[Draft / finite candidate] Paired physical reuse: conditional κ = 3.62108222954e-4 (+5.997% vs #132)

[DanieleCorso]

Status: finite arithmetic candidate only — paired physical implementation not yet certified

Candidate κ = 0.000362108222954, compared against PR CrocSwap#132's 0.0003416202 (+5.99731%). The +3% target was 0.000351868806. This branch combines the independently sourced PR131 physical complex word with PR132's first-stage orthogonal paired cover. The PR130 bit supplier remains unchanged.

Methodology

• PR131 contributes 26,597 physical h24 roles, 2,108 compensated birth-cut aliases, pinned readout reflection, source-gauge inventory and full virtual-role scalar reserve.
• PR132 contributes the first-stage Cayley involution pairing orthogonal 24-dimensional local active spaces in ambient dimension 70.
• Run paired first-stage local frames in lockstep, with combined rank-2r internal children and rank-(22+2s) exteriors; leave stages two and three separate.
• Conservatively correct the optimistic profile by adding a positive rigorous moment penalty for all nonmergeable source and target data-front steps. The penalty uses exact rank mass 2v(h−1), rational log/exp upper bounds and the inequality 1−2^(−a) ≤ a log 2.
• Paired W=141081, rank mass 9870886, deficit 4784, largest child 68, complex saving 0.000362371031.
• Recompute the exact finite assembly with the original weighted bit supplier, full scalar/router/semantic/row reserves, 47 strict constraints, seven margins and next-grid exclusions.

Reproduce

python3 research/paired-pr131-conservative/certificate.py

Outstanding gates — do not merge as a certified exponent

This does not yet include an independently completed combined literal physical paired-word replay. The PR131 single-core arbitrary-dirty restoration proof and PR132 paired first-stage proof are separate inherited dependencies. Their joint signed phases, compensation, cross-core noninterference, rank-zero adapters, chronological inverse and all-column replay must be checked before any mathematical record claim. Inherited analytic and fixed-tape interfaces remain conditional.

Attribution: PR130 icekylinx; PR131 eumemic; PR132 ikeboy; PR124 jamesyc, and all original notices and contributors. Prepared with OpenAI assistance.