Chatterjee ξ threshold calibration

Provenance trace (sibling audit `2026-06-26-rotation-probe-meta-evaluation-audit`, `MEDIAN-VS-WORST-REGIME.md`) found the ξ 0.50 cut is **our** effect-size declaration — NOT from the Chatterjee (2021) paper and NOT from Terry's `CH_FEATURE_BANLIST` (which only authorizes the Spearman 0.95 / 0.85 and h_norm 0.05 cuts).

Grounded: crypto 600/620 + forex 166/190 cell-slices → 5,229 pairs (5,153 feature-only).

- **PASS / orthogonal: ξ < 0.30** — the independent mass (82.5% of pairs); strong support. - **WATCH: 0.30 ≤ ξ ≤ 0.95** — watchlist (document + re-probe; don't auto-ban).

3,355 pairs (65.1%). - **WATCH: everything else** — the moat + smooth middle; document + re-probe. 1,568 (30.4%). - **BAN: `xi_worst > 0.95 AND breadth ≥ 0.80`** — two-dial, data-forced (raw worst-cell separation 0.0001); breadth cut at the empty-valley edge.

**cluster boundary** — just above the certified-orthogonal ceiling (top frozen known-orthogonal pair = 0.494); 0.43-wide empty moat to the nearest known-related pair (0.923); corroborated by independent-mass p75 = 0.469

**BAN gained a second dial** (`breadth = share of cell-slices with ξ ≥ 0.50`). Data-forced: > raw worst-cell separation between the dup floor (0.9995) and the independent tail (0.9994) > is 0.0001 — a single-number BAN line does not exist on this axis

(the §7 expected-shape > statement was contradicted, and per its own terms the contradiction was surfaced, not hidden).

**Consistency gate** (G2): v2 median tiers vs committed tiers — **0 band changes / 5,229 pairs**, max \|Δξ\| 0.0092. The §A declaration's "does not move the tiers" claim converted from assertion to verified fact

**Worst-axis sanity** (G3): all 5 mechanism dups read `xi_worst ≥ 0.9995`, distinct anchors low — instrument trusted on the new axis

(spoke 06: reading §A on worst-cell ξ > would evict 2,130 of 4,250 median-PASS pairs and false-BAN 63).

**Safety check (superset property):** the §B BAN captures **all 50** §A BAN pairs (0 missed) and adds **180** genuinely broad-redundancy pairs (bad in ≥ 80% of windows) that the median statistic diluted below its own BAN line

The median rule contradicts the standing banlist; the worst-cell rule agrees with it. A promotion gate that un-bans declared bans is disqualified on its face.

| `price_impact` ↔ `volume` (crypto) — **a frozen KNOWN-RELATED labeled pair (P2, ρ = 0.9872)** | 0.880 → WATCH | 0.998 | 600/600 |

Terry's ρ-declared Tier-1 duplicates reappear in the ξ > 0.95 cluster — two independent metrics agree on what is a duplicate: - `garman_klass_vol ≡ intra_garman_klass_vol` (ρ banlist Tier-1) → ξ = 1.00

**Sensitivity (reported, cuts not tuned on it):** BAN count under breadth cut 0.80/0.85/0.90/0.95/1.00 = 230/217/186/172/159; under ξ cut 0.90/0.93/0.95/0.97/0.99 (breadth ≥ 0.90 held) = 261/213/186/105/58. Smooth in both directions — no knife-edge.

the two-dial BAN structure, the 0.80 valley edge, the 0.50 cluster boundary, and the WATCH residual are **empirically anchored**. The 0.95 value is an **anchored convention** (any cut in 0.95–0.99 clears the dup cluster; 0.95 chosen for ρ-gate consistency). Nothing here is presented as derived that is chosen.

- `ofi ≡ turnover_imbalance` → expect **ξ ≈ 1.0** (functional dup). - `ofi ~ kyle_lambda_proxy` → expect **ξ low**. If the dup isn't ≈1 or the distinct pair isn't low ⇒ pipeline wrong ⇒ STOP.

We are **not** using a labeled-set / ROC / permutation-null calibration — those were dropped 2026-06-30 per operator decision (they were the AI's additions, not Terry's method).

**Reconsider-when (§B):** the PASS anchor rests on **three** certified-orthogonal pairs — real but thin. If a future **pre-registered, frozen-before-measurement** label expansion moves the certified-orthogonal ceiling, the 0.50 line re-anchors to the new boundary.

## §6 — What this spoke does NOT authorize - Wiring §B into the live ξ gate (`multislice` 0.50 cut) — separate follow-up, operator-gated.