Scoped negative result: partial leaver cells on #1005's word, and the 192-bit coefficient allowance

[higherbeing]

No κ claim. This is a negative result on the obvious next step after #1005: extending its mutable-leaver cells beyond the eight all-K cells. It does not raise κ. Two of the three obstructions will bind any further leaver-style rewrite on this line, so they seem worth recording.

What was tried

Outside #1005's eight cells, only 16 delivery keys have leaver operands, and only in two of their three blocks. That is why #1005 stopped at eight. Each of these keys uses three face copies and one slot copy.

• Exact legality model. A frame fits a target's hyperplane iff every generator is orthogonal to the target's port, and that property is a union under joins. So legality reduces to a few taint bits per register. A layered CP-SAT model over set and taint states finds the circuits.
• Construction. A hook in a copy of Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005's constructor applies one circuit template per key and drops freed copies through the helper map, as Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005 does. The constructor's own exact identity check runs unchanged.
• Port stages. Moving own-row reads breaks the port stage's alignment of the all-K cells. A construction-side option anchors unmatched gates to their next matched gate. It is a byte-identical no-op on Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005's word, and every variant needed zero frame repairs.

Results

Per-call profile deltas are measured on the cold-end word against #1005's cell word. κ uses #1005's global profile with ideal rank-48 packing, an upper bound. Bits are the local replay's coefficient bound, which must stay below 192.

variant	helpers removed	native audit	bits	κ
#1005 baseline	0	pass	188	0.001671387264390146
one helper + target-to-target gates	32	fail (zero-frame compensation reads an entering helper)	—	0.0016827 if it were legal
two kept copies, all 16 keys	16	pass	107	0.0016650 (loss)
one fresh helper, all 16 keys	32	pass	210	0.0016702 (loss)
one fresh helper, 4567 class	16	pass	203	0.0016723 (+0.05 %)
one fresh helper, one key	2	pass	187	0.0016712 (loss)

Obstructions

1. The packet copies are entering helpers. After porting they start with arbitrary dirt, and their original readers pre-read them. A kept copy must keep its exact reader set, and no circuit may copy a dirty target into another target. With own rows first and one helper, CP-SAT proves a key infeasible.
2. Cold-end pairing collapses. Every target in the eight touched blocks belongs to one of the 16 keys. Using their own-row registers as leavers moves them out of the block frame, so pairing falls from 4 to 0–2 per block. The copies were what kept the own rows inside.
3. The 192-bit coefficient allowance is nearly used up. Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005's word already needs 188 bits, reached in the full-frame cleanup of block 4567's scratch. Eight circuits push it to 203 bits and sixteen to 210. Any further leaver mutation on this line will likely hit this bound first.

Reproduce

bash research/leaver-partial-cells/reproduce.sh . /tmp/gauge44-pr635 /tmp/leaver-partial-cells

The script runs #645's no-triangle base and #1005's cell driver with its pins checked. It then runs the census (byte-identical cell word), the raw-level template checks and all five variants through regroup, HPE, cold44, the native audit, ledgers and the local replay. Finally it prices them into RESULTS.json, which matches the committed file. It takes about 45 minutes. A fresh macOS run (Python 3.11) reproduced every row above. The optional circuit search needs ortools; the README gives the command.

Only research/leaver-partial-cells/ is added. No inherited file changes: the patches are applied to copies under the output directory.

Scope and credits

These are finite local measurements on #1005's cell word. Prices assume ideal owner packing and omit #1005's later layers. The negative conclusions hold either way, because the legal variants lose or break the 192-bit rule before any layer applies.

Builds on jeremykothe2's #1005 (leaver cells and the k8 chain), icekylinx's #645 and the no-triangle constructors, and the PR635 supplier lineage. Related scope: #651 (delivery-layer rigidity, which assumed helpers were the only scratch), #717 and #595 (format limits).

Prepared by higherbeing with substantial Claude (Anthropic) assistance.

[Mister-Meeseeks]

Batch review at 75f1089ed05b035c12942f7bac1c8dc37ca05e97.

This remains open after scoped triage. Next review step: Five inherited native/compiler variants need the pinned PR635/645 base and a full approximately 45-minute replay. The committed receipts and local scripts do not alone establish full source-bound reproduction; schedule this complete pipeline separately.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.