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Birth-read reuse on shrunk saturated frames: conditional κ = 1.1239534209971e-4 - #127
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…78e-5 Under PR104's opposite-bank rule every residual is one child, so deferred readouts pay on both networks. Bit: Swapnil Jain's round-seven deferred word, unchanged (stopped saving 1.2402e-4). Complex: PR104's h=24 network with lifted binary frames and deferred readouts on 8,893 of 44,918 roles (8.58628e-5). Replay with arbitrary scratch, exact F2 frame checks, exact moments and the 47-constraint assembly give kappa = 429239/5000000000. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
…0591581647e-4 On PR114's saturated deferred construction over PR117's immutable DAG, one forward pass replaces a lifted frame by the minimal nondegenerate span of its label and predecessor frames whenever that merges increments of the role chains holding it. 16,031 frames shrink; roles, matching, rank mass and 4,706 deferred readouts are unchanged. Complex saving rises from 109305097/10^12 to 110616162/10^12, giving kappa 110591581647/10^15. All PR114 checks are retained: arbitrary-scratch replays, exact F2 chain nesting and nondegeneracy on the shrunk frames, the independent literal reflection audit, exact moments, 47 constraints and 7 margins. A new control rejects PR114's unshrunk profile at the new saving. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
…534209971e-4 Apply PR124's compensated birth-read slot reuse (James Chang) to PR125's frames: PR114 saturated placement (4,706 deferred readouts) plus the shrunk-frame pass (16,031 frames). PR124's matcher finds 2,108 legal reuses, leaving R = 26,597. Complex saving 11242073/10^11 gives kappa 11239534209971/10^17. build_frames.py reconstructs the shrink and saturated placement without upstream imports and matches PR125's complete histogram bin for bin. PR124's lemma, readout bill, forward/reflected literal frame audit and exact assembly run unchanged apart from the pinned profile; the next complex grid point is now also rejected. The Linux memory cap is skipped on macOS, where RLIMIT_AS cannot be set. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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Draft: the package runner passes locally on Python 3.11. Fork CI is running.
Under PR124's retained hypotheses,
κ = 11239534209971/10¹⁷ = 1.1239534209971×10⁻⁴
The complex side still binds.
This composes two orthogonal improvements on #117's DAG:
More and larger deferred frames give the reuse more recipients.
Checks. Run
python3 research/shrunk-birth-reuse/run_checks.py. It pins #125's DAG, profile and certificate by SHA-256. In a temporary tree it then runs:build_frames.py. This rebuilds the shrink pass and saturated placement with no upstream imports. It checks every chain for nesting and nondegeneracy and reproduces Shrunk lifted frames with saturated deferral: conditional κ = 1.10591581647e-4 #125's complete histogram bin for bin.Two harness changes from #124:
RLIMIT_ASis skipped on macOS, where it can't be set.Scope. This is a finite conditional witness. All of #124's and #125's inherited hypotheses remain assumptions. The branch contains #125 (and #114) because it builds on them.
Credit: James Chang/jamesyc (#124 reuse operation, lemma, matcher, bill, audit and assembly, with OpenAI assistance); eumemic (#117, #114); Rohan Arun (#118); Avi Eisenberg/ikeboy (#110); Swapnil Jain; icekylinx; Zhihao Chen and all inherited contributors. The composition and the shrunk-frame step were prepared by Joel Pulikkan with Anthropic Claude assistance.
🤖 Generated with Claude Code