[DanieleCorso]

Finding: the proposed +10.83% bit-side gain is not valid

This branch is a reproducible negative-control research artifact, not a certified higher κ. It tests the tempting idea of restricting PR CrocSwap#128's 87 orthogonal complex groups to h=23 and reusing the 17,597 zero-start bit auxiliary roles between completed cores.

Result: the restricted groups pass binary F₂ Gram checks and formal rank/moment accounting, but all 17,514 distinct within-group triple pairs fail the rational-H orthogonality criterion of PR CrocSwap#129. For triple incidence vectors, Tᵀ(9I−J)U=9(|T∩U|−1); the restricted groups have 15,012 pairs with intersection zero and 2,502 with intersection two, never one. The apparent better bit moment does not correspond to a valid bit supplier.

Reproduce

python3 research/pr128-zero-frame-sharing-screen/verify_screen.py

The branch includes a pinned PR128 bit histogram, the exact h=23 restricted groups, a signed F₂-phase / rational-moment screening verifier, an explicit rational-H negative control, and CI. See research note.

Status and latest baseline

• PR Completed-core sharing: conditional kappa > 2^-13 CrocSwap/integer-mult-bounds#128: conditional κ = 0.00012310001053253.
• PR Shared bit cores and gauged scratch reuse: conditional κ = 1.29186205798e-4 CrocSwap/integer-mult-bounds#129: conditional κ = 0.000129186205798 (the latest higher baseline at investigation time).
• The new +3% target relative to Shared bit cores and gauged scratch reuse: conditional κ = 1.29186205798e-4 CrocSwap/integer-mult-bounds#129 is κ ≥ 0.00013306179197194.
• This candidate does not claim an improved κ and should not be merged as such.

The PR129 sunflower partition of 161 rational-H-orthogonal groups is the proper current starting point. This negative test documents precisely why the proposed binary restriction cannot replace it.

Credits: an664 and collaborators for PR128, eumemic and collaborators for PR129, Zhang–Ge for the original complex packing; OpenAI assistance on this audit.