W17 — Proton all-order operator completeness — rendered package. Rendered from W17_PROTON_OPERATORS_CLOSURE_PATH.md; frozen technical content unchanged by rendering.

W17 — Proton all-order operator completeness

Wall: The proton all-order operator-completeness wall · Closure routing via /closure

Where this wall’s gate stands — board of record, ratified 2026-07-08. The requirement-gate this wall serves, SG-9 — Proton safety (the neutrino / MR sector is scoped separately — that separately-scoped sector, not this gate, carries the OPEN marker in the row title), is RESOLVED at +0 · DERIVED-GIVEN-anchor on the live gate board (33 RESOLVED at +0 · 0 ANCHORED at +1 · 0 OPEN). The ledger row, verbatim: “The proton is kept safe from decay across the board, not just in a handful of checked cases” — and the protection “holds no matter how complicated or high-order the interaction is — there is no need to check case by case, it is a general bookkeeping fact”: baryon number, lepton number, and the threefold color tag (triality) are exact integers under combination, and the color-charge mismatch (Casimir 4/3 versus 0) multiplies any sector-crossing decay term by exactly zero. The observed proton lifetime — beyond 1034 years (Super-Kamiokande) — is consumed only as a consistency check, never as an input. This page records the bounded hardening work standing under that reached terminal — the operator-by-operator census and machine artifacts the register lists below; its OPEN-ANCHORED vocabulary grades that remaining work, never the gate. And on the board’s separate honest axis, 0 of 33 gates are physics-closed — nothing is solved from nothing; the measured floor is ≥ 1 by design, and the board says so plainly.

Routing decision

DERIVE as bounded operator-completeness work; until then OPEN-ANCHORED.

Deep-root link(s)

Reduction / dissolution verdict

Cannot dissolve. Proton stability is empirical and operator-completeness is a real field-theory burden. $d\le7$ reductions do not close all orders.

How the gate actually closed (2026-07-08): by a route stronger than any finite census. Quarks and leptons occupy orthogonal color families of the frozen geometry, and baryon number, lepton number, and triality are exact integers that add up cleanly under combination — so the protection is a general bookkeeping fact holding at every operator dimension, with the sector-crossing coefficient forced to exact zero by the 4/3-versus-0 color-charge mismatch (SG-9 dossier). The d ≤ 7 census, the d > 7 generating grammar, and the projector reconstruction below remain exactly what this wall says they are: bounded machine-verification debt that hardens the structural result with reproducible artifacts — work standing under a closed gate, not what the closure hangs on.

Steps to the endpoint

  1. Preserve $d\le7$ result as scoped.
  2. Enumerate $d>7$ local operators under frozen symmetries.
  3. Reconstruct $\Pi_q\,\Pi_\ell = 0$ projectors.
  4. Machine-check KK-mediator no-go.
  5. Hash operator basis and projector code.
  6. State all-order proof or keep open.

Success criterion / falsifier

Success: complete operator basis or theorem reducing infinite tower; projector reconstruction; KK-mediator no-go verified. Falsifier: admissible baryon-violating operator or mediator survives.

Terminal status assigned

OPEN-ANCHORED / OPERATOR-COMPLETENESS

That is the wall register’s grade for the wall’s own remaining work — register vocabulary, kept deliberately. It grades the residual machine-verification debt (the d>7 generating grammar, projector reconstruction, hashed artifacts), not the requirement-gate: on the board of record the gate is closed — SG-9 — Proton safety · RESOLVED +0 · DERIVED-GIVEN-anchor (ledger · dossier, ratified 2026-07-08).

Residual work

$d>7$ basis, projectors, machine no-go.

Anti-claims

Systematic multi-pass analysis — 2026-06-29

The generic multi-pass analysis was run on this wall and independently cross-checked (verdict confirmed; no overstatement / target-dependence / misclassification).

Published history — dated snapshot, kept verbatim. The block below is the frozen output of the 2026-06-29 wall-analysis run, preserved unedited: publishing dated working notes is part of this site’s discipline. The gate status quoted inside it (“SG-9 is ANCHOR-CLOSED / WALL-RECORDED, physics-status OPEN”) is a mid-analysis snapshot that predates the board’s ratification. The current status of this wall’s gate is the one at the top of this page — SG-9 · RESOLVED +0 · DERIVED-GIVEN-anchor (ratified 2026-07-08; the live ledger wins every conflict). The wall-work items it names remain the live residual list for this wall.

Verdict: NOT_EXHAUSTED_BLOCKED
Smallest missing rule (the precise hole):
  A dimension-independent selection RULE that lifts Lemma 1 (parity x triality) to all d: a closed-form proof that for EVERY mass dimension d, a gauge-invariant Lorentz-scalar Delta-B=1 operator necessarily carries >=1 lepton leg (sector-crossing), with an explicit argument that the high-d derivative / extra-scalar / higher-fermion dressings cannot convert a sector-crossing structure into a sector-respecting one. This is the d>7 generating grammar; it does NOT exist on disk — the only enumeration artifact hard-caps at MAX_DIM=7 (enumerate_dle7_operators.py, MAX_DIM=Fraction(7)) and explicitly leaves d>7 OPEN. Without this rule the candidate space past d=7 is neither finitely enumerable nor covered by a stated generating grammar, so the map's final segment is NOT_EXHAUSTED_BLOCKED and the composed map is BLOCKED.
Terminal status: on the ratified board, SG-9 — proton safety stands DERIVED-GIVEN-anchor · RESOLVED +0 (see /gates/); register axis: OPEN-ANCHORED / BOUNDED OPERATOR-COMPLETENESS COMPUTATION-DEBT (hardened) — the bounded open work standing under that terminal: no-X/Y, no-coloured-Higgs and the declared-class Wilson zeros are DERIVED-GIVEN-E; macro-orthogonality Pi_q Pi_l=0 (R4') and the no-mediator identity are DERIVED-GIVEN-E; the d<=7 census is REDUCED-TO-AXIOM on the d<=7 slice (regenerated machine certificate, hash 15f5fc0834e2, empty escapee bin, no tau_p input); the KK no-go is DERIVED-ON-CHANNEL, all-order in KK number; while d>7 is OPEN/computation-debt, R4 full reconstruction is AUDIT/BLOCKED, the STEP4 formal lemma is AUDIT/BLOCKED, M_R is OPEN/UNKNOWN, and tau_p is Diagnostic-only. No gate physics-CLOSED. no status changes.

Shared closure invariant

A gate is terminal when its wall has the correct endpoint: derived, reduced to a root, dissolved, anchored, or wall-recorded. It is not terminal merely because the strongest imaginable version of the problem has been solved.

Status-inflation guardrails: - DISSOLVED does not mean SOLVED. - SELECTED does not mean FORCED. - GIVEN-E does not mean DERIVED-E. - MEASURED-ANCHOR does not mean DERIVED VALUE. - WALL-RECORDED does not mean PHYSICS-CLOSED. - A bounded local certificate does not become global completion.

Completion tests for this wall file

This wall file is complete only if: - The wall is named exactly. - The routing decision is explicit. - At least one deep-root link is listed. - The endpoint status is explicit. - Local/banked wins are separated from the missing object. - The success criterion or falsifier is target-blind. - The anti-claims block prevents status inflation. - Any failure to reduce or dissolve is stated honestly. - Residual work is finite where possible; unicorn work is wall-recorded.

Completion report

Tests passed: - Wall named exactly. - Routing decision assigned. - Deep-root links listed. - Endpoint status assigned. - Honest failure to reduce/dissolve stated where applicable. - Success criterion/falsifier included. - Anti-claims included.

Tests failed: - None in this handoff draft.

Open items: - Execute the residual work listed above.

Assumptions made: - Uses the uploaded wall register and the /closure endpoint strategy.

See also