[pinterbanget]

Summary

This adds research/pr4546-extended-ceilings/. It recomputes Clear1nsight's #4546 with separately written code, then extends its length cap from four to six unit shears. #4546 certifies zero optimistic paid-moment headroom at C = 0.00302015 in the first twelve #4470 receiver windows. Result: every ceiling stays exactly 0. No new κ (negative result).

Checks

• Windows. They are extracted by this package's own code from main's canonical Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries #4470 constructor (joint-helper-lattice/native_joint.py, run isolated on its pinned inputs). They are cross-checked with Certify zero four-shear headroom in twelve PR4470 receiver windows (no new kappa) #4546's RESULT.json on index, roles, coefficients, phase, start/exit dimensions and old paid profile.
• Length ≤ 4. This reproduces Certify zero four-shear headroom in twelve PR4470 receiver windows (no new kappa) #4546 exactly: 22,621 words, 84 endpoint matches per window, relaxed-profile counts (1, or 4 for windows 10575 and 10579), and best gain 0.
• Lengths 5 and 6. These add 248,832 and 2,985,984 words, with matches found by meet in the middle. Each window has 272 (≤ 5) and 3,812 (≤ 6) matching words, all admitted by the dimension screen. The relaxed-profile sets are unchanged in every window, and the best optimistic gain stays exactly 0.
• All 128 eligible windows (123 in phase B, 5 in cleanup_tail). Certify zero four-shear headroom in twelve PR4470 receiver windows (no new kappa) #4546 tested only the first twelve. Every ceiling is exactly 0, at both length ≤ 4 and length ≤ 6.
• Nonunit coefficients on all 128 windows. Shears with |c| ≤ 2 up to length 6 (37,076 matching words per sign case), and with |c| ≤ 3 up to length 5: every ceiling is still exactly 0. Scalar-height cost is not charged, which only favours the rewrites.
• 88 nonadjacent pairs, where the intervening operations touch none of the three fields. 87 have ceiling 0 in the relaxation. In one pair (11334/11344) the relaxation is loose: it allows gain about 0.0026 for 186 words. An exact search over actual nested subspaces finds no positive gain for any of them, so the incumbent frames are geometrically optimal.
• Single-contact retiming across the whole word. All 16,089 two-operand scalar contacts, in every phase, already sit at a cost-minimising contact dimension given their neighbours' frames. This is exact, since every intermediate dimension is realisable.
• Two-contact joint retiming across the whole word. Over 26,092 consecutive same-field contact pairs, the relaxation finds no gain for 26,042. It suggests about 0.0016 for 50 pairs, but an exact nested-subspace search finds no gain for any of them.
• Agreement with Independently certify all-length receiver-window floors by exact rank dominance #4581's all-length certificate (mihir-s-05). In all 128 windows, Independently certify all-length receiver-window floors by exact rank dominance #4581's all-length terminal profile set is identical to this package's length-≤6 relaxed set, computed by different code with a different relaxation. Its capped-rank majorization and telescoping identity are rechecked exactly. mihir-s-05's Independently certify all-length receiver-window floors with two exact algorithms #4582 and Independently cross-check all-length receiver floors and two pinned certificates #4587 give the same sets in all 128 windows too, so four separate implementations agree exactly.
• Receiver-sharing transfer on twelve PR4470 windows preserves the paid profile (no new kappa) #4543's receiver-sharing rewrite on all 128 windows. In 96 windows the relaxation admits the incumbent profile and nothing better. In 32 phase-B windows the rewrite is infeasible: b's entrance frame is not inside a's exit frame, so a += s·b has no admissible frame. This is a sound impossibility. With exact geometry, the rewrite realises the incumbent profile exactly, with actual nested frames, in all 96 feasible windows, including Receiver-sharing transfer on twelve PR4470 windows preserves the paid profile (no new kappa) #4543's twelve.
• Model. This is Certify zero four-shear headroom in twelve PR4470 receiver windows (no new kappa) #4546's relaxation, re-implemented: forward mandatory spans, backward permissible intersections, integer contact dimensions, every gap charged, and certified r^(1−C) prices.

Why it does not move. Contact frames are capped by intersections of the operands' exits and floored by sums of their starts. For these windows, those bounds already pin each field's rank steps. For example, a 0 → 2 climb has every contact capped at dimension 1, so longer words cannot merge payments. This is stated as an explanation, not proved for all lengths.

python3.12 -B scripts/research_package.py --package research/pr4546-extended-ceilings
  PASS_REGISTERED_RESEARCH_PACKAGE research/pr4546-extended-ceilings outcome=negative-result   (~3 min, stdlib only)

Limitations:

• Only unit coefficients, the same three fields, fixed boundaries and lengths ≤ 6 are covered.
• Window results must not be summed across overlapping windows.

Head: 4437c89e577da1c4982510135b2b7be108e59538. Base: canonical main f626db5c.

Credit: Clear1nsight (#4546), Cinna Davis (#4470), zxv. Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5) assistance.

🤖 Generated with Claude Code