Iteration 70 — H-056 Betting Passes the Entrance Exam on the First Form: the Wealth Identity Is Estimator-Clean

Iteration 70 — H-056 Betting Passes the Entrance Exam EXAM PASS (FIRST FORM) · MMD-SHADOW FIGHT NEXT

In plain words: the next candidate answers the same question as the just-certified kernel distance — "does this feature's distribution differ between regimes?" — but as a GAMBLER instead of a surveyor: it starts with wealth 1 and continuously bets on the difference between the two samples; honest odds guarantee that if there is no difference, wealth cannot grow beyond luck, so accumulated wealth IS the evidence, valid at every moment with no fixed sample size. Its exam had a beautiful property the kernel distance lacked: handed a series and its byte-twin, the gambler finds nothing to bet on and its wealth stays at exactly 1.0 — no estimator quirk, no corrected second form needed. On real regime pairs it got rich fast: wealth 405 to 43 million (the rejection bar is 20), calling the difference as early as 110 pairs into a 1,500-pair stream — the "anytime" advantage on display. One shadow hangs over the ladder, named before the fight: it answers the SAME question as certificate #13, and echoes die at the redundancy gate. Also on record: the reference code ships without a license, so everything was rebuilt from the paper, zero code reuse.

Preflight (A0): 2026-07-10 15:25 — load1 3.86/32c (≤24, falling vs load15 4.46) · one 1-core external python job (under the >2-core bar) · 22 GiB avail, si/so≈0 · clickhouse-server + opendeviationbar-sidecar + kintsugi + fxview-sidecar all active → ALL PASS. Sync: main up-to-date, worktree 0 behind. One capped run (0.39 min), readonly=2 loader, e-process anchor — zero permutations needed.

Exam results (betting_exam.py — clean-room from arXiv:2112.09162, zero code reuse)

Leg	Reading	Ruling
E1 — the certain zero point	Twin vs duration on the same rows: payoff identically 0 ⇒ final wealth == 1.0 bit-exactly in all 3 envs — the multiplicative identity has no analogue of the U-statistic bias that felled MMD's form v1 (row 78)	PASS (estimator-clean)
E2 — gauge consistency	Wealth paths of (twin_A vs dur_B) and (dur_A vs dur_B) bit-equal on all 3 regime pairs	PASS
E3 — the boundary role + the paper-native anchor (Ville, α=0.05 ⇒ bar = wealth 20)	gold↔covid 405 (crossed at pair 110) · gold↔midcycle 4.4×10⁵ (336) · midcycle↔covid 4.3×10⁷ (538) — anytime-valid rejection long before the stream ends	PASS
Dial audit	Bandwidth derived AND predictable (med_bw on burn-in only — the Ville guarantee stays honest) · burn-in derived ⌈√N⌉=39 · ONS constants paper-native · α campaign standard	ZERO DIALS
Provenance	Reference repo has NO license file — flagged by the feed, honored here: clean-room construction from the paper under the H0 S3 escape	CAUTION RECORDED
Verdict (row 81)	EXAM PASS (first form) — ladder walk unlocked; the decisive fight is named

Leg

Reading

Ruling

E1 — the certain zero point

Twin vs duration on the same rows: payoff identically 0 ⇒ final wealth == 1.0 bit-exactly in all 3 envs — the multiplicative identity has no analogue of the U-statistic bias that felled MMD's form v1 (row 78)

PASS (estimator-clean)

E2 — gauge consistency

Wealth paths of (twin_A vs dur_B) and (dur_A vs dur_B) bit-equal on all 3 regime pairs

PASS

E3 — the boundary role + the paper-native anchor (Ville, α=0.05 ⇒ bar = wealth 20)

gold↔covid 405 (crossed at pair 110) · gold↔midcycle 4.4×10⁵ (336) · midcycle↔covid 4.3×10⁷ (538) — anytime-valid rejection long before the stream ends

PASS

Dial audit

Bandwidth derived AND predictable (med_bw on burn-in only — the Ville guarantee stays honest) · burn-in derived ⌈√N⌉=39 · ONS constants paper-native · α campaign standard

ZERO DIALS

Provenance

Reference repo has NO license file — flagged by the feed, honored here: clean-room construction from the paper under the H0 S3 escape

CAUTION RECORDED

Verdict (row 81)

EXAM PASS (first form) — ladder walk unlocked; the decisive fight is named

▶ Next iteration

Next firing: H-056 M3 census over the 130-subject grid — per-feature readout = final log-wealth of the betting test averaged over cross-regime pairs (prequential, derived bandwidth per feature). The DECISIVE pre-registered check is the MMD shadow: certificate #13 answers the same boundary question with a different engine — |ρ| ≥ 0.95 vs the MMD readout and the echo dies at the redundancy gate (the H-053 oracle-shadow precedent). Also standard: k_v incumbent, IPP/calgap cousins, corpse affinity, dial law. Clear → M4/M5′; fail → BONEYARD, B-04 advances to H-074 LGC-switch. Standing for the operator: the M4-bar question (row 80), the H-062 proposal (row 76), the inverted-mechanism investigation (5 corroborations), the 73 cycle-1 drafts, the Frontier #4 review, the STABLE-declaration proposal, and PR #599.

Iteration 70 · 2026-07-10 · CHECKPOINT (row 81) — H-056 EXAM PASS · capped (0.39 min) · readonly=2 · zero generated values · zero code reuse (no-license clean-room) · append-only · evidence: betting_exam.py · betting_exam_results.json

Iteration 70 — H-056 Betting Passes the Entrance Exam EXAM PASS (FIRST FORM) · MMD-SHADOW FIGHT NEXT

Exam results (betting_exam.py — clean-room from arXiv:2112.09162, zero code reuse)

▶ Next iteration

Exam results (`betting_exam.py` — clean-room from arXiv:2112.09162, zero code reuse)