code": "F1.2",
       "section": "formule",
       "position": 29,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -695,7 +695,7 @@
       "code": "F1.3",
       "section": "formule",
       "position": 30,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -717,7 +717,7 @@
       "code": "N1",
       "section": "inertie",
       "position": 31,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -739,7 +739,7 @@
       "code": "N1.1",
       "section": "inertie",
       "position": 32,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",
@@ -761,7 +761,7 @@
       "code": "O1",
       "section": "ordonnancement",
       "position": 33,
-      "inertia": "standard",
+      "inertia": 3,
       "versions": [
         {
           "label": "1.0.0",