diff --git a/.claude/board/AGENT_LOG.md b/.claude/board/AGENT_LOG.md
index 0dc2e369..b52bf511 100644
--- a/.claude/board/AGENT_LOG.md
+++ b/.claude/board/AGENT_LOG.md
@@ -1,3 +1,6 @@
+## 2026-06-21 (cont.³⁵) — run-NaN actor-side half PROVEN green — run_to_absorbing drives a full Rubicon cycle, lance-free
+
+**Main thread (Opus), self-directed ("what do you choose next").** Chose the highest-value LIGHT move over forcing a disk-heavy lance build: answered the buildable half of the capstone's **run-NaN HYPOTHESIS**. New `lance-graph-supervisor::kanban_actor::run_to_absorbing(actor, max_ticks)` — repeatedly `drive_version_tick` until the owner reports an absorbing column (`Commit`/`Prune`), returning the forward-arc `KanbanMove` trace; `max_ticks` is a defensive non-termination guard (pure forward arc always reaches `Commit`). This is the actor-side, lance-free, symbiont-free analog of `symbiont::kanban_loop::run_to_absorbing`. **+1 test (14 total green):** `run_to_absorbing_drives_a_full_rubicon_cycle_no_nan_no_panic` — a mailbox runs `Planning → CognitiveWork → Evaluation → Commit`, terminates, every move is a legal Rubicon edge, no panic, no spurious `Illegal`, idempotent at rest (second run empty, phase unchanged). The phase/i4 path is integer-only ⇒ **NaN is structurally impossible on this half**, so green IS the actor-side run-NaN answer. clippy + fmt clean; light build, no lance/disk/symbiont gate. **Remaining run-NaN (symbiont/disk-gated):** the cognitive half — instrument `symbiont::kanban_loop::run_to_absorbing` over the energy column for a live-cycle NaN% (other session owns symbiont; coordinate). Plan run-NaN status annotated "actor-side half PROVEN". Rides a PR on jirak. Capstone actor-side substrate now complete: S4 (#576/#577) + S2 (#578) + S3 (#579) + run-to-absorbing (this).
 ## 2026-06-21 (cont.³⁴) — S3 IN-leg driver SHIPPED (actor-side) — version tick → owner forward-arc advance, no-op suppressed
 
 **Main thread (Opus), self-directed ("PR, easy").** Closed the actor-side half of S3 on the same light crate, mirroring the S2 atomic pattern. New in `lance-graph-supervisor::kanban_actor` (feature `supervisor`): (1) `KanbanMsg::Tick { at, reply }` — the **atomic** in-actor realization of the contract's `NextPhaseScheduler`: a substrate version tick advances the owner along the Rubicon forward arc (`phase().next_phases().first()`) in ONE serialized message, reading the phase at the instant of mutation (the codex-#578 atomicity lesson applied to the IN-leg); absorbing column → `None`, **the no-op tick is suppressed** (not an error; forward arc is legal by construction so the infallible `advance_phase` is used). (2) `drive_version_tick(actor, at)` — thin async wrapper. (3) `drive_scheduled_tick(scheduler, view, at, exec, actor)` — generic consumer that drives the EXISTING `VersionScheduler` trait ("propose, don't dispose": scheduler proposes from a view, owner disposes via `Advance`, `None` suppresses), for custom policies (version-delta gating, `Plan`/`Prune`, batching) reading a richer view; documented as advisory (proposal computed outside the owner message → may relay a typed `Illegal` rather than corrupt). **+3 tests (now green):** `version_tick_advances_forward_arc_then_suppresses_at_absorbing` (Planning→CognitiveWork→Evaluation→Commit then suppressed), `concurrent_version_ticks_serialize_along_the_arc` (two ticks chain, no stale-phase collision), `custom_scheduler_proposes_and_owner_disposes` (drives `NextPhaseScheduler` propose→dispose + suppresses an absorbing proposal). `cargo test -p lance-graph-supervisor --features supervisor --lib` = 12 passed/0 failed; clippy clean (no supervisor-crate warnings; pre-existing ontology/callcenter warnings only) + fmt clean; light build, no lance/disk/symbiont gate. **Remaining S3 (lance/disk-gated):** wire the LIVE `LanceVersionScheduler::drive_at_latest` over a real `VersionedGraph::versions()` to feed `at` — the apply + no-op-suppress loop is now done, only the live `versions()` poll remains. OUT-leg actor side now: S4 owner-advance (#576) + delivery edge (#577) + S2 driver (#578) + **S3 driver (this)**. Plan S3 status annotated. Rides a PR on jirak.
diff --git a/.claude/plans/capstone-out-leg-wiring-v1.md b/.claude/plans/capstone-out-leg-wiring-v1.md
index 1560459a..dcc3968c 100644
--- a/.claude/plans/capstone-out-leg-wiring-v1.md
+++ b/.claude/plans/capstone-out-leg-wiring-v1.md
@@ -199,7 +199,25 @@ ractor `cast` — **same ownership, same `try_advance_phase`**. No no-owner test
 
 ## run-NaN — the measurement (Wave-0's third metric)
 
-**Census state:** HYPOTHESIS. `symbiont::kanban_loop::run_to_absorbing
+**Status (2026-06-21): actor-side half PROVEN green** (lance-free, symbiont-free).
+`lance-graph-supervisor::kanban_actor::run_to_absorbing(actor, max_ticks)` drives a
+mailbox to its absorbing column through the REAL actor messages (the `Tick` arc)
+and returns the forward-arc `KanbanMove` trace. Test
+`run_to_absorbing_drives_a_full_rubicon_cycle_no_nan_no_panic`: a mailbox runs
+`Planning → CognitiveWork → Evaluation → Commit`, terminates within the bound,
+every move is a legal Rubicon edge, no panic, no spurious `Illegal`, and the run
+is idempotent at rest (a second run is an empty trace, phase unchanged). The
+phase/i4 path is integer-only → **NaN is structurally impossible on this half**,
+so the green run IS the actor-side run-NaN answer. 14 tests green; clippy + fmt
+clean; light build.
+
+**Remaining (symbiont/disk-gated):** the *cognitive* half — instrument
+`symbiont::kanban_loop::run_to_absorbing(&NextPhaseScheduler)` over the energy
+column + observable outputs (not just the phase trail) for a live-cycle NaN%.
+That harness drives the full domino sweep over a real SoA and is owned by the
+cognitive-compilation session — coordinate first.
+
+**Census state (orig):** HYPOTHESIS. `symbiont::kanban_loop::run_to_absorbing
 (&NextPhaseScheduler)` is the runnable harness.
 
 **Work:** instrument one `run_to_absorbing` cycle; count valid vs
diff --git a/crates/lance-graph-supervisor/src/kanban_actor.rs b/crates/lance-graph-supervisor/src/kanban_actor.rs
index de315eed..b715822b 100644
--- a/crates/lance-graph-supervisor/src/kanban_actor.rs
+++ b/crates/lance-graph-supervisor/src/kanban_actor.rs
@@ -347,6 +347,40 @@ where
     }
 }
 
+// ─── Capstone run-to-absorbing: drive a mailbox to its terminal column ─────────
+
+/// Drive a mailbox to its **absorbing column** by repeatedly ticking
+/// ([`drive_version_tick`]) until the owner reports no further move
+/// (`Commit`/`Prune`). Returns the full forward-arc [`KanbanMove`] trace.
+///
+/// This is the actor-side, lance-free analog of the cognitive loop's
+/// run-to-absorbing: it proves the OUT/IN-leg substrate carries a mailbox through
+/// a complete Rubicon cycle to a terminal state with no panic and no spurious
+/// rejection (the integer-only phase/i4 path cannot produce NaN). The live S3
+/// source feeds real `versions()` ticks through the same `drive_version_tick`;
+/// here the loop counter stands in for the version stream.
+///
+/// `max_ticks` bounds the loop defensively. The pure forward arc always reaches
+/// `Commit` (`Planning → CognitiveWork → Evaluation → Commit`), so the bound is a
+/// guard against a future non-terminating policy, not a normal exit: exceeding it
+/// returns [`KanbanRouteError::Rpc`] with a non-termination note rather than
+/// looping forever.
+pub async fn run_to_absorbing(
+    actor: &ActorRef<KanbanMsg>,
+    max_ticks: usize,
+) -> Result<Vec<KanbanMove>, KanbanRouteError> {
+    let mut trace = Vec::new();
+    for tick in 0..max_ticks {
+        match drive_version_tick(actor, DatasetVersion(tick as u64 + 1)).await? {
+            Some(mv) => trace.push(mv),
+            None => return Ok(trace), // absorbing column reached — the cycle ended
+        }
+    }
+    Err(KanbanRouteError::Rpc(format!(
+        "run_to_absorbing did not reach an absorbing column within {max_ticks} ticks"
+    )))
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
@@ -737,4 +771,57 @@ mod tests {
             handle.await.expect("actor join");
         }
     }
+
+    #[tokio::test]
+    async fn run_to_absorbing_drives_a_full_rubicon_cycle_no_nan_no_panic() {
+        // Capstone run-NaN (actor-side, lance-free): a mailbox driven from
+        // Planning runs to the absorbing Commit column through the REAL actor
+        // messages — it terminates, never panics, never emits a spurious Illegal,
+        // and the trace is the deterministic forward arc. The integer phase/i4
+        // path cannot produce NaN, so a green run here IS the actor-side half of
+        // the loop's run-NaN answer.
+        let (actor, handle) = Actor::spawn(
+            None,
+            KanbanActor::<TestBoard>::default(),
+            board(KanbanColumn::Planning),
+        )
+        .await
+        .expect("spawn");
+
+        let trace = run_to_absorbing(&actor, 16)
+            .await
+            .expect("reaches an absorbing column within the bound");
+
+        // Forward arc: Planning → CognitiveWork → Evaluation → Commit (3 moves).
+        let arc: Vec<_> = trace.iter().map(|m| m.to).collect();
+        assert_eq!(
+            arc,
+            vec![
+                KanbanColumn::CognitiveWork,
+                KanbanColumn::Evaluation,
+                KanbanColumn::Commit,
+            ]
+        );
+        // Every move en route is a legal Rubicon edge (no corruption).
+        for m in &trace {
+            assert!(
+                m.from.can_transition_to(m.to),
+                "{:?} -> {:?} must be legal",
+                m.from,
+                m.to
+            );
+        }
+
+        // The owner rests in the absorbing column: a further run is empty, and
+        // the phase is unchanged (idempotent at rest — no spurious advance/error).
+        let again = run_to_absorbing(&actor, 4)
+            .await
+            .expect("idempotent at the absorbing column");
+        assert!(again.is_empty(), "absorbing column yields no further moves");
+        let phase = ractor::call!(actor, |reply| KanbanMsg::Phase { reply }).expect("rpc");
+        assert_eq!(phase, KanbanColumn::Commit);
+
+        actor.stop(None);
+        handle.await.expect("actor join");
+    }
 }