Iteration 7 — k-of-N: Parametric Variant Killed by Its Own Null

Iteration 7 — k-of-N: Parametric Variant Killed by Its Own Null · "Nothing Is Invariant" Reinterpreted 1 KILL 1 MAJOR FINDING

What happened in this iteration, in plain words: we built the instrument the statuses have been waiting for — one that asks, per feature, "in HOW MANY of the 10 market regimes does your relationship hold?" (instead of the old all-or-nothing question). Then the lab's own safety net caught it cheating: fed real data with the regime structure deliberately destroyed, the instrument still shouted "regime break!" almost everywhere — a truth-teller must go quiet there. A precision probe showed exactly why: the textbook test it used is fine on homogeneous data (calibrated to within half a percent) but breaks when one side of the comparison is a blend of nine different regimes. So the first version of the instrument is dead — killed at the assumptions gate by its own control, mechanism identified, replacement designed (calibrate each feature against its own shuffled-regime distribution). Kills are wins. And on the way we found something bigger: the campaign's headline "nothing is regime-invariant (0 of 92)" turns out to be the wrong reading of the instrument. Cracking open the invariance engine shows that for all 100 features it never actually rejected invariance — it just couldn't identify which anchor combination is the invariant one (many candidates pass, they don't overlap). "Nothing is invariant" becomes "nothing is identified" — a very different scientific claim that reshapes the STABLE-ceiling question.

Preflight (A0)

2026-07-03 10:19 UTC — load1 4.81 / 32 cores (≤24) · no competing nasimubd jobs · 21 GiB available, si/so=0 · clickhouse-server active · sidecar active + /health healthy → ALL PASS. Runs: two capped read-only spikes (0.26 min + probe), readonly=2, 5c/5G scope, pre-authorized (03b), zero synthetic values (03c). SSoT maintenance: rule 3e (no-synthetic) folded into LOOP-PROMPT.md's PROMPT block (was in the running loop, missing from the file).

Part 1 — the kill: parametric Chow k-of-N dies at M2, caught by its own null

THE INSTRUMENT: per feature f, per regime e — coefficient-equality F-test (anchors → f) between env e and the pooled REST of the envs. k(f) = #regimes where the relationship holds. α=0.05 (G3), BH q=0.10 (G11). All conventions inherited, no new knobs. MEASURED (real envs): mean k = 1.88 of 10 (k_BH = 0.77) MATCHED NULL (env structure destroyed by permuting REAL rows): mean k = 1.91 of 10 ← MUST have been ≈10. FAIL. │ VERIFY-BEFORE-REPORT PROBE (single env, random halves — pure exchangeability): rejection rate 4.57% at nominal 5% → TEST IS CALIBRATED │ MECHANISM (by elimination): not heavy tails, not the harness — the e-vs-REST design itself: "rest" = a 9-REGIME MIXTURE; mixture heteroskedasticity violates the F-test's iid-error assumption → over-rejection BY CONSTRUCTION on any multi-regime panel. ▼ VERDICT: EXCLUDE(TEXTBOOK-ONLY) at M2 — LEDGER row 9, BONEYARD entry. Per §0: its counts may be reported, never gated. SUCCESSOR (next Frontier #2 slice): permutation-calibrated per-feature k-of-N — each feature's Chow statistic judged against its OWN env-shuffle permutation distribution: matched null by construction, no distributional assumptions.

Part 2 — the finding: "ICP 0/92" is an identification failure, not an invariance rejection

The admitted wiring reads len(estimate) — the INTERSECTION of all accepted anchor-subsets. Zero can mean two OPPOSITE things: (a) NO subset accepted → invariance genuinely rejected (b) MANY subsets accepted, → invariance NOT rejected; intersection empty the invariant set is UNIDENTIFIED This iteration extracted the accepted-sets family itself, all 100 features: rejected_everywhere: 0 unidentified_nonempty_family: 100 ← EVERY feature is case (b) identified: 0 CORRECT READING of the committed campaign evidence: "0/92 regime-invariant" → "0/92 IDENTIFIED; invariance rejected for NONE" Practical consequence unchanged (declarations stay regime-conditional). Scientific consequence large: the STABLE ceiling may be an IDENTTIFIABILITY limit, not an absence of invariance — Frontier #3 (F014) now carries both questions, converging with the NP-hardness/ε-frontier reframe already on file.

Technical record

Item	Value
Frontier item	#2 per-environment k-of-N (crypto) — bounded slice 1 of the successor design
Harnesses	`k_of_n_invariance_crypto.py` (measurement + disambiguation + null) · `k_of_n_size_probe.py` (calibration probe) — both capped, readonly=2, real rows only
Ledger rows	9 (ADMISSION → EXCLUDE(TEXTBOOK-ONLY) at M2, parametric variant — kill recorded proudly) · 10 (NOTE — evidence reinterpretation of the committed 0/92)
BONEYARD	parametric Chow e-vs-rest k-of-N, with revisit path = permutation-calibrated successor
Conventions	α=0.05 (G3) · BH q=0.10 (G11) · anchors/act[:4]/target standardization mirrored from the admitted v3 wiring — zero new magic numbers
Numbers	real mean k 1.88 · null mean k 1.91 (fail) · single-env calibration 4.57% @ 5% (pass) · accepted-family disambiguation 0/100/0 (rejected/unidentified/identified) · wall 0.26 min + probe
Forex note	the reinterpretation presumably applies to iteration 6's forex zeros too — verification rides the full-grid slice
Compute / prod impact	two sub-minute capped spikes · ~11 readonly=2 SELECTs · zero writes outside audit folder + dashboard

Item

Value

Frontier item

#2 per-environment k-of-N (crypto) — bounded slice 1 of the successor design

Harnesses

k_of_n_invariance_crypto.py (measurement + disambiguation + null) · k_of_n_size_probe.py (calibration probe) — both capped, readonly=2, real rows only

Ledger rows

9 (ADMISSION → EXCLUDE(TEXTBOOK-ONLY) at M2, parametric variant — kill recorded proudly) · 10 (NOTE — evidence reinterpretation of the committed 0/92)

BONEYARD

parametric Chow e-vs-rest k-of-N, with revisit path = permutation-calibrated successor

Conventions

α=0.05 (G3) · BH q=0.10 (G11) · anchors/act[:4]/target standardization mirrored from the admitted v3 wiring — zero new magic numbers

Numbers

real mean k 1.88 · null mean k 1.91 (fail) · single-env calibration 4.57% @ 5% (pass) · accepted-family disambiguation 0/100/0 (rejected/unidentified/identified) · wall 0.26 min + probe

Forex note

the reinterpretation presumably applies to iteration 6's forex zeros too — verification rides the full-grid slice

Compute / prod impact

two sub-minute capped spikes · ~11 readonly=2 SELECTs · zero writes outside audit folder + dashboard

▶ Next iteration

Iteration 8 = Frontier #2, successor slice: the permutation-calibrated k-of-N. In plain words: same question ("in how many regimes does each feature's relationship hold?"), but each feature's regime-break score is now judged against that feature's own shuffled-regime distribution — a built-in lie detector for every single measurement, immune to the mixture problem that killed version 1. Technically: per feature, Chow statistic per env vs its env-shuffle permutation distribution (real rows only, ~200 draws), permutation p-values → k(f) at α=0.05, BH q=0.10 panel summary; the env-destroyed global null must now read k≈N (the successor's acceptance test); runtime estimate ~40–90s capped. If it passes its own null, the FRAGILE↔CONDITIONAL split becomes measurable and the instrument enters the ladder for admission. Steering alternatives: full forex grid extension (fix-plan step 6), or jump to Frontier #3 (F014 — now sharpened by the identifiability finding).

Iteration 7 · 2026-07-03 · Frontier #2 slice 1: parametric variant killed at M2 by its own matched null + committed-evidence reinterpretation · capped read-only · zero synthetic data · append-only