Ledger intermediate F0 magnitudes on the L359 dirty ray.

[unpaidmoon]

Change and mathematical scope

Scoped scalar ledger. No new κ and no selected-frontier change. Selected κ stays 0.001672660197076918.

On the common-chart scalar projection of the literal reviewed programs.F_0 word, the ray L359 = T with data and private inputs zero reaches intermediate coefficient 128T in data register L103 and 68T in helper L609, then restores the input exactly. The published restoration-preserving cut at event 24438 is only 4T.

The data ray L112 = 1 peaks at coefficient 1 and never writes a helper or private register. A unit injection after the data-peak add (event 24280) leaves 71 helpers dirty, so that site is not the published fault.

||F|| <= 58 in the #2965 completed-output contract is not a bound on these intermediate registers and is not contradicted. Frame annotation 1 is not re-proved here as a constant payload vector, so 128T and 68T are scalar coefficients, not Hilbert norms. No F17 consumer bill is claimed.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main; priority revision 6).
• Head: cc32c9704c9b67649a310c1ce8c17d08f3eb7355.
• Task: joint-query-controller, scope refined.
• Object: one literal F0 scalar projection; rays L359 and L112 only.

The catalogue card asks for an intermediate magnitude ledger of one literal producer, including dirty helpers. This session is the 10th parallel slot. After excluding catalogue tasks whose overlap terms already appear in open PR titles, fewer than ten tasks remain eligible. The tenth slot is a refinement of joint-query-controller. Open PR #3552 already compares four stored final L359 magnitudes with the #2965 tolerance and does not replay the word. This package adds the intermediate peaks and checks that the scalar-projection digest matches #3552's published receipt.

Flag 9's head-step repair in PR #4107 is a different card and was not repeated.

Validation

CPython 3.12.3, standard library only:

python3.12 -B research/qq16-f0-dirty-ray-magnitude/verify.py
python3.12 -B research/qq16-f0-dirty-ray-magnitude/test_verify.py
python3.12 -B scripts/research_package.py --package research/qq16-f0-dirty-ray-magnitude

Observed: PASS_QQ16_F0_DIRTY_RAY_MAGNITUDE, PASS_QQ16_F0_DIRTY_RAY_MAGNITUDE_TESTS groups=3, and PASS_REGISTERED_RESEARCH_PACKAGE ... outcome=completed.

Dense and sparse forward scans agree. The tests cover a synthetic three-operation word and a mutation of the peak coefficient from 64 to 63. The literal scan is finite and exact on this projection; it is not a physical-frame proof or an all-helper range. Native 512-vector replay, Lean, and the selected cold replay were not run.

Credit

The F0 word is the reviewed joint-query program (Ali Romman and the joint-query lineage). Arham Tahir's research/qq16-producer-dirty-fault supplies the expansion, the cut (-4, 1), and the final-defect formula this ledger does not replace. Nick Petalas's #2965 contract supplies ||F|| <= 58 and the open producer-interior question. Tekalign's research/qq16-native-dirty-fault is the frame-vector predecessor and is not replayed. jwr404's open PR #3552 is the final-magnitude comparison distinguished above.

Prepared by unpaidmoon, with substantial assistance from Grok 4.7 in Cursor. Apache-2.0.

Open next questions

1. Do frame annotations 1 at events 24280 and 24338 denote the constant payload vector, so the Hilbert norms are exactly 128T and 68T? Bind those two events to the frame-1 vector already checked by research/qq16-native-dirty-fault. This package does not load native recipes.
2. Is register 359 special, or does another helper force an intermediate data coefficient at least this large? Repeat the sparse scan on one other helper. Only 359 was scanned.

Workflow feedback (optional)

Handoff-first selection is right, but the weighted picker is random and most catalogue overlap terms already hit some open PR title, so ten parallel sessions do not get ten disjoint cards without a published eligible-list snapshot. A short machine-readable list of uncovered open questions, refreshed with the overlap cache, would remove that guess.