[maxime-fleury]

No new κ, no existing file changed. #212 bounded the bit coarse saving of one word — #200's physical bit word, shared by #205, #206 and #207 — over every admissible choice of operation frames. #217 holds the current record on a different word: 440 four-input XOR reassociations (880 graph nodes and scalar controls) on top of #211's cascade frames and #200's construction. This applies #212's method, unchanged, to that word.

Result

At 1,200 Lagrangian rounds, the round count of #212's published run, on #217's head b739fc2:

Ledger	#200's word (#212)	#217's butterfly word (here)
own: floor on C	2,804,210	2,800,700
own: coarse <	6.904e-4	6.913e-4
own: κ <	6.900e-4	6.908e-4
completed banks: floor on C	2,780,144	2,776,634
completed banks: coarse <	6.964e-4	6.973e-4
completed banks: κ <	6.959e-4	6.968e-4

The like-for-like pair at 400 rounds moves the same way (own 6.909e-4 vs 6.918e-4, banked 6.969e-4 vs 6.978e-4), so the comparison does not depend on the round count.

The word's own numbers, recomputed here from its certificate:

quantity	#200's word	#217's butterfly word
certified coarse saving, own	6.7777395e-4	6.7938424e-4
D/C of the certified layout, own	6.7837287e-4	6.7998615e-4
certified coarse saving, completed banks	6.8366e-4 (#207)	6.8516596e-4
D/C of the certified layout, banks	6.8427e-4 (#207)	6.8578301e-4
κ of the composition	6.831904550365e-4 (#207)	6.84696826673891e-4

The butterflies raised the ceiling and the achieved value by about the same 0.13%, leaving slightly less frame room than before: +1.68% from the achieved D/C to the ceiling here against +1.77% on #200's word, and +1.77% against +1.86% on the κ basis. Reassociation is not a way to enlarge the frame slack; it is a different word with its own, slightly higher, ceiling — which is what #212's scope statement already said.

How the word was obtained and checked

#217's own candidate.py rebuilt the changed word from #202's head 8d8d67b (fetched from pull/202/head), #211's pinned frame payload and the frozen butterfly overlay, checking those hashes itself. The three emitted payloads reproduce #217's declared hashes exactly — graph_p12.json 2bb271df…, word_p12.json ef77a7d3…, frames_p12.json 4e0fce06… — and the word has 41,288 operations, 18,908 roles, 1,760 reuse pairs, 3,960 gauges and 11,671 changed operation frames, the number its expected-bit.json declares.

ceiling.py --tree then passed every self-test on that word: the certified layout lies inside every derived joint bound, its slot chains reproduce #217's certified ledger child for child (W 20,668, rank 1,486,160), the terminal record substitutes [3, 21] per sink and stage, and every per-slot floor is below its actual chain. Fact 1 reproduces the certificate to eight digits (6.7938424e-4 < D/C = 6.7998615e-4, gap 0.089%), matching an independent closed-form computation.

rebuild_word.py and build_tree.py reproduce the run end to end; the tree's certificate is a shim whose bit record is #217's own post-terminal profile plus the pre-sink profile restored by the terminal record, and every field of it is re-derived by #212's own self-tests.

Added after the first push: what combining PR216's cuts with this word can reach

PR216 (research/coordinated-crossover-pr200-v2, head 34abdc5) is a third layout on the same lineage, keeping PR211's frames and admitting 220 further operation-frame changes (kappa = 6.838643131376e-4). Since this note's ceiling bounds every frame layout of PR217's word, transfer_check.py (added in the second commit) settles the structural side of the obvious combination question from the two packages' own words:

• both have 41,288 operations and identical DAG-fixing records (11,856 arcs, 25,900 order entries, 1,760 reuse pairs, 3,960 gauges, 6,624 root roles, 17,688 phase-1 and 7,728 plain operations, the same 1,760 sources and reads); exactly 880 operation contents differ -- PR217's reassociation set -- along with 7,068 operation frames;
• PR216's admission records are [op_index, [basis vectors ...]] in that same index space: 6,191 current bases, 6,258 override records, 2,268 canonical subspaces, of which only 3 of 6,258 touch a rewritten operation and none of the 2,268 does;
• so a merge is well defined at the index level, but PR216 admits with the scalar word fixed and PR217's change is exactly there: a merged layout is a new submission needing fresh admission and a fresh column replay;
• and it is capped: any frame layout of this word gives kappa < 6.968e-4, at most +1.77% over the 6.84696826673891e-4 record, while PR216's own layout on the plain word sits 0.122% below it. The bank absorption of Build #208's bank-absorption target: rank-22 residual absorption — certified accounting κ = 7.00427501305159e-4 (R1–R4 open; not a completed witness) #219 (+2.30% over the same record, accounting ledger) is the route this comparison favours.

Scope

This bounds frame layouts of #217's word only, in the sense #212's floor has. The reassociations are part of the word, so nothing here bounds further reassociation, other circuits, reuse, gauges or sinks — the escapes #212 lists. The pre-sink profile is reconstructed rather than read from #217's receipt (its own run_bit.py needs Linux resource/signal.alarm and pinned numpy 2.3.5 / scipy 1.17.0); the delta is exact and #212's child-for-child self-test is the check. All κ remain conditional on each submission's stated interfaces.

Credits: #212 (Chafik Boukhalfa) for the method and the script, unmodified; #217 (hcg890) for the word and candidate.py; #211 (Rohan Arun) for the pinned cascade frames; #200/#168 v4 for the base word and vendored checker. Prepared with Anthropic Claude assistance; Apache-2.0.

[Mister-Meeseeks]

Thank you @maxime-fleury. This contribution is now retained on main in the scoped 100-PR review and contributor credits.

Contribution: PR212's frame floor applied to PR217's actual butterfly word.

Review and limits: Prior exact-head 1200-round scoped replay. The bound concerns that fixed word, not new primitive families.

The complete original source, notices and relevant execution evidence are retained through the pinned source archive. The review distinguishes fresh local runs, source-bound historical Linux CI and prior exact-head review; it does not claim 100 fresh full mathematical audits. Closing this historical PR as reconciled. This preserves parallel and cumulative credit without replacing the selected frontier or promoting priced research targets to completed constructions.

Reviewed head: aa947f2f0fb624e17c027a463286b42fc810fdeb. Publication: 50d768818f579d4e165b4c257c6ee25bca300802.