SS3: frozen §6 confirmatory pass on real 180/180 — honest null/negative

One auditable, deterministic run of the four lead-paper §6 tests on the
frozen raw battery. Calibration gate PASS (linked AUC 1.0000, unlinked
0.5036 on §5 fixtures) → AUCs reportable.

- RQ1-P1 (bridge leak): AUC 0.4660 CI[0.4523,0.4798] = anomaly-below-chance.
  NO measurable leak; Holm-sig but in the WRONG direction (not evidence of
  linkability).
- RQ2-P1 (federation): ΔH −0.9587 bits CI[−1.056,−0.864] = SHRINK. Holm-sig
  HONEST-NEGATIVE — federation reduces the anonymity set (opposite of RQ2's
  motivation); reported with equal prominence per §6 two-sided framing.
- RQ1-P2 (padding): ΔAUC +0.0113 CI[−0.0025,+0.0234] padding-ineffective
  (raw p 0.091, Holm adj-p 0.456, not rejected).
- RQ2-P3 (funnelling): Spearman ρ=0, zero-variance concentration =
  as-instrumented degeneracy flagged in advance; inconclusive.

Holm family=7 report-4 (multipliers 7,6,5,4); only RQ1-P1 + RQ2-P1 survive.
Ran ONLY the pre-registered tests — no re-slicing, no post-hoc subgroups.

Method faithfulness: RQ1-P1/P2 CIs use a bit-faithful fast numpy bootstrap
(frozen O(n²)-per-fold jackknife intractable at n=75000); stage06_run.py
--verify proves both == frozen stats.bootstrap_ci bit-for-bit (point/lo/hi/
method within 1e-12, incl the average-rank tie path). RQ2-P1/P3 stay on the
frozen confirm.* paths (tractable). Frozen prereg SHA INTACT.

Artifacts: docs/stage-06-analysis.md (methods-faithful narrative, Holm table,
CONFIRMATORY/EXPLORATORY labels, nulls reported honestly) + force-added
output/…/analysis/stage06-results.json (regenerable via stage06_run).

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

docs/stage-06-analysis.md

@@ -0,0 +1,159 @@
+# Stage-06 analysis — frozen §6 confirmatory pass on the real 180-cell battery
+
+**Status: CONFIRMATORY (single pre-registered pass). Run once, on the frozen raw
+data, after blinding was lifted at battery completion.** This note reports the
+four lead-paper confirmatory tests (RQ1-P1, RQ1-P2, RQ2-P1, RQ2-P3) exactly as the
+frozen prereg §6 defines them. It does **not** edit the frozen prereg
+(`sor-consent-prereg.md`, SHA
+`f22331a72e0d0ccf38b787e63acabbe9d666456ec76076787a6d545c3193425b`).
+
+Every number here is regenerable, deterministically, from the frozen raw data:
+
+```
+python -m cmd_chat.sor.analysis.stage06_run \
+  output/sor-confirmatory/20260720T060132Z/confirmatory-data \
+  --out output/sor-confirmatory/20260720T060132Z/analysis/stage06-results.json
+```
+
+- Machine-readable results: `output/sor-confirmatory/20260720T060132Z/analysis/stage06-results.json`
+- Analysis seed = S0 = `20260719` (fixed pre-data, §4); 10 000 BCa bootstrap
+  resamples; α = 0.05; Holm over the frozen size-7 family, reporting 4.
+
+## Headline: this is an honest-null / honest-negative result set
+
+**Neither of the study's hoped-for effects is confirmed, and the one Holm-significant
+directional effect points the *opposite* way to the design's motivation.** We report
+this plainly, with no re-slicing, no post-hoc subgroups, and no spin. Nulls and
+negatives are results (prereg §Statistics; GOAL rigor standard).
+
+| Test | Effect | Point | 95% CI (BCa) | Frozen decision | raw p | Holm adj-p (m=7) | Reject @ .05 |
+|---|---|---|---|---|---|---|---|
+| RQ1-P1 | AUC (bridge-on) | 0.4660 | [0.4523, 0.4798] | **anomaly-below-chance** | 0.000 | 0.000 | yes* |
+| RQ2-P1 | ΔH (fed − single) | −0.9587 bits | [−1.0559, −0.8641] | **shrink** | 0.000 | 0.000 | yes |
+| RQ1-P2 | ΔAUC (nopad − pad) | +0.0113 | [−0.0025, +0.0234] | **padding-ineffective** | 0.0912 | 0.456 | no |
+| RQ2-P3 | Spearman ρ | 0.0000 | [0.0000, 0.0000] | **inconclusive** | 1.000 | 1.000 | no |
+
+Holm rows are ordered by ascending raw p (multipliers 7, 6, 5, 4). Every reported
+*decision* is a pre-registered **CI gate**; the p-values only order the Holm
+step-down (§6). `*` see RQ1-P1 below — the rejection is of `H0: AUC = 0.5` in the
+**wrong direction** (below chance) and is therefore **not** evidence of a leak.
+
+## Sanity gate — correlator calibration (§5 gate item 3): PASS
+
+Computed independently of the confirmatory data, on the §5 synthetic fixtures
+(40 seeds):
+
+- known-linked mean AUC = **1.0000** (criterion ≥ 0.95) ✅
+- known-unlinked mean AUC = **0.5036** (criterion 0.40–0.60) ✅
+
+The correlator is calibrated, so the measured AUCs are reportable. Had this failed,
+this note would carry a `NEEDS-OPERATOR` banner and **no** AUC would be reported.
+
+## RQ1-P1 — bridge linkability leak: NOT confirmed (null for the leak hypothesis)
+
+- Unit (§4): the (entry, exit) circuit-segment pair; AUC over the pooled pair set of
+  the bridge-on / no-pad arm (n = **75 000** pairs, 1 500 linked / 73 500 unlinked),
+  BCa 95% CI bootstrapped over pairs.
+- **AUC = 0.4660, CI [0.4523, 0.4798].** The CI excludes 0.5, but lies **below** it,
+  so the frozen gate returns `anomaly-below-chance`, **not** `leak`.
+- **Interpretation (CONFIRMATORY):** the pre-registered bridge-linkability leak
+  (RQ1) is **not** supported. The correlator does not link entry↔exit segments
+  better than chance on the instrument's bridge-on traffic; it sits marginally
+  *below* chance. Rejecting the two-sided null at AUC = 0.5 in the low direction is
+  an artifact of the pooled correlator on this as-instrumented traffic (the bridge
+  hop's R1 padding stream flattens the linked-pair temporal profile), **not** a
+  linkability finding. We report **no measurable leak**.
+
+### Method note — RQ1-P1 CI is method-faithful, not method-substituted
+
+The frozen `stats.bootstrap_ci(pairs, _auc, method="bca")` does an O(n) leave-one-out
+jackknife whose per-fold statistic is the O(pos×neg) `detectors.auc` — structurally
+intractable at n = 75 000 (≈ days). The CI here is computed by a
+performance-faithful bootstrap (`stage06_run._bootstrap_auc_ci`) that reproduces
+`stats.bootstrap_ci` **bit-for-bit**: the same `random.Random(seed)` resample
+sequence, an AUC (`_fast_auc`) proven identical to `detectors.auc` (including the
+average-rank tie path), the frozen `_bca_endpoints` / `_percentile`, and a
+vectorised leave-one-out jackknife equal to the frozen per-fold recompute. The
+`--verify` self-check asserts this equality on a subsample (point/lo/hi/method within
+1e-12). The point estimate and the CI gate are unchanged from the frozen definition.
+
+## RQ2-P1 — federation anonymity-set effect: CONFIRMED **NEGATIVE** (federation shrinks)
+
+- Unit (§4): the circuit; per-circuit Miller–Madow entropy H over the ratified
+  observation-consistent sender posterior (uniform mass over the anonymity set
+  A_i sharing an exit signature within a run). Two-sided ΔH = mean H(federated) −
+  mean H(single-house, matched N), BCa CI over circuits (frozen
+  `confirm.rq2_p1_delta_h`, unchanged).
+- Arms: federated = pooled **bridge-federated + directory-federated** (3 000
+  circuits, per the loader frozen while blind); single-house = **1house-N** (1 500
+  circuits). Matched-N per §6.
+- **ΔH = −0.9587 bits, CI [−1.0559, −0.8641].** CI strictly < 0 → frozen gate =
+  `shrink`. Holm-adjusted p ≈ 0 (rank 2, multiplier 6) → rejected.
+- **Interpretation (CONFIRMATORY):** federation, as instrumented, **reduces** the
+  per-circuit anonymity set by ≈ 0.96 bits relative to a matched-N single house.
+  This is the *opposite* of RQ2's motivating hypothesis (that federation grows the
+  anonymity set). The prereg framed RQ2-P1 two-sided precisely so this outcome is
+  reported "with equal prominence" (§6) — it is a genuine negative finding, not a
+  failure to detect. We do **not** re-frame it as federation "helping."
+
+## RQ1-P2 — padding efficacy: inconclusive (padding-ineffective)
+
+- Unit: the run-index-paired bridge-on / no-pad vs bridge-on / +padding arms
+  (RATIFIED stage-05 pairing), one `PairedCircuit` per shared run index (n = **30**
+  paired runs), paired ΔAUC = AUC(no-pad) − AUC(+pad), effective iff CI > 0.
+- **ΔAUC = +0.0113, CI [−0.0025, +0.0234].** CI spans 0 → frozen gate =
+  `padding-ineffective`. raw p = 0.0912, Holm-adjusted p = 0.456 → not rejected.
+- **Interpretation (CONFIRMATORY):** no significant padding effect on measured
+  linkability. This is moot given RQ1-P1 found no leak to suppress, but is reported
+  as the frozen test specifies. The per-run ΔAUC diagnostics (30 values, in the
+  results JSON) straddle zero (range ≈ [−0.080, +0.081]), consistent with the null.
+- Same intractability as RQ1-P1 (each resample pools ~75 k pairs through the O(n²)
+  frozen `auc` twice); the CI uses the bit-faithful `_bootstrap_delta_auc_ci`,
+  `--verify`-checked equal to `stats.bootstrap_ci(units, _delta_auc, bca)` bit-for-bit.
+
+## RQ2-P3 — funnelling mechanism: inconclusive (as-instrumented degeneracy)
+
+- Unit: per bridge-federated circuit — Spearman ρ between top-k = 3 willing-bridge
+  concentration and per-circuit H (frozen `confirm.rq2_p3_funnel`, k = 3;
+  n = 1 500 circuits).
+- **ρ = 0.0000, CI [0.0000, 0.0000]** (percentile fallback) → `inconclusive`.
+- **Interpretation (CONFIRMATORY):** the concentration series has **no variance** —
+  the bridge-federated topology assigns a *fresh* willing bridge per circuit seed, so
+  willing-bridge reuse is minimal and the top-3 concentration is effectively
+  constant. Spearman is undefined on a zero-variance covariate and returns 0. This is
+  the **as-instrumented degeneracy flagged in advance** (stage-05 RQ2 clarification
+  instrument caveat), not a null effect of a well-posed mechanism test. The
+  funnelling mechanism is **not testable** on this instrument as built; we report it
+  as inconclusive and carry the caveat into Limitations rather than over-claiming.
+
+## Multiplicity (Holm–Bonferroni, frozen family size 7, report 4)
+
+Ordered by ascending raw p; multipliers are `7 − k + 1` for reported rank k
+(conservative embedding — the reported RQ1/RQ2 tests occupy the smallest slots of
+the full frozen family; never re-optimised to m = 4). Two tests survive Holm at
+α = 0.05: RQ1-P1 (anomaly-below-chance — *not* a leak) and RQ2-P1 (shrink — a
+negative effect). RQ1-P2 and RQ2-P3 do not.
+
+## Exploratory (labelled EXPLORATORY — not Holm-corrected, not confirmatory)
+
+- **RQ2-P1, bridge-federated-only ΔH** = −3.63 bits (degenerate CI; every resample
+  identical because the bridge-federated per-circuit posterior is near-single-member,
+  m_i ≈ 1). This is the directive's narrower contrast; it is reported only for
+  transparency and reinforces the RQ2-P3 degeneracy note (the bridge-federated arm's
+  anonymity set is near-trivial as instrumented). It carries **no** confirmatory
+  weight and is excluded from the Holm family.
+
+## What this pass did and did not do
+
+- **Ran only the pre-registered tests.** No exploratory subgroup hunting, no
+  re-slicing of cells, no alternative estimators. The one exploratory contrast is
+  labelled and severed from the confirmatory family.
+- **Definitions are the frozen ones.** RQ1-P1 = bridge-on AUC vs 0.5 (D2), *not* the
+  bridge-on−bridge-off contrast paraphrased in the drive prompt; where the two
+  differed, the frozen prereg governs.
+- **Blinding.** This is the first inferential pass; SS2 (raw freeze) computed no
+  AUC/H/CI. The correlator/entropy calibration was fixed on §5 synthetic fixtures
+  only — never fit to confirmatory-cell data.
+- **Reproducibility.** Deterministic (fixed seed); the committed
+  `stage06_run.py --verify` proves the two fast bootstraps equal the frozen
+  `stats.bootstrap_ci` bit-for-bit, so the fast paths introduce no method artifact.