[unpaidmoon]

Change and mathematical scope

Scoped proof on one finite schedule. No new κ. The selected value stays 781451/250000000.

On the pinned round-three centre word, with every emitted final chart kept, a round trip of any nonempty set of the 112 rank-8 Y exits through frame 1 raises the exponent-1 paid moment by at least twice the number of exits. When the emitted scalar, scale, and warp events stay on their recorded charts, every one of the 3298 transports is forced by the next pin, and the same round trip raises the paid moment by exactly 2k at every exponent in (0, 1]. Deleting a helper transport cannot pay for that increase while the helper final chart stays.

This is not a selected-word decoder, a supplier admission, or a claim that a dimension-changing warp is impossible.

Task and overlap

Base: 17469fff78c22941280f04d39dc5a1faee09c840 (upstream CrocSwap/integer-mult-bounds main, rechecked at submission). Card complex-rank-shape-decoder, priority revision 8. Scope status: changed. The card asks for a decoder or coframe change. This package answers the first open question of research/y-exit-rank-lift-obstruction on the #4610 round-three word, not a new #6030 itinerary.

The predecessor prices the all-112 round trip at 224 rank-1 children against an optimistic centre credit of 64. That credit drops the centre roles off chart 0. No open upstream PR found for a partial restored Y-exit round trip. The added value is the nonempty-subset statement under restored final charts, plus the pinned-histogram statement at every exponent.

Validation

python3 -B research/y-exit-partial-round-trip/verify.py
python3 -O -B research/y-exit-partial-round-trip/verify.py
python3 -I -W error -B research/y-exit-partial-round-trip/verify.py
python3 -B scripts/research_package.py --package research/y-exit-partial-round-trip --check-only
python3 -B scripts/research_package.py --package research/y-exit-partial-round-trip

Marker: PASS_Y_EXIT_PARTIAL_ROUND_TRIP with forced_transports=3298, rank_mass=5327, moment_increase_per_exit=2, and one_exit_preserves_operator=true. Package replay returned PASS_REGISTERED_RESEARCH_PACKAGE with outcome=negative-result. python3 -B scripts/research_selected_baseline.py returned PASS_RESEARCH_BASELINE_BINDINGS_ONLY. Python 3.12, standard library.

The positive fixture inserts the round trip on Y role 112 and matches the retained matrix. Controls reject a deleted transport, a width-2 reading of the frame-1 gap, and the empty exit set. Not run: a physical caller, Lean, Docker, and make frontier6030-verify.

Credit

The word is Cao Yifan / intqwq, PR #4610. The emitter and width law are the retained centre extension. The all-Y obstruction and the open question are research/y-exit-rank-lift-obstruction, which credits discussion #1166 comment 19133861, Chris R / Clear1nsight.

Prepared by unpaidmoon with substantial Cursor Grok assistance.

Open next questions

1. Can the one-way move of every Y exit onto frame 1 be accepted as an endpoint? The restored-exit argument does not apply. The predecessor gap of at least 48 still replaces each rank-8 exit by frame 1.
2. Does one retained warp opcode change dimension? All 240 emitted warps preserve dimension. A dimension-changing warp would be a different alphabet and is not constructed here.

Workflow feedback (optional)

The handoff-first pass on discussion #1166 is mostly completion notes. The concrete queue that was still open was the open_questions list on recent TASK.json files. A machine-readable index of those questions, with answered-by PR links, would make the fifth-item split across parallel sessions mechanical.