[unpaidmoon]

Change and mathematical scope

Independent operator check. No new κ. The selected conditional result is unchanged.

On the literal mode-0 word in the merged deferred-K component, K^{-1} X_1 K = -X_7 on all 512 computational basis states. Bare axis-0 Q sends |0⟩ to a|0⟩ + b|1⟩. The same Q wrapped by this K sends |0⟩ to a|0⟩ - b|7⟩. With rightmost-first composition, full nine-axis R equals D Q, where Q is one positive C on axis 0 and D is the positive C product on axes 1 through 8. This K commutes with R and does not commute with bare Q. Source-axis embedding [0,9,10,11,12,13,14,15,16] sends local mask 7 to global mask 1537.

This recomputes a witness the component checker recorded as inherited and not evaluated by an engine. It does not install Q120, emit a global occurrence ledger, or fund the eight-H1 overlay.

Task and overlap

• Base: 32890bc5de034ab8fc93ac88ead7279a6a416d04 (upstream CrocSwap/integer-mult-bounds main).
• Catalogue card: independent-moment, scope changed. The taken handoff is discussion comment 19160035 (deferred-k-global-invoice): inspect the literal correction and source-phase Q placement before any global ledger.
• Nearest work: merged Save eight H1 queries with a verified deferred-K correction (no new κ) CrocSwap/integer-mult-bounds#5423, which states the counterexample and explicitly does not recompute it. No open PR retitled this operator check.
• Eligible-list item 16 after dropping four delivered structured Handoffs and requests for independent checks CrocSwap/integer-mult-bounds#1166 handoffs (typed actual-width H; the uniform truncated-source estimate; the PR2250 Compact ADD overlap closure; the one-slot centre Gram degree closed by merged Prove exact degree 881 for the one-slot doubled centre Gram CrocSwap/integer-mult-bounds#5168). The ordered list is in the session report.

Validation

python3 scripts/research_package.py --package research/deferred-k-q-placement-audit --check-only
python3 -B scripts/research_package.py --package research/deferred-k-q-placement-audit

Both normal and optimized modes printed PASS_DEFERRED_K_Q_PLACEMENT. The failure control clears one linear phase and no longer yields -|7⟩. Native, phase-table, emitter, and economics replays were not run. One mode took about one minute on CPython 3.12.

Credit

Chris R / Clear1nsight, PR CrocSwap#5423, and the pinned BALANCED-J-CURRENT-Q-FRAME-audit report own the component and the inherited reading of Km0. Dillon Amburgey / dillona CrocSwap#5402, Ali Romman CrocSwap#5411, zxv CrocSwap#5419, and the native, helper, and precision authors named in that package retain their credit.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

Can a version-correct global occurrence ledger fund a gain from the eight-H1 overlay? The component still needs at least 28 further H1 deletions or genuine reuses at C = .00330007 if only H1 counts change, and the standalone profile loses for every 0 < C < 1. The blocker is the missing caller ledger. The helper/owned raw inverse-transpose is a separate open emission.

Workflow feedback (optional)

The fork's main does not contain upstream 32890bc5d, so this draft compares against cursor/upstream-main-32890bc-508c, which is that exact commit.