diff --git a/docs/audit/substrate-liveness-registry.md b/docs/audit/substrate-liveness-registry.md
new file mode 100644
index 00000000..d19253b6
--- /dev/null
+++ b/docs/audit/substrate-liveness-registry.md
@@ -0,0 +1,191 @@
+# Substrate Liveness Registry
+
+**Scope:** [substrate-liveness-audit-scope](../decisions/substrate-liveness-audit-scope.md) (v2)
+**Status:** Active audit — append-only as layers are completed.
+**Discipline:** [feedback-adr-cross-reference-discipline](../../../.claude/projects/-Users-kaizenpro-Projects-core/memory/feedback-adr-cross-reference-discipline.md), [feedback-cleanup-as-you-find](../../../.claude/projects/-Users-kaizenpro-Projects-core/memory/feedback-cleanup-as-you-find.md)
+
+## Audit progress
+
+| Layer | Status | Verdict | Cleanup performed | Last audited |
+|---|---|---|---|---|
+| L0 — Algebra primitives | ✅ Audited | **CLOSED** | None — no dead code found | 2026-05-24 |
+| L1 — Field substrate | ⏳ Pending | — | — | — |
+| L2 — Vault | ⏳ Pending | — | — | — |
+| L3 — Language packs | ⏳ Pending | — | — | — |
+| L4 — Recognition | ⏳ Pending | — | — | — |
+| L5 — Cognition pipeline | ⏳ Pending | — | — | — |
+| L6 — Chat runtime + surface composition | ⏳ Pending | — | — | — |
+| L7 — Teaching loop | ⏳ Pending | — | — | — |
+| L8 — Inter-session memory + contemplation | ⏳ Pending | — | — | — |
+| L9 — Epistemic state + verdicts | ⏳ Pending | — | — | — |
+
+L10 / L11 are not audit targets (no design to audit; flagged in scope as
+gaps the audit will surface need for).
+
+---
+
+## L0 — Algebra primitives
+
+**Audit date:** 2026-05-24
+**Auditor:** primary agent (Claude)
+**Verdict:** **CLOSED**
+
+### Scope-hypothesis correction (per audit step 0)
+
+The scope's layering table cited `algebra/backend/` (directory). Reality:
+`algebra/backend.py` (single 267-line file). Hypothesis drift, not a
+finding — recorded so the scope's layering map can be amended if it
+matters elsewhere.
+
+### ADRs in scope for L0
+
+Triaged from the broader algebra/versor/CGA keyword grep against
+`docs/decisions/`:
+
+| ADR | Title | Status | Belongs at L0? |
+|---|---|---|---|
+| ADR-0001 | VocabManifold Versor Invariant | Accepted | Yes — defines the `versor_condition < 1e-6` invariant L0 must preserve |
+| ADR-0003 | Coordinate System Dissolution | Accepted | Yes — algebraic foundation |
+| ADR-0004 | Rotor as Operator, Not Vocabulary Property | Accepted | Yes — defines rotors as L0 primitives |
+| ADR-0009 | Compositional Physics | Accepted | Yes — versor composition rules |
+
+Other ADRs surfaced by the grep but assigned to higher layers (not
+audited at L0): ADR-0006 (L1), ADR-0019 (L2), ADR-0010 (L3 identity),
+ADR-0021/0022/0023/0024/0025 (L5 policy), ADR-0020 (cross-cutting Rust
+parity, audit when relevant).
+
+### Modules in scope for L0
+
+| Module | Lines | Live-import sites (outside `algebra/`, outside `tests/`) | Test-import sites |
+|---|---|---|---|
+| `algebra/__init__.py` | 5 | (re-export shim) | — |
+| `algebra/backend.py` | 267 | 21 | 16 |
+| `algebra/cga.py` | 84 | 16 | 17 |
+| `algebra/cl41.py` | 165 | 8 | 10 |
+| `algebra/holonomy.py` | 100 | 2 | 5 |
+| `algebra/rotor.py` | 179 | 5 | 8 |
+| `algebra/versor.py` | 180 | 20 | 19 |
+
+Every module has at least 2 live-import sites outside `algebra/`. No
+dormant modules at L0.
+
+### Caller-trace evidence
+
+Sample of live callers (full grep: `grep -rn "from algebra\|import algebra" --include="*.py" | grep -v "^algebra/" | grep -v "tests/"` — 38 distinct caller files):
+
+- `field/propagate.py:23` — versor application during field propagation (L1 → L0)
+- `ingest/gate.py:33` — versor/energy at injection boundary (L1 → L0)
+- `language_packs/compiler.py:14` — versor construction during pack compilation (L3 → L0)
+- `chat/runtime.py` — versor operations in the live turn loop (L6 → L0)
+- `generate/intent_ratifier.py`, `generate/admissibility.py`, `generate/proposition.py` — versor-gated generation (L5 → L0)
+- `core/cli.py:446-469` — versor diagnostics surfaced to operator (CLI → L0)
+
+Every live caller traces back to the runtime entry through at least one
+of: `core chat`, `core eval cognition`, or the field/ingest pipeline.
+
+### Exercising suite lane
+
+`core test --suite algebra` — 13 test files, every L0 module covered:
+
+| Module | Tests in algebra suite |
+|---|---|
+| `versor.py` | test_versor_closure, test_holonomy, test_energy, test_motor, test_versor_condition_rust_parity, test_versor_apply_rust_parity |
+| `rotor.py` | test_versor_closure, test_energy |
+| `holonomy.py` | test_holonomy, test_holonomy_resonance |
+| `cga.py` | test_holonomy_resonance, test_null_cone, test_vault_recall |
+| `cl41.py` | test_vault_recall_vectorised |
+| `backend.py` | test_vault_recall_vectorised, test_vault_recall_rust_parity, test_cga_inner_rust_parity, test_geometric_product_rust_parity, test_versor_condition_rust_parity, test_versor_apply_rust_parity |
+
+**Verification:** `python3 -m core.cli test --suite algebra -q` →
+**82 passed, 50 skipped** (skipped are Rust-parity tests on a Python-
+only environment; not a closure gap).
+
+### Cross-layer contract check
+
+**Pass 1 — mechanical (consumer-exists per exposed symbol):**
+
+| Exposed symbol | Consumer evidence |
+|---|---|
+| `versor_apply` | `field/propagate.py`, `generate/stream.py`, `chat/runtime.py` (3+ live consumers) |
+| `versor_condition` | `core/cognition/trace.py:34`, `evals/cognition/runner.py:60` (gated in evals at `< 1e-6`) |
+| `normalize_to_versor` | `generate/intent_ratifier.py`, `generate/admissibility.py` |
+| `cga_inner` | `vault/store.py`, `algebra/backend.py` (`_CGA_INNER_METRIC`), `evals/lab/vault_epistemic_trace.py` |
+| `embed_point`, `is_null`, `null_project` | `vault/store.py`, `language_packs/compiler.py`, `field/operators.py` |
+| `using_rust`, `vault_recall` (backend) | `vault/store.py`, all Rust-parity tests |
+| `word_transition_rotor`, `make_rotor_from_angle` | `field/operators.py`, `generate/intent_ratifier.py` |
+| `holonomy_encode`, `holonomy_similarity` | `vault/store.py`, `evals/lab/` |
+| `N_COMPONENTS` (cl41) | `algebra/backend.py`, `algebra/cga.py` |
+
+No exposed L0 symbol with zero downstream consumers.
+
+**Pass 2 — semantic (judgment-required):**
+
+ADR-0001's `versor_condition < 1e-6` invariant is the primary semantic
+contract. Verified:
+
+- **Measured per turn:** L0's `versor_condition()` is computed and
+  folded into the deterministic trace payload (`core/cognition/trace.py:34,70`)
+  on every turn.
+- **Surfaced to operator:** displayed by `core chat` and `core` info
+  commands (`core/cli.py:398,461,469`).
+- **Gated at eval boundary:** evals refuse to count a turn as
+  `versor_ok` if `versor_condition >= 1e-6` (`evals/cognition/runner.py:60`,
+  `evals/run_cognition_eval.py:54`).
+- **NOT enforced inline as exception:** a turn with `vc >= 1e-6` still
+  completes; the violation is visible in trace + eval, not raised as
+  an error. This matches CLAUDE.md's discipline ("Do not weaken this
+  threshold to make tests pass. Fix the operator/construction
+  boundary that violated it.") — violations are surfaced for fix,
+  not catastrophically refused at runtime.
+
+**Semantic mismatches flagged for human review:** none. The contract
+is consistently consumed.
+
+### Closure criteria scorecard
+
+| Criterion | Status | Evidence |
+|---|---|---|
+| 1. Design artifact | ✅ | ADR-0001, ADR-0003, ADR-0004, ADR-0009 |
+| 2. Code artifact | ✅ | `algebra/{backend,cga,cl41,holonomy,rotor,versor}.py` |
+| 3. Live caller | ✅ | 38 distinct caller files outside `algebra/` and `tests/` |
+| 4. Exercised by suite lane | ✅ | `core test --suite algebra` — 82/82 non-skipped pass; every L0 module covered |
+| 5. Cross-layer consistency | ✅ | All exposed symbols consumed; `versor_condition` invariant measured + traced + gated |
+
+**Verdict:** **CLOSED.**
+
+### Cleanup performed
+
+**None.** Audit found no dead, redundant, superseded, or orphaned code
+at L0. Every module has live callers; every exposed symbol is consumed;
+the suite lane exercises every module; the invariant is preserved
+end-to-end.
+
+### Findings / notes for downstream layers
+
+- **L1 (Field substrate) auditor:** L0's `versor_condition` is consumed
+  at L5 (trace) and at the eval boundary, but L1 itself does not appear
+  to enforce the invariant — L1's propagation produces field states
+  that may later violate the invariant, with measurement deferred to
+  L5. Worth verifying that L1's propagation correctness is itself
+  tested independently of L5's downstream measurement.
+- **L2 (Vault) auditor:** `vault/store.py` is one of the heaviest
+  consumers of L0 (cga_inner, embed_point, is_null, holonomy_encode).
+  L2's closure depends on L0's exact-CGA-recall guarantees; the L2
+  audit should verify the vault honors the exact-match discipline
+  end-to-end, not just at the algebra layer.
+- **L6 (Chat runtime) auditor:** ADR-0020 (Phase 5 / Rust Parity
+  Sequencing) is cross-cutting; the 50 skipped tests in the algebra
+  suite are Rust-parity tests skipped in a Python-only environment.
+  Audit ADR-0020 wherever Rust integration is live (when it lands)
+  rather than at any single layer.
+
+### Audit method footnote
+
+This entry follows the per-layer audit format established here:
+ADRs in scope → modules in scope → caller traces → suite lane
+exercise → cross-layer contract (mechanical + semantic) → closure
+scorecard → cleanup → notes for downstream. Subsequent layers should
+follow the same format so the registry is uniformly machine- and
+human-scannable.
+
+---