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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>
Author
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Archiving this preliminary Draft as part of the research closeout. It composed the terminal-accumulator elimination in #122 with the shrunk-frame work in #125; those inherited constructions remain credited to their authors. At head |
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Summary
This draft composes SovereignSteak's terminal-accumulator elimination from PR #122 with Joel Pulikkan's shrunk lifted frames from PR #125. The construction is evaluated on the pinned #125 profile and preserves its frame contract.
Under the inherited hypotheses, the finite conditional candidate is
This is about 0.257% above the fixed #125 parent. The current public numerical frontier is higher: Draft PR #139 reports κ = 4.50198447040e-4 for a separate triple-core lockstep candidate. This PR does not claim to exceed that result or to establish a global frontier. It contributes the independently auditable #122 × #125 composition described below.
Construction
The parent is pinned to #125 head dda535b. On its shrunk-frame profile, 381 terminal roles are removed. Their 1,167 incoming direct updates are redirected to corresponding outputs at the original gate indices and frames.
The candidate profile has R = 28,324; W = 122,848,704; total rank = 70,758,991,424; deficit = 1,862,080; and maximum child = 574. The strict complex saving is 13862528107/125000000000000. Every direct update remains charged in the exact scalar bound.
Because #125 is still unmerged, the upstream PR carries its pinned source tree as a prerequisite. The new composition and independent audit are under research/shrunk-frames/. For focused review of the composition-only delta, see the 16-file compare from the pinned parent to this candidate. Source attribution and license records retain credit for both predecessor PRs.
Verification
Scope
This is a finite conditional witness. General transfer, analytic, fixed-tape, and all-size assembly interfaces remain inherited proof obligations. Finite certificate success is not a formal verification of the full multiplication theorem or a practical runtime benchmark. Independent mathematical review is pending, so this PR is intentionally a Draft.
Credit
The terminal-elision source is SovereignSteak's PR #122; the shrunk-frame parent is Joel Pulikkan's PR #125. The composition and independent finite audit were prepared by Sennemmi with substantial OpenAI Codex assistance. Earlier contributors, source-specific notices, and original licenses remain applicable.