[unpaidmoon]

Change and mathematical scope

Scoped route obstruction on the PR #5708 word. No new κ. Selected κ stays 781451/250000000.

The published route table has 2369 edges. Every edge drops frame dimension, and the rank equals that drop. Frame 1 is the only dimension-8 frame and has indegree 0, so a conversion and its inverse do not both emit. There is no route-legal two-query paid/target delta.

Helper 222 starts on frame 1. Events 5638 through 5643 are ADDs declared on frame 1. Those ADDs are ill-typed after any published exit, because no route returns to frame 1.

At the opening cut, each of the 413 public helpers is a one-field carrier of boundary rank 1 and internal rank 1. Frame 1 has 189 empty compatible exits, 9 of rank 1 and 180 of rank 2. The edge (1, 517, 1) creates that singleton channel and then leaves the six ADDs ill-typed. It is not a completed word.

No non-member field has an odd singleton pairing at any cut. Across published exits into occupied compatible banks, 2650155 span-admitted pairings keep boundary rank 0. An off-route move of field 208 from frame 622 into frame 509 raises boundary rank from 0 to 1, and that edge is not in the route table.

Task and overlap

Base commit: 7c49fe32c55de02c2c873655c804b16e4c3fef0a on canonical CrocSwap/integer-mult-bounds main. Priority revision 8. Catalogue card bit-helper-contract. Scope status: refined.

The card asks whether a changed G20 path improves the complete BIT moment. This package does not build a new word. It answers the paid frame-conversion question left by Nick Petalas's free-carrier certificate on the same PR #5708 word.

Session r78, item 1 of the ordered eligible list. The 19 October handoffs are closed. Later handoffs whose artifact is an open pull request, including the H25 requests and the PR #6353/#6361 chain, are excluded. The remaining list is the revision-8 first-mention open questions of #5679, #5708, #5718, #5615, and #5717, after dropping delivered items:

1. This package. Split one G20 helper into independent rank4 jobs at ordinary BIT saving 0.003507410738409 #5679's different physical role. The common-frame part is already certified. The paid conversion and its inverse were open.
2. Split one G20 helper into independent rank4 jobs at ordinary BIT saving 0.003507410738409 #5679: another paid-query removal on the changed split word.
3. Split one G20 helper into independent rank4 jobs at ordinary BIT saving 0.003507410738409 #5679: a stronger Gaussian caller for that BIT component.
4. Raise G20 ordinary BIT saving to0.003507719059749 with scalar conjugations #5708: a noncoordinate public input contract.
5. Improve P104 helper split with distinct input and output bases #5718: other legal boundary pairs.
6. Improve P104 helper split with distinct input and output bases #5718: one retained framework assumption.
7. Certify exact dyadic helper-channel capacity with Smith witnesses #5615: a current source cut under the full dyadic criterion.
8. Independently audit P104 callers with explicit owned lifetimes #5717: rebind the explicit-inventory audit to a changed ABI.
9. Independently audit P104 callers with explicit owned lifetimes #5717: compiler, precision, storage and analytic premises.
10. Conditional kappa .00310915222: distributed scalar updates #5713: whether the emitted artifact matches the credited edit.

Nearest work: Ali Romman's PR #5708 supplies the word and routes. Nick Petalas's free-carrier package shows that every common-frame bank has boundary rank 0 and leaves paid frame changes open. research/g20-moved-correction-frame moves one A2 correction; it does not decide this carrier round trip.

Validation

CPython 3.12, standard library only:

python3 -B research/g20-frame-round-trip-gap/verify.py
python3 -O -B research/g20-frame-round-trip-gap/verify.py
python3 -B scripts/research_package.py --package research/g20-frame-round-trip-gap

Observed PASS_G20_FRAME_ROUND_TRIP_GAP in both modes and PASS_REGISTERED_RESEARCH_PACKAGE. The registered replay also passed normal and optimized isolated runs. python3 -B scripts/research_selected_baseline.py printed PASS_RESEARCH_BASELINE_BINDINGS_ONLY.

Not run: member exits into occupied banks, a rewritten frame-517 schedule, Lean, Docker, and the selected cold replay.

Credit

The word, the routes, and the open role question are Ali Romman's PR #5679 and PR #5708. The common-frame obstruction and cut algebra are Nick Petalas's. Gaussian elimination and rank-nullity are classical.

Prepared by unpaidmoon with substantial Cursor Grok assistance.

Open next questions

• Can a published exit of a group member into an occupied compatible bank raise the boundary rank? The non-member census does not answer it.
• Can the six frame-1 ADDs of helper 222 be retargeted onto frame 517 with a finite route and restoration bill? The singleton pairing is not that word.

Workflow feedback (optional)

The free-carrier handoff named one conversion and its inverse directly, which made the route-table check a finite census. A link to discussion #1200 is enough; no separate session report.