# P-vs-NP Verification Project Index

This folder holds working artifacts for the `SUNDOG_V_P_V_NP` roadmap.

Main roadmap:

- [`../SUNDOG_V_P_V_NP.md`](../SUNDOG_V_P_V_NP.md)

Machine-checked deductive core (Lean, 2026-06-08):

- [`../SUNDOG_V_CERTIFICATE_LEAN.md`](../SUNDOG_V_CERTIFICATE_LEAN.md) - this lane's certificate
  **soundness + lossiness**, proved in Lean 4 (`sorry`-free, axiom-clean,
  **referee-free**). Public and reproducible at
  [github.com/humiliati/sundogcert](https://github.com/humiliati/sundogcert) (`lake build` re-certifies
  every theorem). The *deductive* complement to the empirical v1-v6 cost receipts below; hardness stays
  imported, never proven. The same public repo now also carries real-analysis shadow decay, halo
  minimum-deviation geometry, an Aharonov-Bohm gauge-invariance core (vector calculus), and the general
  characteristic-function law behind the shadow decay as method examples, not P-vs-NP evidence. Includes the full characterization of the `colWeightLb` reject bound
  (sound / tight-scaling / basis-loose / degradation), closing the **degenerate cheap-reject (RISK 1)**
  question from the prototype note: the non-degenerate column-weight bound rejects at `τ > 0`, with its
  basis-dependence proved to be the shadow of the imported hardness.

Phase-4 synthesis:

- [`SUNDOG_CERTIFICATE_PROBLEM.md`](SUNDOG_CERTIFICATE_PROBLEM.md) — theorem-shaped
  synthesis (2026-06-04). Banks Phase 3 as the honest boundary and states the formal
  promise problem (tightening §4–§6), the three separated claims (cheap
  verification = op-count; capacity-relative mesa spoof resistance =
  bounded+fragile;
  disclosure robustness = the v3 null), the substrate migration off marginal mesa
  toward an AB/topological-style design, and **one constructed instance** (the
  syndrome/SIS certificate: check-cheap, witness-recovery capacity-hard, shadow lossy-by-algebra,
  failure branches pre-named). It began as a **design / existence note** and now carries
  the measured v1→v3 ISD ladder (§5).
- [`SUNDOG_CERTIFICATE_SYNDROME_PROTOTYPE_NOTE.md`](SUNDOG_CERTIFICATE_SYNDROME_PROTOTYPE_NOTE.md)
  — the constructed instance **built + mechanism verified** (2026-06-04,
  `scripts/pvnp-certificate-syndrome.py`, deterministic). On a real `[48,24]` GF(2)
  regime: P1 lossy-by-algebra (`z=He`, `s` gone, 2²⁴/syndrome); P2 cheap+sound
  (check 2,376 ops vs ~5.1M decode, 0 false accepts); P3 `s` one-way; and the
  find-vs-check capacity curve (witness recovery 0.00→1.00 with budget while check
  stays flat).
  The verify-first PASS v4 never got. Honest limits: toy regime, naive non-ISD
  forger, imported hardness, degenerate cheap-reject (RISK 1). Frozen scaled
  ISD-attacker runs v1→v3 are the measured threshold series below.
- [`SUNDOG_CERTIFICATE_SYNDROME_V1_SLATE.md`](SUNDOG_CERTIFICATE_SYNDROME_V1_SLATE.md)
  — **FROZEN + EXECUTED 2026-06-04 → bounded positive**: the §5 capacity experiment
  pre-registered. Frozen regime `[128,64] w=12 τ=12` (non-enumerable
  `C(128,12)≈2.4×10¹⁶`, answering the toy critique); capacity probe = recover the
  valid light deviation witness `e*` from the syndrome `z` (= syndrome decoding)
  via **Prange ISD**;
  ladder Small/Medium/Large/XL with a pre-registered breakpoint at ~5,000 iters /
  ~2.6×10⁹ ops vs the flat 8,192-op check (gap ~3.2×10⁵×). The measured `C` is
  honestly a threshold *against Prange* (upper bound vs better ISD). `s` is
  unconditionally hidden (vacuous, not capacity); spoof is structurally impossible
  (sound verifier). **FROZEN 2026-06-04** after three pre-freeze repairs (existence
  predicate `Safe(y):=∃e*`, parent-doc invert-`e` framing, Prange rank-valid `B`
  convention) reconciled across all artifacts; seeds locked (code_seed 2026128,
  body-base 7000000, T=64), Prange ISD smoke-validated, then **EXECUTED 2026-06-04 →
  BOUNDED POSITIVE (measured capacity-relative one-wayness against Prange ISD)**: the
  invert-`e` curve rose `0→1` with the 50%-breakpoint **on the pre-registered
  prediction** (`B≈5007`, max |Δ|=0.031), verifier check flat at 16,576 ops, average
  attacker cost ≈4.5×10⁹ ops/witness → **find-vs-check gap ≈2.7×10⁵×** — the lane's
  first measured capacity threshold. Rank-valid `B` convention audited (1.19M
  rank-fail draws). Receipt
  [`receipts/2026-06-04_certificate_syndrome_v1.md`](receipts/2026-06-04_certificate_syndrome_v1.md).
  Boundary: against Prange (upper bound vs better ISD), imports decoding hardness, no
  crypto/P-vs-NP claim. A stronger attacker class / scaled regime = a new slate.
- [`SUNDOG_CERTIFICATE_SYNDROME_V2_SLATE.md`](SUNDOG_CERTIFICATE_SYNDROME_V2_SLATE.md)
  — **FROZEN + EXECUTED 2026-06-05 → bounded-positive + named LB↔Stern model-deviation**
  (measured `C` all within the locked factor-2 band, but the locked Stern-best prediction
  reversed: **Lee-Brickell is best**, `C_best=8.31×10⁷` ≈86× over Prange; Stern
  underperforms at `w=12`. Receipt
  [`receipts/2026-06-05_certificate_syndrome_v2.md`](receipts/2026-06-05_certificate_syndrome_v2.md)):
  the stronger-ISD tightening. Same
  **code** as v1 (`[128,64] w=12`, code_seed 2026128) but **decoupled targets** (a
  fresh `target_seed=2026220` + an emitted `target_manifest.json`, fixing v1's
  interleaving of target sampling with attack draws; Prange is re-baselined in-ladder,
  with v1's trial-count as a cross-check — **not** its ops, since v2 re-baselines Prange
  *with* the full systematic form `U·H` that v1 omitted, so v2 Prange ops ≈ 2× v1).
  Measures the witness-recovery `C` against a
  **Prange→Lee-Brickell(p=2)→Stern(p=2,l=8)** attacker ladder in **ops**.
  **Locked** work-factor ladder (two-size throwaway-smoke calibration; per-iter =
  `base(m)=3.95·m^3.07` incl. rank-fail ρ≈3.46 + analytic enum): all three attackers
  smoke-validated (curves track analytic at both sizes); `C` drops **~73× (LB)** and
  **~81× (Stern, l=8)** vs Prange (locked predicted `C_best =
  min(C_LB,C_Stern) = 8.66×10⁷` ops, Stern-set), with the LB→Stern margin
  **compressed (~1.11×)** at this small `w`
  (Stern's big win is a large-`w` phenomenon, e.g. `[256,128] w=24` — the scaled-regime
  lever). Freeze comparator =
  [`SUNDOG_CERTIFICATE_SYNDROME_V2_PREDICTION_LOCK.json`](SUNDOG_CERTIFICATE_SYNDROME_V2_PREDICTION_LOCK.json)
  (locked formulas incl. the Stern collision term + two-size-calibrated constants +
  tolerance; SHA-256 `4e46be88...`), now **produced and durably filed**. Ladder gate:
  Prange→LB must resolve; LB→Stern expected within-`T=64`-noise (a pass, not a
  violation). The reported bound is `C_best` across the tested stronger attackers; it
  is still an upper bound (BJMM/MMT = future slate; the measured best is now **LB, not
  Stern**). **EXECUTED 2026-06-05** via the `--frozen` harness (manifest-before-attackers
  + 12-file bundle, GREEN 5-dimension pre-freeze audit, byte-deterministic): find-vs-check
  gap holds (verifier flat 16,576 ops, gap ≈5,015× at `C_best`); the Stern work-factor
  heuristic was optimistic at `w=12`, the named deviation. A confirmatory follow-up
  (corrected Stern success model + the large-`w` regime) is the v3 slate below.
- [`SUNDOG_CERTIFICATE_SYNDROME_V3_SLATE.md`](SUNDOG_CERTIFICATE_SYNDROME_V3_SLATE.md)
  — **EXECUTED 2026-06-06 → crossover LOCATED + gap scales with `n`**: the **scaling-ladder**
  successor. 4-rung ladder (`[128,64]w12` anchor reuse → `w16` → `[160,80]w16` →
  `[192,96]w18`), **LB + Stern measured at each** (Prange formula-predicted at scale),
  empirically pre-calibrated. **Claim B:** Stern **overtakes LB at the higher-`w` rungs 1 & 3**
  (St/LB 0.75, 0.76) — confirming v2's "Stern wins at large `w`" (the `w12` LB-win reverses
  by `w16`); winner non-monotone in `(n,w)`, with rung-2 a named pre-cal heavy-tail
  model-deviation (mean-vs-median; the median-implied diagnostic nails all 3 Stern rungs
  within factor 2). **Claim A:** find-vs-check gap scales with `n` to **218,999×** (5,015×→
  219k×, 43.7×), though the frozen "interior ≥5×" gate was mis-fit to the fixed-`n` rung-1.
  Empirical pre-cal caught the analytic wrong **both ways** (LB ~8× easier at `w16`); base(`m`)
  re-validated to v2 within 0.1%. Receipt
  [`receipts/2026-06-06_certificate_syndrome_v3.md`](receipts/2026-06-06_certificate_syndrome_v3.md).
  Next (future slate): median-based prediction lock + larger pre-cal target count; clean
  rung-2 retest at `l∈{8,9}`.
- [`SUNDOG_CERTIFICATE_SYNDROME_V4_SLATE.md`](SUNDOG_CERTIFICATE_SYNDROME_V4_SLATE.md)
  — **EXECUTED 2026-06-07 → dual result, neither half a clean pass (adversarially audited)**:
  median-calibration + rung-2 (R2′) resolution. **(A)** the directly-measured censored-median
  fix is validated as an *in-sample retrofit* on v3 rungs 1/3 (ratios 1.00–1.33, closing v3's
  5.32× mean miss) but is **`method_still_off`** on the fresh R2′ regime — the median missed
  Stern `l8` by **2.77×** (`model_deviation`), so it is **not** a proven universal predictor.
  **(B)** R2′ `[160,80]w16` (same code as v3 rung-2 via `code_digest`, fresh targets, fixed
  `l∈{8,9}`) is a **near-tie** (St/LB=0.978, inside the regime's 1.43–2.77× seed-noise floor +
  a Stern-flattering censoring asymmetry) — it **dissolves v3's dramatic `l=10` LB-win artifact
  down to a dead heat**, NOT a clean Stern crossover; "monotone in w" is withdrawn. The
  load-bearing claim: v3's off-pattern point was an `l`-selection artifact, not a 2-D LB feature;
  the v3 ladder is untouched. Integrity clean (code_identity, witnesses, privilege, determinism).
  Open: heavy-tail prediction (neither mean nor median nails R2′ Stern), a `near_tie` outcome bin,
  the slate's Gates-vs-verdict scope inconsistency. Receipt
  [`receipts/2026-06-07_certificate_syndrome_v4.md`](receipts/2026-06-07_certificate_syndrome_v4.md)
  (supersedes the auto `V4_SUMMARY.md`). W14 midpoint deferred.
- [`SUNDOG_CERTIFICATE_SYNDROME_V5_SLATE.md`](SUNDOG_CERTIFICATE_SYNDROME_V5_SLATE.md)
  — **PAUSED / TODO 2026-06-09** (stage-1 **FROZEN**, harness built + **stats-layer audit GREEN**,
  precal **not complete**): MHK-v5 distributional-band repair for v4's heavy-tail miss. Freezes a
  Kaplan-Meier median-in-op-units band over `K=8` same-size precal seeds (`g=1.25`, `W_max=3.0`) with
  an honest `precal_insufficient` decline rather than widening to pass; fixes v4's cross-attacker
  asymmetry with a common op horizon plus pairwise `LB vs stern_l8` / `LB vs stern_l9`
  survival-difference + log-rank (Bonferroni p<0.025) verdicts and a near-tie bin. R2′ `[160,80]w16`
  is the primary fresh resolution; v3 rungs 1/3 method-validation only; R0 out of scope. **Shelved on
  an environment blocker** (detached background runs get silently killed ~every 30 min; the resumable
  precal banked only **2/24 R2′ slices**). The slice cache is preserved + resumable; resume when the
  environment is stable (self-paced loop / detached scheduled task). **v1–v4 are the banked,
  complete arc.**

Lit-pass:

- [`../P_V_NP_LITPASS_MEMO.md`](../P_V_NP_LITPASS_MEMO.md) - 2026-05-28
  prior-art and citation spine for promise-bounded verifier scaffolding.

Phase specs:

- [`PHASE1_TOY_VERIFIER_SPEC.md`](PHASE1_TOY_VERIFIER_SPEC.md) - draft spec
  for the first formal toy verifier, including promise domain, certificate
  schema, baselines, cost accounting, and falsifier mapping.
- [`PHASE1_V0_SLATE.md`](PHASE1_V0_SLATE.md) - frozen first implementation
  slate with split namespaces, calibration insulation, attacker budgets, and
  success thresholds.
- [`PHASE1_V1_SLATE.md`](PHASE1_V1_SLATE.md) - repair slate opened after the
  v0 named quarantine, focused on certificate integrity binding, non-vacuous
  sensor/invariance checks, and probe-derived geometry promise detection.
- [`PHASE1_V2_SLATE.md`](PHASE1_V2_SLATE.md) - repair slate opened after the
  v1 named quarantine, focused on decision-relevant invariance checks,
  basin-shape boundary closure, coverage disposition, and checker overhead.
- [`PHASE1_V3_SLATE.md`](PHASE1_V3_SLATE.md) - repair slate opened after the
  v2 safety-repair-landed quarantine, focused on cost batching,
  `sensor_health_v1` disposition, acceptance-volume sanity, and optional
  inversion-target widening.
- [`PHASE1_V4_SLATE.md`](PHASE1_V4_SLATE.md) - cost-gate slate opened after
  the v3 cost-only quarantine, focused on stable cost comparators,
  cache-eligible reuse accounting, and bounded-positive promotion criteria.
- [`PHASE1_V5_SLATE.md`](PHASE1_V5_SLATE.md) - cost-closure slate opened
  after the v4 cost-only quarantine, focused on short-circuit instrumentation
  overhead and median-of-3 cost promotion.
- [`PHASE1_V6_SLATE.md`](PHASE1_V6_SLATE.md) - op-count cost slate opened
  after the corrected v5 named quarantine, focused on using the only
  reproducible cost signal while keeping wall-time diagnostic-only.
- [`PHASE2_MESA_BRIDGE.md`](PHASE2_MESA_BRIDGE.md) - Phase 2 mesa
  verification bridge spec / charter (opened 2026-05-31). Carries forward
  the v6 claim boundary and maps mesa intervention evidence to verifier-failure
  tests. The frozen v0 slate below supersedes its initial "no slate frozen"
  status.
- [`PHASE2_MESA_BRIDGE_V0_SLATE.md`](PHASE2_MESA_BRIDGE_V0_SLATE.md) -
  frozen first mesa-bridge execution slate. Re-reads the current mesa Phase 4
  and Phase 5 artifacts from disk, gates only a reward-blind bridge-smoke, and
  uses the measured L-Mixed breach thresholds as the capacity-breach falsifier.
  Certificates must recompute from per-seed raw trial logs, and the op-count
  comparator must be a same-artifact-tier raw-trace audit rather than a full
  mesa battery regeneration.
- [`PHASE2_MESA_BRIDGE_V1_SLATE.md`](PHASE2_MESA_BRIDGE_V1_SLATE.md) -
  frozen provenance-repair slate after the v0 named quarantine. Chooses
  raw-logged Small reruns over Medium-only downscope.
- [`PHASE3_CAPACITY_ONE_WAYNESS_V0_SLATE.md`](PHASE3_CAPACITY_ONE_WAYNESS_V0_SLATE.md) -
  frozen capacity-relative one-wayness slate after the Phase 2 v1 bounded
  positive. Registers the attacker/capacity battery and source-bound
  seed-extension plan before any execution.
- [`PHASE3_CAPACITY_ONE_WAYNESS_V1_SLATE.md`](PHASE3_CAPACITY_ONE_WAYNESS_V1_SLATE.md) -
  frozen block-consensus repair slate after the v0 falsified registered cell.
  Targets source-bound seed-block mean drift without changing the base response
  thresholds.
- [`PHASE3_CAPACITY_ONE_WAYNESS_V2_SLATE.md`](PHASE3_CAPACITY_ONE_WAYNESS_V2_SLATE.md) -
  opened disclosure-consensus repair slate after the v1 named quarantine.
  Targets block-unstable objective-conflict disclosure while keeping v1
  promotion consensus unchanged.

Templates:

- [`RECEIPT_TEMPLATE.md`](RECEIPT_TEMPLATE.md)

Result convention:

- Computational outputs should write under `results/pvnp/<phase-or-probe>/`.
- `results/pvnp/` is treated as transient run output. Durable conclusions
  belong in dated receipt notes under `docs/pvnp/receipts/` once reviewed.
- A run without a manifest, verifier-access declaration, baseline comparison,
  and falsifier disposition is not a receipt.

Receipts:

- [`receipts/README.md`](receipts/README.md) - receipt index, including the
  Phase 1 v0-v5 named-quarantine receipts, the v6 op-count positive receipt,
  the Phase 2 v0 mesa-bridge named quarantine, the Phase 2 v1 mesa-bridge
  bounded-positive receipt, the Phase 3 v0 falsified-cell receipt, and the
  Phase 3 v1 named-quarantine receipt.

Current state:

- Roadmap opened: 2026-05-28.
- Lit-pass filed: 2026-05-28.
- Project scaffold opened: 2026-05-28.
- Phase 1 toy-verifier spec drafted: 2026-05-28.
- Phase 1 v0 slate frozen: 2026-05-28.
- Phase 1 v0 harness executed: 2026-05-28. Verdict = named quarantine;
  `capacity_threshold = <=small` after field-only spoof breach.
- Phase 1 v1 repair slate opened: 2026-05-28.
- Phase 1 v1 harness executed: 2026-05-28. Verdict = named quarantine;
  v0 spoof channel closed, but invariance vacuity, boundary leak, and cost
  overhead remain open.
- Phase 1 v2 repair slate opened: 2026-05-28.
- Phase 1 v2 harness executed: 2026-05-28. Verdict = named quarantine with
  safety repair landed; false-accept rate 0%, `capacity_threshold =
  not_estimated`, zero accepted basin-shape out-of-promise rows, but cost
  overhead, `sensor_health_v1` disposition, and acceptance-volume sanity
  remain open.
- Phase 1 v3 repair slate opened: 2026-05-28.
- Phase 1 v3 harness executed: 2026-05-28. Verdict = named quarantine on
  cost alone; all safety-repair labels pass, absolute signature+verify wall
  time improves to 907.52 ms, but the rollout-ratio and raw cache-hit gates
  remain unsuitable for bounded-positive promotion.
- Phase 1 v4 cost-gate slate opened: 2026-05-28.
- Phase 1 v4 harness executed: 2026-05-28. Verdict = named quarantine on
  cost alone; safety, denominator restatement, and cache-eligible reuse all
  pass, but absolute wall-time and full-state-ratio cost gates miss by a small
  margin.
- Phase 1 v5 cost-closure slate opened: 2026-05-28.
- Phase 1 v5 harness executed: 2026-05-28. Verdict = named quarantine:
  safety-complete, wall-time cost unadjudicated. The earlier stable cost claim
  is withdrawn after artifact re-check: four clean full-harness invocations
  span `C_total_signature` 890 / 2192 / 2242 / 3185 ms, while the on-disk
  `cost_multirun_report.json` shows 2569 / 2091 / 2242 ms and
  `cost_repair_passed=false`. Determinism is confirmed by two fresh
  byte-identical v5 environment generations (`5549b4c4e8b7`; first env
  `pvnp-v5-cal-0001`). The stable cost signal is the op-count ratio 0.9487,
  which became the pre-registered v6 cost gate.
- Phase 1 v6 op-count cost slate opened: 2026-05-31. v6 keeps the v5 safety
  gates frozen, demotes wall-time to diagnostic-only, and gates cost on
  `C_total_signature_ops / C_rollout_ops <= 1.0`.
- Phase 1 v6 harness executed: 2026-05-31. Verdict = bounded positive under
  the registered v6 op-count protocol; wall-time remains diagnostic-only.
  Cost gate passed (`527297 / 555876 = 0.948587 <= 1.0`), cache reuse was 100%,
  short-circuit audit passed, privilege audit was green, and safety gates stayed
  clean (0/2304 false accepts, 0/453 field spoofs, 0/453 source spoofs, 5/5
  integrity probes, 0/768 OOP accepts, `capacity_threshold = not_estimated`).
  Independent disk re-verification 2026-05-31 confirmed all of the above and
  flagged one conservative op-count imprecision (numerator counts 2496
  signature calls incl. 64 calibration envs x 3 policies vs 2304 measurement
  rollout calls) that makes the reported ratio slightly higher than the clean
  measurement-only ~0.879 — directionally conservative, does not change the
  pass.
- Phase 2 mesa verification bridge opened: 2026-05-31. Spec/charter
  [`PHASE2_MESA_BRIDGE.md`](PHASE2_MESA_BRIDGE.md) filed; carries forward the
  v6 claim boundary.
- Phase 2 mesa bridge v0 slate frozen: 2026-05-31. Slate
  [`PHASE2_MESA_BRIDGE_V0_SLATE.md`](PHASE2_MESA_BRIDGE_V0_SLATE.md) locks
  source artifacts, verifier-access rules, mesa label mapping, op-count
  accounting, and pre-named falsifiers.
- Phase 2 mesa bridge v0 executed: 2026-05-31. Verdict = named quarantine.
  The bridge implementation recomputes from per-seed raw trial logs where they
  exist, keeps reward-blind access, catches the registered fixed-attractor /
  capacity-breach / mixed-objective falsifiers, and passes the same-artifact
  op-count comparator (`0.734877`). It cannot promote because 7/15 registered
  cells lack raw trial logs (`trial_logs_saved=false` for Small-tier source
  manifests), leaving raw recomputation, integrity, and the 3/4 signature
  accept floor failed.
- Phase 2 mesa bridge v1 slate frozen for implementation: 2026-05-31.
  [`PHASE2_MESA_BRIDGE_V1_SLATE.md`](PHASE2_MESA_BRIDGE_V1_SLATE.md) selects
  the raw-logged Small rerun repair, preserves the v0 population and
  thresholds, records full-size timing probes, and stages exact Phase 4 rerun
  commands.
- Phase 2 mesa bridge v1 executed: 2026-05-31. Verdict = bounded positive
  under the frozen v1 mesa-bridge contract. The run regenerates 6/6 Small raw
  policy batteries, preserves the original 15-cell population, recomputes
  15/15 cells from per-seed raw logs, accepts 4/4 signature cells, closes the
  registered fixed-attractor / capacity-breach / mixed-objective falsifiers,
  and passes the same-artifact raw-trace op-count comparator (`0.73760368`).
  Wall-time remains diagnostic-only; the result is not mesa-general,
  body-resistance, wall-time-cheap, or P-vs-NP evidence.
- Phase 3 capacity-relative one-wayness v0 slate frozen for implementation:
  2026-05-31 local / 2026-06-01 UTC. The slate carries forward the v1 caveats
  as registered Phase 3 design constraints: Small-tier near-threshold
  fragility, signature-only vs full-bridge separation, and conservative
  objective-conflict flag overfire. It also aligns with the updated
  cross-substrate note: mesa remains marginal on dimensional body-resistance,
  AB is the earned exact topological regime-2 witness, and Phase 3 is only a
  mesa-local inversion/spoof capacity battery.
- Phase 3 capacity-relative one-wayness v0 executed: 2026-05-31 local /
  2026-06-01 UTC. Verdict = **falsified in a registered cell**;
  `capacity_threshold <= small` for this mesa bridge battery. The harness
  (`scripts/pvnp-phase3-capacity-one-wayness-v0.mjs`, plus
  `scripts/pvnp-phase3-seed-extension.mjs` and the
  `scripts/lib/pvnp-phase3-*.mjs` cores) preserved the 15-cell population,
  reproduced the v1 verifier decisions byte-for-byte, and scored 24 source-bound
  seed-extension blocks. One block of the registered unsafe controller
  `phase5_l_mixed_lambda_0_7_small` was accepted by the bridge verifier without a
  breach/quarantine flag (signature 0.23545148, geometry 0.28284839), a spoof
  success at the smallest attacker tier on both views, found at 6.25 % of the
  small-tier candidate budget. Inversion also succeeded at the small tier (AUROC
  0.96–0.98) but is near-tautological. The v1 repair slate opens a
  block-consensus repair for per-seed-block mean drift and keeps inversion
  diagnostic-only. Receipt:
  [`receipts/2026-05-31_phase3_capacity_one_wayness_v0.md`](receipts/2026-05-31_phase3_capacity_one_wayness_v0.md).
- Phase 3 capacity-relative one-wayness v1 repair slate frozen and wired:
  2026-06-01. It does not revise v0; `capacity_threshold <= small` remains the
  v0 verdict. The repair keeps the base response thresholds unchanged but
  removes single-block promotion: accept requires 3-of-4 source-bound holdout
  blocks, while mixed or unstable block patterns quarantine. The harness is
  `scripts/pvnp-phase3-capacity-one-wayness-v1.mjs`, exposed as
  `npm run pvnp:phase3:capacity-one-wayness:v1`. The pre-holdout dry run
  correctly named-quarantines with 0/52 holdout blocks present, while the v0
  falsifier regression no longer consensus-accepts. The 52-block holdout
  battery remains operator-staged under the repository's runtime rule.
- Phase 3 capacity-relative one-wayness v1 executed: 2026-06-01. Verdict =
  **named quarantine**, repair strength **consensus-only repair**. The 52-block
  holdout battery was generated (`scripts/pvnp-phase3-v1-holdout.mjs`, 52/52
  integrity-clean) and scored by the consensus harness. The repair works on the
  unsafe side: the v0 falsifier no longer consensus-accepts and 0 unsafe cells
  reach `consensus_accept`; two unsafe single blocks still cross by seed-block
  drift (`l_mixed_lambda_0_7_small` seed 70000, `l_mixed_lambda_0_9_small` seed
  90000) but neither reaches 3-of-4, the registered consensus-only signature.
  The run cannot promote because the mixed-objective-laundering gate fails on the
  protected anchor `l_mixed_lambda_0_95_medium`, whose objective-conflict flag is
  block-unstable (2/4 < M=3) — the same drift mechanism as v0, now in the
  disclosure flag. Signature floor passed 3/3. v0 stays falsified;
  `capacity_threshold <= small` unrevised. Receipt:
  [`receipts/2026-06-01_phase3_capacity_one_wayness_v1.md`](receipts/2026-06-01_phase3_capacity_one_wayness_v1.md).
- Phase 3 capacity-relative one-wayness v2 disclosure slate opened for review
  and then provenance-corrected/frozen: 2026-06-04. It does not revise v0 or
  v1. The draft keeps v1's promotion consensus unchanged and targets only the
  disclosure aggregation failure: a bridge-view consensus accept is unqualified
  only if the clean/no-conflict side itself has stable consensus; a 2/2
  objective-conflict split is reported as block-unstable disclosed ambiguity.
  A full seed-100000/110000/120000/130000 holdout battery ran before the slate
  status was frozen; it is clean on disk but diagnostic-only and cannot promote.
  The promotion-eligible successor path is `phase3-capacity-one-wayness-v2b`
  with fresh seeds `140000, 150000, 160000, 170000`; its corrected fresh holdout
  battery is complete on disk (52/52 blocks, 0 failed, 52/52 raw trial logs
  saved).
- Phase 3 capacity-relative one-wayness v2/v2b harness implemented and scored:
  2026-06-04. Harness `scripts/pvnp-phase3-capacity-one-wayness-v2.mjs` +
  `scripts/lib/pvnp-phase3-v2-config.mjs`, exposed as
  `npm run pvnp:phase3:capacity-one-wayness:v2` (and `:v2:pre-freeze`); the v1
  scorer is left untouched. Verdict = **bounded positive,
  `consensus-only disclosure repair`** on the v2b promotion battery: the v2
  rule gives the objective-conflict flag its own K/M consensus, so the v1 anchor
  `l_mixed_lambda_0_95_medium` (2/4 flags) reads as `block_unstable_disclosure`
  (disclosed ambiguity), not an unqualified clean accept. 0 unsafe consensus
  accepts, 0 `clean_consensus` laundering, signature floor 3/3, v0 falsifier
  non-promoting; the v1-regression blocks reproduce the v1 receipt digit-for-digit;
  determinism confirmed (byte-identical re-score). Consensus-only (not strong):
  `l_mixed_lambda_0_7_small` seed 140000 (sig 0.24505205) still crosses without
  consensus → no source-block-safety claim. Disclosed seed-fragility: the
  pre-freeze diagnostic battery (seeds 100000–130000) quarantines because the
  anchor's observation mean drifts below the 0.5 flag line to `clean_consensus`.
  v0/v1 not revised. See
  [`receipts/2026-06-04_phase3_capacity_one_wayness_v2b.md`](receipts/2026-06-04_phase3_capacity_one_wayness_v2b.md).
- Phase 3 capacity-relative one-wayness v3 disclosure-robustness slate frozen and
  **executed**: 2026-06-04 local. Harness
  `scripts/pvnp-phase3-capacity-one-wayness-v3.mjs` +
  `scripts/lib/pvnp-phase3-v3-config.mjs`, npm
  `pvnp:phase3:capacity-one-wayness:v3`; v1/v2 scorers left byte-untouched
  (per-battery layer reproduces v1/pre-freeze/v2b digit-for-digit). Multi-battery
  robustness gate: a registered mixed cell passes only if never `clean_consensus`
  across N = 3 fresh disjoint batteries (seeds 180000–290000); thresholds/K/M/0.5
  unchanged, no band. Verdict = **`named_quarantine — disclosure_robustness_null`**
  (the pre-registered expected outcome, landed decisively): the anchor
  `l_mixed_lambda_0_95_medium` is `clean_consensus` on **all three** fresh
  batteries (not robustly disclosed), while the other 3 registered mixed cells are
  `robustly_disclosed`. Unsafe side closed: 0 unsafe consensus accepts across all
  batteries, floor 3/3 each, v0/v1 regression clean; 8 breach single-blocks cross
  without consensus (no source-block-safety claim). Six-battery anchor picture:
  block_unstable on v1/v2b, clean on pre-freeze + all 3 fresh (4/6) → the v2b
  positive does not generalize across seeds. v0/v1/v2b not revised. See
  [`PHASE3_CAPACITY_ONE_WAYNESS_V3_SLATE.md`](PHASE3_CAPACITY_ONE_WAYNESS_V3_SLATE.md)
  and [`receipts/2026-06-04_phase3_capacity_one_wayness_v3.md`](receipts/2026-06-04_phase3_capacity_one_wayness_v3.md).
- Phase 3 capacity-relative one-wayness v4 basin-channel disclosure slate **ON HOLD —
  mechanism FALSIFIED before freeze (2026-06-04)**. The draft proposed adding the
  basin-position channel (`mixed_objective_flag_v4 = (obs >= 0.5) OR (basin_response
  >= 0.23)`) as a reward-blind behavioral mixed-objective detector. An adversarial
  pre-freeze audit (verified in code + on disk) killed it: the basin-position
  action-divergence response is identically **0** for every exported policy, because
  the basin move sets only `falseBasinCenter` (`mesa-core.mjs:509-510`) which feeds
  only `rewardChannels()` (`:524`); `falseBasinField` is never in the observation
  path, and feed-forward policies are reward-blind at inference. Empirically 0
  (maxdiff 0) on v3-A for the anchor, reward, signature, and mixed cells alike — so
  the OR term never fires and v4 collapses to v3. The only *informative* basin
  scalar (`old_basin_pref`) is the forbidden GT label, so a reward-blind behavioral
  basin detector is incoherent on this substrate. The owner's 4 pre-freeze findings
  (overstated "unseen"; ban aggregate-CSV reads; paste full v4 commands; claim-cap
  the pure-signature anomaly) are all confirmed but unapplied pending a path
  decision. Owner chose **Path A (make the basin action-visible)**; a verify-first
  experiment was run before pre-registration: the basin-observation channel is
  action-visible + decoupled (mechanism works) but **NOT specific** — a
  pure-signature policy responds 0.431 (reward 0.558; ratio 1.29×, worsening with
  training), so Design 1 does not justify the ~45–76-policy retrain. **PAUSED**;
  scaffolding kept (default-off `basinChannel` env + `--basin-channel` trainer);
  the v3 `disclosure_robustness_null` stands as the boundary unless a new
  pre-registered fresh-seed variant is opened. See
  [`PHASE3_CAPACITY_ONE_WAYNESS_V4_SLATE.md`](PHASE3_CAPACITY_ONE_WAYNESS_V4_SLATE.md)
  and [`PHASE3_V4_PATHA_VERIFY_NOTE.md`](PHASE3_V4_PATHA_VERIFY_NOTE.md).