# RESULT — Campaign100 row 040 whitening-robustness

**Tier:** T3-exploratory (basis-robustness / hygiene audit + one candidate gate-fix test).
**Status:** DONE + harvested (harvest agent). CPU-only box run (CVD=""), tmux `c100_040`, 115.6 s audit;
run.log clean, ends `=== 040 done Sun Aug 2 23:40:10 UTC 2026 ===`.
**History (flagged):** this row was DOUBLE-ASSIGNED at t40 — two managers collided; the second yielded
(implementation + smoke gates preserved in `src/_prior_v1/` with `YIELD_NOTE.md`, incl. the t43
kill-server incident, already logged in STATE). The owning manager's t42-repaired run produced `out/`.

## Question
Do the campaign findings NOT covered by 037's anisotropy audit survive a change of basis — raw / center /
ABTT-k (k=1,3,10) / full ZCA whitening / random orthogonal rotation (control)? Headline: is the
021/025 **cosine-gate fabrication blindness** a basis artifact — i.e. does a **whitened** cosine gate
beat the raw cosine gate (AUC on 021's 54 labeled greedy fabrications, n=1500)?

## ★ Verdict — BASIS-ROBUST in the main; whitened-gate fix = CLEAN NULL; one confounded ZCA attenuation
The cosine-gate blindness is **basis-invariant**: no transform improves the gate — whitening makes it
slightly *worse* (raw AUC 0.9220 vs ZCA 0.9108; every Δ within ±0.012, none near the prereg's +0.05
bar). This kills the "the gate is blind because the basis is anisotropic" hypothesis and confirms the
037-based expectation: SONAR z is near-isotropic (EVR top-1 0.033 reconfirmed), so there is almost no
anisotropy for whitening to remove — the blindness is a manifold/self-consistency property. Operator
success (033/034) is unchanged under every invertible transform (whiten-fit-then-map-back algebraic
identity verified to 3.5e-7) and degrades only gracefully under native in-basis refits; geodesic
coherence (032) holds — indeed strengthens — under every transform. The one attenuation: the 028 SAE
length/difficulty axis survives centering and mild PC-removal but drops below the |r|>0.4 bar under
full ZCA in the implemented (off-distribution) variant — confounded, see below.

## Numbers per transform

### (a) Cosine gate — fabrication AUC (n=1500 pairs, 54 fabs; 021 labels_v1)
| mode | raw | center | abtt1 | abtt3 | abtt10 | zca | rot0..4 |
|------|-----|--------|-------|-------|--------|-----|---------|
| AUC | **0.9220** | 0.9203 | 0.9206 | 0.9201 | 0.9195 | 0.9108 | 0.9220 (dev 0.0, exact) |

ΔAUC(best-whitened − raw) = −0.0016 (center); ZCA −0.0112. **No basis fixes the gate.**

### (b) SAE 028 axis — raw-trained SAE fed transformed z (off-distribution variant)
Raw corrs: m90~toklen **0.6306**, m90~density **−0.7255**, eff~toklen **0.7129** (n=1500, p≈0).
| mode | m90~toklen | m90~density | eff~toklen | m90_mean |
|------|-----------:|------------:|-----------:|---------:|
| center | 0.608 | −0.709 | 0.666 | 15.5 |
| abtt1 | 0.597 | −0.708 | 0.668 | 15.4 |
| abtt3 | 0.574 | −0.621 | 0.645 | 16.4 |
| abtt10 | 0.435 | −0.463 | 0.617 | 17.8 |
| zca | **0.313** | **−0.376** | 0.491 | **2.4** |

Axis clearly survives center/abtt1/abtt3; borderline at abtt10; under full ZCA two of three metrics
fall below 0.4 — but m90_mean collapses 15.5→2.4, i.e. the raw-trained SAE is essentially dead on
ZCA-whitened inputs, so this is off-distribution collapse, not a clean flip of the axis. SAE rotation
certificate FAILS (corr → ~−0.05 under rot) — **expected**: SAE features are basis-tied, not
rotation-equivariant; this is an architecture fact, not a campaign-claim flip.

### (c) Operators 033/034 — numeric whiten-fit-then-map-back identity (per prereg, no decodes)
succ_orig **identical** across all invertible transforms (center/zca/rot): rot max dev **3.5e-7**,
invert max err 2.6e-16 — the identity W⁻¹(Wz+Wd)=z+d holds numerically. Native in-basis ZCA refit
(succ_native): tense 0.968, number 0.966, negation 0.959, question 0.956, compose 0.950, 034-negation
0.996 (raw ≈0.98–0.997); voice 0.827, sentiment 0.757 (raw 0.871/0.865); entity 0.496 (raw 0.665 — the
already-weakest operator dips most; consistent with 033's non-linear verdict for entity). ABTT succ_orig
degrades (e.g. 0.93 at k=10) as expected — projection is non-invertible, not a robustness failure.

### (d) Geodesic 032 coherence (150 paths, k=15, nsub=12k)
mean_gap negative (geodesic more coherent) in EVERY mode and monotonically stronger with more
normalization: raw −0.279 → center −0.330 → abtt10 −0.384 → zca −0.452; frac_gap_pos ≤ 0.027 in all
modes; rotation exact-invariant (gap dev 0.0, path Jaccard 1.0). Path identity churns under
non-orthogonal transforms (Jaccard vs raw: center 0.716 → zca 0.515) — the *verdict* is basis-robust,
the specific k-NN paths are not.

## Sanity gates — ALL PASS (owning run) + v1 cross-checks agree
Owning run: G_rot max cos err **1.3e-15**; G_invert max err 2.6e-16; ZCA cov diag mean 0.986 / offdiag
absmax 0.074; EVR top-1 0.0332 (matches 037); `all_pass: true`.
Yielded-v1 smoke gates (independent implementation, `src/_prior_v1/YIELD_NOTE.md`) cross-check:
**G_mu** re-derived μ == 037's aniso_fit μ (max|Δ| 6.5e-10); G_zca exact unit variance (3.6e-15,
full n=29,029); G_rot 1.8e-16; G_encode fresh CPU encode matches 021 stored cos (mean|Δ| 1.6e-6) and
027 z0 cache (rel-L2 2.5e-4); effective rank 1018/1024, whitening condition number 31.6. Two
independent pipelines agree on the shared normalization and rotation-invariance sentinels.

## Predictions (frozen in PREREG_LITE.md) → **Brier**
| id | statement | p | outcome | note |
|----|-----------|---|---------|------|
| a | 022 entropy + 024 prior transform-invariant (trivial survive) | 0.97 | **TRUE** | analytic identity (decoder-token quantities take no z input; both managers' derivation) — NOT empirically re-run by the owning pipeline (deviation, see limitations) |
| b | whitened-cosine gate beats raw by >0.05 AUC | 0.30 | **FALSE** | all Δ ≤ −0.0016; ZCA −0.0112 — clean null, the direction both managers expected |
| c | 028 SAE axis survives whitening, \|r\|>0.4 same sign | 0.80 | **FALSE** (confounded) | under full ZCA m90~toklen 0.313 / m90~density −0.376 fail the bar (eff~toklen 0.491 passes); but only the off-distribution variant was run and m90_mean collapses to 2.4 — evidence-limited negative |
| d | nothing FLIPS (every SURVIVES verdict holds) | 0.72 | **FALSE** | (c)'s ZCA attenuation breaks universality; everything else survives |

**Brier (a–d, scored strictly against PREREG_LITE.md) = 0.3123** (0.0009 + 0.09 + 0.64 + 0.5184)/4.
The cost is concentrated in (c)/(d), both traced to the single confounded ZCA-SAE cell.
Note: `SUMMARY.json` reports an internal `brier: 0.5408` — that is the owning manager's self-score
against its OWN in-code predictions (rotation-invariance-of-everything F because the SAE is not
rotation-equivariant; center-survival T; zero-flips F), **not** against the frozen PREREG_LITE.md.
The harvest scores against the frozen prereg only, per protocol.

## Limitations
- **Double-manager history:** two managers collided on this row; the yielded v1 implementation +
  smoke gates are in `src/_prior_v1/` (YIELD_NOTE.md). Used here only as cross-checks (μ, rotation,
  encode-space) — they agree with the owning run. The t43 `tmux kill-server` incident by the yielded
  manager is already logged in STATE; no relitigating here.
- **Stale v1 smoke files in out/:** `encode.json`, `gate_021.json`, `whiten.json` predate run.log and
  are v1 SMOKE leftovers (n=20, 0 fabs → NaN AUCs in gate_021.json). Do NOT read `gate_021.json` as a
  result; the real per-mode AUCs live in `audit.json:a_cosine_gate`. (`whiten.json`/`encode.json`
  carry the useful v1 gates quoted above.)
- **(c) not tested as pre-registered:** the prereg's PRIMARY SAE test was recon-cosine in the
  whitened METRIC (cos(Wz, Wẑ)) vs length; the run implemented only the declared off-distribution
  caveat variant (raw-trained SAE fed transformed z). The ZCA failure is therefore confounded with
  SAE input-distribution collapse (m90_mean 2.4). The strict FALSE scoring stands (that is what was
  measurable), but the substantive question "does the difficulty axis survive in a whitened metric"
  is unresolved.
- **pcaw{1,10} modes** from the prereg were not run (raw/center/abtt{1,3,10}/zca/rot only).
- **(a) scored analytically**, not by recomputation — near-zero information; excluding it moves the
  Brier from 0.3123 to 0.4161 (a–d→b–d).
- Operator "success" here is the prereg's numeric surrogate (identity + cosine-level agreement), not
  fresh decode-based success; decode-level invariance follows from the identity but was not re-decoded.
- Gate AUC deltas (±0.01) sit on 54 positives / 1500 pairs — well within resampling noise; the null
  claim (no +0.05 jump) is safe, the sign of small deltas is not interpretable.

## Follow-up — Y (narrow)
Run the prereg's primary (c) test — recon-cosine in the whitened metric vs token length — to
deconfound the ZCA-SAE cell (cheap CPU pass over stored z + SAE recons). Beyond that, the row's answer
is complete: basis-dependence is NOT a threat to the campaign's claims (near-isotropy makes basis
choice a second-order concern), and whitening is NOT a fabrication-gate fix — future gate work should
target manifold/self-consistency signals (029/030 line), not reparameterizations.