diff --git a/crates/aura-registry/src/lib.rs b/crates/aura-registry/src/lib.rs
index fc9ac9e..50bf38a 100644
--- a/crates/aura-registry/src/lib.rs
+++ b/crates/aura-registry/src/lib.rs
@@ -7,8 +7,9 @@
 //!
 //! Orchestration **families** (sweep / Monte-Carlo / walk-forward, C12/C21) are
 //! stored as related records in a sibling family store (`families.jsonl`): each
-//! member is a `RunReport` stamped with a shared `family_id`, re-derived as a unit
-//! by [`group_families`]. The flat runs store and its API are untouched.
+//! member is a `RunReport` stamped with its `family` name + `run` index (the
+//! `family_id` handle is derived from the pair), re-derived as a unit by
+//! [`group_families`]. The flat runs store and its API are untouched.
 
 use std::cmp::Ordering;
 use std::fmt;
@@ -317,6 +318,10 @@ mod tests {
         let fam = &families[0];
         assert_eq!(fam.id, "f-0");
         assert_eq!(fam.kind, FamilyKind::MonteCarlo);
+        // the split (family, run) fields are stamped on each member, and the
+        // user-facing handle is derived from them (id is "{family}-{run}").
+        assert_eq!((fam.members[0].family.as_str(), fam.members[0].run), ("f", 0));
+        assert_eq!(fam.members[0].family_id(), "f-0");
         // members re-derived as a unit, ordinal-ordered, equal to the stamped reports
         let member_reports: Vec<_> = fam.members.iter().map(|m| m.report.clone()).collect();
         assert_eq!(member_reports, reports);
diff --git a/crates/aura-registry/src/lineage.rs b/crates/aura-registry/src/lineage.rs
index 491727b..4ada357 100644
--- a/crates/aura-registry/src/lineage.rs
+++ b/crates/aura-registry/src/lineage.rs
@@ -1,13 +1,15 @@
 //! Registry lineage for orchestration families (C18/C21): a family — a sweep,
 //! Monte-Carlo, or walk-forward run — is a set of run records sharing one
-//! `family_id` (the parent reference). This module adds the persisted lineage
+//! parent identity — the `(family, run)` pair, from which the user-facing
+//! `family_id` handle (`"{family}-{run}"`) is derived. This module adds the
+//! persisted lineage
 //! unit ([`FamilyRunRecord`]), the family-store accessors on [`Registry`]
 //! ([`Registry::append_family`] / [`Registry::load_family_members`]), and the
 //! round-trip that re-derives a [`Family`] from the stored links
 //! ([`group_families`]). The family store is a sibling JSONL of the flat runs
 //! store (`families.jsonl`), so the flat `runs.jsonl` path and API are untouched.
 
-use std::collections::{HashMap, HashSet};
+use std::collections::HashMap;
 use std::fs;
 use std::io::Write;
 
@@ -25,18 +27,30 @@ pub enum FamilyKind {
 }
 
 /// One persisted family member: a run record stamped with its lineage link.
-/// `family_id` is the shared parent reference; `ordinal` is the member's position
-/// in the family's canonical order (odometer / seed-input / roll).
+/// The parent reference is split into its two factors — `family` (the parent
+/// name) and `run` (the per-name run index) — from which the user-facing
+/// `family_id` handle (`"{family}-{run}"`) is derived rather than stored.
+/// `ordinal` is the member's position in the family's canonical order
+/// (odometer / seed-input / roll).
 #[derive(Clone, Debug, PartialEq, Serialize, Deserialize)]
 pub struct FamilyRunRecord {
-    pub family_id: String,
+    pub family: String,
+    pub run: usize,
     pub kind: FamilyKind,
     pub ordinal: usize,
     pub report: RunReport,
 }
 
-/// A re-derived family: the members sharing one `family_id`, ordinal-sorted — the
-/// round-trip result of [`group_families`].
+impl FamilyRunRecord {
+    /// The user-facing family handle — `"{family}-{run}"`, derived, never stored or parsed.
+    pub fn family_id(&self) -> String {
+        format!("{}-{}", self.family, self.run)
+    }
+}
+
+/// A re-derived family: the members sharing one `(family, run)` key (and thus one
+/// derived `family_id`), ordinal-sorted — the round-trip result of
+/// [`group_families`].
 #[derive(Clone, Debug, PartialEq)]
 pub struct Family {
     pub id: String,
@@ -45,22 +59,20 @@ pub struct Family {
 }
 
 impl Registry {
-    /// Assign a fresh `family_id = "{name}-{counter}"` (counter = the smallest `k`
-    /// for which `"{name}-{k}"` is absent in the family store — a per-name run
-    /// index), stamp `reports` as ordinal-ordered members, and append them as N
-    /// JSONL lines to the family store (a sibling of the flat runs store,
-    /// `families.jsonl`, leaving the flat path untouched). Returns the assigned id.
-    /// Reads the store once to pick the counter (a read-before-write; single-process
-    /// CLI invocations do not race).
+    /// Assign a fresh per-name `run` index (one past the highest `run` already
+    /// stored for `name`, or `0` if unseen), stamp `reports` as ordinal-ordered
+    /// members carrying `name` + that `run`, and append them as N JSONL lines to
+    /// the family store (a sibling of the flat runs store, `families.jsonl`,
+    /// leaving the flat path untouched). Returns the derived id `"{name}-{run}"`.
+    /// Reads the store once to pick the run index (a read-before-write;
+    /// single-process CLI invocations do not race).
     pub fn append_family(
         &self,
         name: &str,
         kind: FamilyKind,
         reports: &[RunReport],
     ) -> Result<String, RegistryError> {
-        let existing: HashSet<String> =
-            self.load_family_members()?.into_iter().map(|r| r.family_id).collect();
-        let family_id = next_family_id(name, &existing);
+        let run = next_run(name, &self.load_family_members()?);
 
         let path = self.path.with_file_name("families.jsonl");
         if let Some(parent) = path.parent().filter(|p| !p.as_os_str().is_empty()) {
@@ -69,16 +81,16 @@ impl Registry {
         let mut file = fs::OpenOptions::new().create(true).append(true).open(&path)?;
         for (ordinal, report) in reports.iter().enumerate() {
             let record = FamilyRunRecord {
-                family_id: family_id.clone(),
+                family: name.to_string(),
+                run,
                 kind,
                 ordinal,
                 report: report.clone(),
             };
-            // a finite RunReport wrapped in a FamilyRunRecord serializes infallibly.
             let line = serde_json::to_string(&record).expect("a finite FamilyRunRecord serializes");
             writeln!(file, "{line}")?;
         }
-        Ok(family_id)
+        Ok(format!("{name}-{run}"))
     }
 
     /// Parse every stored family member, in file order. A missing file is an empty
@@ -104,32 +116,36 @@ impl Registry {
     }
 }
 
-/// The next free `"{name}-{counter}"` id: the smallest `k >= 0` for which
-/// `"{name}-{k}"` is not in `existing`. Robust to `-` inside `name` — it tests
-/// membership of generated candidates, never parses the stored strings. Module-
-/// private: the id form is an `append_family` implementation detail.
-fn next_family_id(name: &str, existing: &HashSet<String>) -> String {
-    (0usize..)
-        .map(|k| format!("{name}-{k}"))
-        .find(|id| !existing.contains(id))
-        .expect("the usize counter space is effectively unbounded")
+/// The next per-name run index: one past the highest `run` already stored for
+/// `name`, or `0` if the name is unseen. A clean numeric max over the `run`
+/// field — no string parsing (the old fused-id form had to generate-and-check to
+/// stay robust to `-` inside a name; the split removes that concern).
+fn next_run(name: &str, records: &[FamilyRunRecord]) -> usize {
+    records
+        .iter()
+        .filter(|r| r.family == name)
+        .map(|r| r.run + 1)
+        .max()
+        .unwrap_or(0)
 }
 
-/// Group member records into families by `family_id` (first-seen family order;
-/// each family's members ordinal-sorted). The round-trip: `append_family(...)`
-/// then `group_families(load_family_members())` recovers the families.
+/// Group member records into families by their `(family, run)` key (first-seen
+/// family order; each family's members ordinal-sorted), deriving the family's
+/// `id` once at construction. The round-trip: `append_family(...)` then
+/// `group_families(load_family_members())` recovers the families.
 pub fn group_families(records: Vec<FamilyRunRecord>) -> Vec<Family> {
-    let mut order: Vec<String> = Vec::new();
-    let mut by_id: HashMap<String, Family> = HashMap::new();
+    let mut order: Vec<(String, usize)> = Vec::new();
+    let mut by_key: HashMap<(String, usize), Family> = HashMap::new();
     for rec in records {
-        let fam = by_id.entry(rec.family_id.clone()).or_insert_with(|| {
-            order.push(rec.family_id.clone());
-            Family { id: rec.family_id.clone(), kind: rec.kind, members: Vec::new() }
+        let key = (rec.family.clone(), rec.run);
+        let fam = by_key.entry(key.clone()).or_insert_with(|| {
+            order.push(key.clone());
+            Family { id: rec.family_id(), kind: rec.kind, members: Vec::new() }
         });
         fam.members.push(rec);
     }
     let mut families: Vec<Family> =
-        order.into_iter().map(|id| by_id.remove(&id).expect("id was inserted")).collect();
+        order.into_iter().map(|k| by_key.remove(&k).expect("key was inserted")).collect();
     for fam in &mut families {
         fam.members.sort_by_key(|m| m.ordinal);
     }
diff --git a/docs/design/INDEX.md b/docs/design/INDEX.md
index 8cb712f..a2b23c7 100644
--- a/docs/design/INDEX.md
+++ b/docs/design/INDEX.md
@@ -664,12 +664,12 @@ the reverse.
 **Realization (cycle 0045 — lineage as related records, #70).** The *lineage*
 depth is now realized as a **family store**: a sweep / Monte-Carlo / walk-forward
 run (the C12 axes) is persisted as a *set of related records* — each a
-`FamilyRunRecord` (a `RunReport` stamped with a shared `family_id` + `kind` +
+`FamilyRunRecord` (a `RunReport` stamped with its `family` + `run` + `kind` +
 `ordinal`) — in a sibling JSONL (`families.jsonl`), leaving the flat `runs.jsonl`
 path and its `append`/`load`/`rank_by`/`optimize` API byte-for-byte unchanged.
-`family_id = "{name}-{counter}"` (an author-supplied name plus a per-name
-generate-and-check run index — not a content hash; re-running the same family
-mints a fresh id). `group_families` is the round-trip that re-derives a family
+the user-facing `family_id = "{family}-{run}"` handle is **derived** from the
+stored `family` name plus a per-name `run` index (assigned as a numeric max+1 —
+not a content hash; re-running the same family mints a fresh id). `group_families` is the round-trip that re-derives a family
 from the stored links (re-listable / rankable as a unit — C21). The manifest *is*
 the re-derivation recipe (#71): no input-stream blob / path / payload enters a
 record, and a member's window is **producer-supplied** via