[unpaidmoon]

Change and mathematical scope

Scoped proof on one recorded alphabet. No new κ. The selected value stays 363005817/100000000000.

On the pinned round-three centre word, the recorded warp alphabet is the 72 maps in canonical["warps"] together with the inverses retained by model.inv. Each map is a linear automorphism of GF(2)^9. Under the native chart-image law, every admitted chart pair has equal dimension. Opcode 1 joins frame 292 to frame 293, both of dimension 4, and the two spans are distinct (Fourier rank 4). No retained opcode, and no finite product of retained opcodes, admits a warp from a dimension-8 Y exit onto the dimension-9 frame 1.

This is a proof under those hypotheses, plus an exhaustive census of the 72 maps. It is not a selected-word decoder, a supplier admission, or a statement about any other warp alphabet.

Task and overlap

Base: e54523517d0f03e58352e647c403a5af3e525a57 (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 second open question of PR CrocSwap#7102 on the CrocSwap#4610 round-three alphabet.

PR CrocSwap#7102 already shows that all 240 emitted warps preserve dimension, and it leaves a dimension-changing retained opcode as a different alphabet. The added value is the alphabet statement: bijectivity of every recorded map forbids an unequal chart image, including the Y-exit pair with frame 1, which those 240 events never use. A sample of the emitted events is rejected by the checker.

Overlap searched open upstream PRs and discussions for this question. The exact sentence is open in CrocSwap#7102 and is not answered by another open PR. The one-way Y-exit endpoint and the restored round-trip theorem of CrocSwap#7102 are left untouched.

Validation

python3 -B research/retained-warp-opcode-dimension/verify.py
python3 -O -B research/retained-warp-opcode-dimension/verify.py
python3 -I -W error -B research/retained-warp-opcode-dimension/verify.py
python3 -B scripts/research_package.py --package research/retained-warp-opcode-dimension --check-only
python3 -B scripts/research_package.py --package research/retained-warp-opcode-dimension

Marker: PASS_RETAINED_WARP_OPCODE_DIMENSION with opcodes=72, dimension_changing_opcodes=0, opcode_1=292->293 dim=4 chart_fourier_rank=4, y_exit_to_frame1_admitted=0, emitted_warps=240, and emitted_on_other_charts=168. 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 is opcode 1’s recorded columns and chart image. Controls reject a zeroed column, a 71-opcode sublist, the pair (Y exit, frame 1), a same-dimension chart outside the image, a ten-event sample used as the alphabet, and a width-0 reading of the one-dimension gap. Not run: model.build on the full contact graph, a physical caller, Lean, Docker, and make frontier7000-verify.

Evidence class: proof of the dimension lemma for a bijective linear map, and an exhaustive finite census of the 72 recorded maps (the list is exactly opcodes 1 through 72, each evaluated on all 512 vectors). The 240 emitted events are a separate exhaustive recount. They already preserve dimension in CrocSwap#7102. That recount is not the prohibition on the unused Y-exit pair.

Credit

The word is Cao Yifan / intqwq, PR CrocSwap#4610. The emitter is the retained centre extension. The chart-image law and model.inv are the contact-graph model, which credits PR CrocSwap#4672, PR CrocSwap#4654, PR CrocSwap#4610, and the PR CrocSwap#4470 lineage. The question is the second open question of PR CrocSwap#7102. The Y-exit indexing follows research/y-exit-rank-lift-obstruction, which credits discussion CrocSwap#1166 comment 19133861, Chris R / Clear1nsight.

Prepared by unpaidmoon with substantial Cursor Grok assistance.

Open next questions

1. Which dimension-8 charts, if any, does opcode 1 carry a Y-exit chart onto? The image has dimension 8, so it is not frame 1, and it may still equal another rank-8 chart. A warp onto that chart would move the exit with no paid transport, inside this alphabet. The first step is to map the exit basis of Y role 112 by opcode 1’s columns and test it against the other 111 Y-exit spans. Nothing algebraic blocks that census. Accepting frame 1 as an endpoint is a different contract.

Workflow feedback (optional)

The assigned question was an open_questions entry on PR CrocSwap#7102. Searching that sentence across open PRs returned CrocSwap#7102 itself. A machine-readable index of those questions, with answered-by links, would make this split mechanical. Feedback discussion: CrocSwap#1200