iter 2 — A7: negative-control null calibration

BREAKS → DEFENDED → CLOSED  2026-07-10 · attack A7 · 62/62 cells · 1,302 shuffle draws + 4,340 shift draws · two estimator defects found in chatterjee_xi, fixed in both probe files, attack re-run clean · consecutive-clean counter reset to 0

Claim under attack (assumed true only to destroy it)

On the probe's substrate (stride-20 value-rows, recent-80k fetch), permutation nulls of REAL columns collapse the probe's statistics to ≈0 — no null draw comes near a frozen decision line, so xi_worst / breadth / rho_worst cannot be contaminated by spurious dependence. (KB §6: "permute a real column → ξ,ρ collapse to ≈0".)

Falsifiers (pre-declared; frozen lines quoted, never retuned)

• F1 plain-shuffle null: any |ξ| > 0.10 — 10σ of the theoretical independence null √n·ξ→N(0, 2/5) at n≈3990 (KB §1)
• F2 circular-shift null: any ξ ≥ 0.50 (frozen §B PASS/breadth line)
• F3 circular-shift null: any |ρ| ≥ 0.85 (frozen WATCH line)

Null constructions use REAL rows only: shuffle = hash-based deterministic permutation (argsort of sha256(key|i)); shift = np.roll by 10 deterministic offsets (preserves marginals AND autocorrelation — the sharper null for the documented overlap-inflation failure mode).

ATTACK RESULT — 29 breaches (all F1)

Every breach sits on the one heavy-ties integer pair (715 distinct values / 3,990 rows). A FULLY PERMUTED real column — zero dependence by construction — read ξ up to 0.25: the estimator, not the data.

Diagnostic — two estimator defects isolated

Direction-split null on the worst cell (a7_diagnostic.json, 50 draws/direction):

1. Wrong tie ranks. chatterjee_xi used rank(method="average"). Chatterjee's tie-correct estimator requires max-ranks: r_i = #{j: y_j ≤ y_i}, l_i = #{j: y_j ≥ y_i}. Exact worked case: for a permuted binary column (n/2 zeros, n/2 ones), average-ranks give ξ → 1 − (n·n²/4)/(3n³/8) = 1/3 at the null; max-ranks give exactly 0.
2. Stable tie-breaking leaks time. np.argsort(x, kind="mergesort") keeps tied-x rows in TEMPORAL order. The definition requires x-ties broken uniformly at random. With autocorrelated y (all count series here), within-tie y-ranks are adjacent → Σ|Δr| shrinks → ξ inflates. This is the +0.244 bias: it appears exactly when x is permuted (ties everywhere) and y is the real, autocorrelated series — and it equally inflates ξ for ANY real pair with tied x and autocorrelated y.

DEFENSE (mechanism only — no band touched)

- r  = rank(yo, "average")            + r  = rank(yo, "max")            # Chatterjee tie-correct
- li = rank(-yo, "average")           + li = rank(-yo, "max")
- order = argsort(x, "mergesort")     + tiebreak = (arange(n)·2654435761) & 0xFFFFFFFF   # Knuth hash
                                      + order = lexsort((tiebreak, x))   # scattered, deterministic, no rng

Applied in lockstep to BOTH probe files (rotation_robust_eval.py, rotating_slice_orthogonality_probe.py — duplicate implementations).

Proof the defense closes the gap

Evidence (every claim above cites these)

Consequence

A real estimator defect — invisible to iter 1's worked-example gate (true duplicates read ξ≈1 under any tie handling) — is found, mechanically explained, fixed in both probe files, and pinned by a regression test. The convergence counter resets: clean rounds 0 of 3.

Open threads

• 750-dbps thin-substrate thread (opened iter 1) — still open; all 750 cells were grounded and clean in both A5/A7 at 80k-bar fetch; the thin-fetch variant remains unattacked.
• A1 metamorphic invariants · A3 block-length · A2 low-power blind spot · A4 cluster bootstrap — unattacked.

iter 2 · attack A7 · verdict BREAKS → DEFENDED → CLOSED · one atomic commit: iter 2: A7 negative-control null calibration — BREAKS→DEFENDED · append-only.