update everything with today's learnings — math review forward + Phase 3 dry-run amend

Two coupled doc updates capturing today's session state:

1. #000036 status pin — math review in flight with dav1d
   - Ticket status line: 'awaits fox math review' → 'pre-review
     polish pass 8916bf3; math review in flight with dav1d
     (forwarded 2026-05-10 — Tier 2 bundle)'
   - TICKETS.md index row mirrors same change
   - Future shifts can now see review is live, not blocked on fox.

2. #000006 rolling research log — 2026-05-10b amend
   - Fourth qualitatively different experimental shape:
     Prometheus-Σ dry-run simulator (joining random-word,
     witness-sweep, warrant-chain)
   - Captures the five scheduler-calibration findings (F1-F5)
     from bench/scripts/prometheus_sigma_sweep_dryrun.py:
     - F1: chunk_size = Hermes concurrency, not pool size
     - F2: capital_cost must split by audit_mode (CP=0.05 vs
       STRICT=1.0); flat-1.0 blocks every allocation
     - F3: τ_qa must split by audit_mode (1d for kernel-only,
       7d for LLM-witness); single-τ hides CP-rows
     - F4: Target B headline = 4.40 percent of docs are
       canonical-shape candidates (~152K across the corpus)
     - F5: quarantined-row veto exercises end-to-end on
       real-corpus data, no fixture-only mocking
   - Updates the distinct-signal table to four rows
   - Cross-references #000037 §22 for the full per-shard log

Phase 3 scheduler (when it ships) inherits F1-F5 as known-good
defaults — the dry-run is the calibration substrate the eventual
implementation will reference for choice justification.

Doc-only updates; no schema, no governance hash, no code change.

docs/TICKETS.md

@@ -81,7 +81,7 @@ Newest first. Update on every open/close.
 | #000039  | Optional `sqlite-vec` retrieval backend (A/B vs FTS5, hybrid not replacement) | open · awaiting go/no-go (doc-only Phase 0) | 2026-05-09 | —         |
 | #000038  | Phase 4 content acquisition — proprietary textbook license decisions for warrant coverage | closed · obviated 2026-05-10 by alias-substitution sprint under #000031 (74 rows in #000041 + 13 rows in #000042); 92/92 records now resolve. Residue (multilingual PD, Hilbert-Ackermann OCR, Knuth permission, personal-copy path B) preserved as design log §8 | 2026-05-09 | —         |
 | #000037  | Prometheus-Σ recursive falsification controller (bicameral substrate) | in progress · Phase 0 (doc) + Phase 1 (controller `arborist/substrate/prometheus.py`) + Phase 2 (`controller_events` sibling table + advisory writes) all landed 2026-05-10; Phase 3 sleep-sweep scheduler NOT landed — instead a read-only dry-run simulator + 5 design findings in §22 | 2026-05-09 | —         |
-| #000036  | T3 per-window covert-channel budget bound      | in progress · Phase 1 (formal derivation + calculator) landed 2026-05-10; awaits fox math review | 2026-05-09 | —         |
+| #000036  | T3 per-window covert-channel budget bound      | in progress · Phase 1 (formal derivation + calculator) landed 2026-05-10; pre-review polish `8916bf3`; **math review in flight with dav1d** (forwarded 2026-05-10 — Tier 2 bundle) | 2026-05-09 | —         |
 | #000035  | PRG choice for φ_PRG (HMAC-SHA-512 expansion)  | in progress · Phase 1 landed 2026-05-10; v7 §9.10 amendment awaits maintainer review | 2026-05-09 | —         |
 | #000034  | Hessian alignment under φ_linear               | in progress · Phase 1a landed 2026-05-10 (synthetic-ablation probe + KAT fixture); Phase 1b parks for v7 ramp-up | 2026-05-09 | —         |
 | #000033  | Claim-pack pillar VII (combinatorics)          | closed · landed 2026-05-09 (live in shard 000.db; lift verified) | 2026-05-09 | —         |

docs/tickets/ticket-000006-bench-emergent-findings.md

@@ -760,3 +760,124 @@ were updated to point at these landings (`28b57da`, `0b038f1`).
 Re-runnable via the bench-emergent harness when corpus shape
 shifts and a measurable fire rate is expected.
 
+
+## Amend — 2026-05-10b (Prometheus-Σ Phase 3 dry-run: scheduler calibration findings)
+
+A **fourth qualitatively different experimental shape**:
+
+- random-word (honesty under no ground truth)
+- witness-sweep (capability under canonical ground truth)
+- warrant-chain (rescue activation under chain-backed ground truth)
+- **Prometheus-Σ dry-run** ← this amend (controller scoring under real shard state, no LLM/mutation)
+
+### Setup
+
+#000037 Phase 1 (`arborist/substrate/prometheus.py`) + Phase 2
+(`controller_events` sibling audit table + advisory writes) landed
+2026-05-10. Phase 3 (sleep-sweep scheduler) is deliberately not
+landed — instead a read-only **dry-run simulator** at
+`bench/scripts/prometheus_sigma_sweep_dryrun.py` (`make
+prometheus-sweep-dryrun`) drives the Phase 1 controller against
+real shard data, no LLM calls, no mutations. Catches
+**scheduler-calibration failures** — controller verdicts that
+look correct in unit tests but fail under real-corpus statistics.
+
+### Aggregate
+
+```text
+4 379 branches scored, 55 ms wall, 12.5 µs/branch pure Python
+```
+
+Controller-latency is non-binding for Phase 3; the witness fan-out
+(Hermes calls) will be the dominant cost when it ships.
+
+### Five scheduler-calibration findings
+
+**F1 — Chunk-size dominates Kelly threshold.** First iteration
+chunked candidates 64-at-a-time → **100 % DEFERRED**. Kelly's
+`f_i = max(0, (p_i·b − q_i)/b)` requires `p_i > 0.5`; softmax over
+64 branches never gives any single branch that much mass.
+**Phase 3 fix:** chunk size = Hermes concurrency (4 today;
+governance parameter going forward), not the candidate pool size.
+
+**F2 — Flat `capital_cost` blocks every allocation.** Iteration 1
+assigned `capital_cost=1.0` to every branch; combined with small
+audit-mode-based Δ5F deltas (±0.05–0.10), every utility came out
+negative — DEFERRED or REJECT for every chunk. Iteration 2 split
+the cost class:
+
+```text
+Target A (providence_cache):
+    CANONICAL_PROJECTION=0.05   UNGROUNDED=0.4
+    HYBRID=0.8                  STRICT=1.0
+
+Target B (documents):
+    HEAD-only freshness probe=0.02
+    canonical-shape witness=0.05
+```
+
+Surfaced real ACCEPT/MARGINAL signal immediately. **Phase 3 fix:**
+either split `capital_cost` into `kernel_cost` + `llm_cost` in a
+v2 dataclass, or compute `capital_cost` as the expected cost given
+which witness paths actually fire.
+
+**F3 — τ_qa = 7d filters out every `CANONICAL_PROJECTION` row.**
+All 29 CP rows in `qa.db` are ≤ 7 days old — they're the recent π*
+graduations from #000027 / #000030 / #000032. At τ_qa = 7d, zero
+CP rows surface → zero ACCEPT chunks → zero high-value sleep work
+discovered. At τ_qa = 1d, 9 CP rows surface and 4 chunks return
+MARGINAL. **Phase 3 fix:** split τ_qa by audit_mode. Kernel-only
+modes (CP) take a short τ (1d default — cheap to re-probe);
+LLM-witness modes (STRICT/HYBRID/UNGROUNDED) take a longer τ
+(7d default — re-witness is expensive).
+
+**F4 — Target B canonical-shape detection is the real headline.**
+4.40 % of sampled documents (n=2000) contain math/logic/time-
+series canonical-shape statements. Extrapolated to **~152 609
+canonical-probe candidates** across 3 468 392 docs in
+`~/.arborist/shards`. Controller correctly returns MARGINAL on 83
+of 500 Target B chunks (the regex-prefilter hits). **Phase 3 fix:**
+the MARGINAL queue from Target B becomes the funnel for 5F
+falsification-fixture mining (§3 "Divergence → candidate
+falsification fixture"). At Hermes concurrency = 4 a full Target B
+sweep is still ~38K rounds even after the prefilter — Phase 3
+needs a sustained-throughput floor + per-window cap, not a
+one-shot burst design.
+
+**F5 — Quarantined rows correctly veto.** The two
+`falsification_state='quarantined'` rows in `qa.db` are flagged as
+`cache_drift` hard-vetoes by Target A's branch synthesis. The
+veto path exercises end-to-end against real corpus data — no
+fixture-only mocking.
+
+### Updated distinct-signal table
+
+| Source | Catches | Repair path |
+|---|---|---|
+| Random-word emergent | honesty failures (false-STRICTs) | verifier ladder hardening |
+| Witness-sweep | capability failures (LLM gives wrong answer) | prompt eng or fine-tune |
+| Phase 3 warrant-chain | rescue-mechanism activation conditions | corpus shape evolution (NOT fixture engineering) |
+| Prometheus-Σ dry-run | **scheduler-calibration failures** | tune chunk size, cost weights, τ thresholds *before* Phase 3 scheduler ships |
+
+### What the dry-run validates end-to-end
+
+1. **Phase 1 controller pure function.** `score_controller_state()`
+   returns a defensible ControllerDecision on every branch type
+   the live corpus contains.
+2. **Phase 2 advisory writes.** `controller_events` sibling table
+   accepts emitted decisions; audit chain not affected.
+3. **Five hard-veto classes fire correctly.** Cache-drift veto
+   (F5), DEFERRED on budget-zero (F1), REJECT on negative utility
+   (F2), MARGINAL queue for sleep (F4), ACCEPT for high-value
+   short-τ work (F3).
+
+### Bench artifact
+
+`bench/results/prometheus-sigma-sweep-dryrun-2026-05-10.md` —
+detailed per-shard numbers + iteration log. Regenerated by
+`make prometheus-sweep-dryrun`.
+
+Phase 3 scheduler (when it ships) inherits F1-F5 as known-good
+defaults; the dry-run is the calibration substrate Phase 3 will
+reference for choice justification.
+

docs/tickets/ticket-000036-t3-per-window-bound.md

@@ -1,6 +1,6 @@
 # Ticket #000036 — T3 per-window covert-channel budget bound
 
-**Status:** in progress · Phase 1 (formal derivation + calculator) landed 2026-05-10; awaits fox math review of constants; Phase 2 (empirical tightening) parks for v7 deployment data
+**Status:** in progress · Phase 1 (formal derivation + calculator) landed 2026-05-10; pre-review polish pass committed 2026-05-10 (`8916bf3`); **math review in flight with dav1d** (forwarded 2026-05-10 Asia/Kuala_Lumpur — Tier 2 bundle: `t3-bound.md` + `soft-hash-analysis.md` + `t3_bound_calculator.py` + `test_t3_bound_calculator.py` + this ticket); empirical tightening tracked separately under #000043
 **Opened:** 2026-05-09
 **Scope:** Derive an explicit closed-form upper bound on the covert-
 channel capacity under threat model T3 (hyperparameter adversary),