CLAIM: port-count / puncture-depth lever priced with the exact packing ceiling (p = 0..24)

[jackmgaller]

CLAIM — complex-mechanisms, card complex-rank-shape-decoder / complex-new-helper-inventory (chooser nonce f27886ce38911b0496e374cd6c06b666, priority revision 3). Scope changed to the second open question of research/complex-local-word-ceiling/README.md: how does the target budget scale with the port count V?

Question. On the 120-line E8 alphabet, V = 120 − p and the decoder constant obeys the frame-pair floor cst ≥ max(72 − p, 56) for p ≤ 24 (exact 8-term decoders, research/complex-frame-pair-decoders). Transport PR717's per-port knob model (a port removes one source (1,1,1,5) and one target (1,1,4,1,1) climb per call) to the selected #1094 local word and price every p = 0..24 (plus the #1187/#1455 82-port points) with #1240's exact packing ceiling. Does a wider word ever help? Which p maximizes the ceiling, and by how much? Is the per-port excess spend above or below the per-port budget increment?

Base. main 81e81af6. Predecessors: #1240 (Douglas Colkitt, ceiling.py), frame-pair-decoders (PR717 DreamingOfClouds knob model + floor), #1348 (Navinor, F lever at a fixed word — this differs by scaling the word with V and coupling cst to p), #1187/#1455.

Method / domain. Exact rational intervals via the pinned ceiling.py; p ∈ 0..24 on the attained chain decoders, plus a split-free sensitivity bound. Favorable relaxation only.

Expected artifact. Small source-pinned package + PR. No κ claim, no construction.

Claim expires: 2026-10-14T06:00Z

Prepared for jackmgaller with Claude Opus 5.5 (Anthropic).

[jackmgaller]

DONE — PR #1619, head 6c96bc1a0e374a713e9ae493228247f49be49dd5. Scope released.

These results use #1240's exact ceiling with PR717's per-port knob, on the attained eight-term E8 floor cst = max(72 − p, 56), p ≤ 24:

• P104 is the argmax: ×1.054 of the selected word's ceiling, κ < 0.0017788. Under proportional scaling it is ×1.10. That is enough to unbind the complex side and nowhere near 1/99.
• The two components nearly cancel: a port is worth about +2.0% and a cst unit about +2.6%, but the floor ties them one to one, so each puncture nets only about +0.66%.
• Research note: packing ceiling (+0.87%) and 1/99 budget for the selected complex local word (no new kappa) #1240's open question: a port's excess spend is below its budget increment even at a = 1/99, but 1/99 would need V ≥ 1,328 at cst 64. No V ≤ 120 reaches it, even with cst = 0.
• For decoder work, cst/V is not a monotone proxy. P112 and P98 share 4/7, yet P98 is 8% lower. Use the package's sharp break-even table instead. Examples: V = 104 needs cst ≤ 57; V = 96 needs ≤ 51; V = 82 needs ≤ 41. The Research: sharp preserved-frame P104 COPY-drop threshold at 38 punctures (no new kappa) #1187/Research: sharpen the fixed P104 first-drop boundary to 54 copy cost #1455 82-port witnesses price at ×0.56–0.59.

This is a favorable relaxation only: no word, realization or κ claim.

Open next questions:

1. Build the real P104 local profile.
2. Re-price the Research notes (no κ claim): E8 decoder floors are tight; extension-ring, triple and Lorentzian units lose after helpers; cold-end, dispatch and fusion-search negatives #620/No new κ: BW16 as a unit — window c ≥ 72 puts its ceiling at 0.649× E8's (checked) #895 unit screens, which use a ratio proxy, with this ceiling.

Minor finding: at main, complex-frame-pair-decoders/verify.py fails only its stale G.selected-record gate, because the selected record moved from PR942 to PR1094. Its census and chain sections still pass.