Shrunk lifted frames with saturated deferral: conditional κ = 1.10591581647e-4

[GamingPuzzled]

Status: the package verifier and full repository verification ("Verify research artifacts") pass on the fork; see the comment below. The inherited cyclic-deferred check fails on #114's own head too.

Under the inherited stopped-product, endpoint, analytic and fixed-tape hypotheses,

κ = 110591581647/10¹⁵ = 1.10591581647×10⁻⁴

PR	κ	This PR is above it by
updated #114	1.09281094468e-4	1.19920%
#124 (best open at submission)	1.1038332094346e-4	0.189%
#122	1.0941620808215e-4	1.07%
#120	1.0911630664e-4	1.35%
#118	1.085428e-4	1.89%

The complex side still binds.

This builds on eumemic's updated #114 (7dfa16edfa5d6452f2b10dadcbef20d26222827e) and leaves its construction unchanged:

• Deferred bit word and a 28,705-role complex producer under stopped-product accounting: conditional κ = 1.044939e-4 #117's immutable 91,770-addition DAG;
• the same carrier matching and 28,705 roles;
• Deferred readouts on both stopped networks: conditional κ = 8.58478e-5 #110's lifted frames and deferred readouts;
• Shared completed cores and physical frames: conditional κ = 1.23988197806e-4 #114's saturated placement with priority 2^dim / targets².

One step is new: shrunk lifted frames.

Idea. #110's frame contract for an addition x asks for a nondegenerate U_x with label(x) + Σ U_pred ⊆ U_x ⊆ lifted kernel. U_x must also lie in every successor frame. The lift takes the largest choice, but nothing requires it. Each role pays one child per strict increase along its frame chain, and t·log(m/t) is subadditive. Increments of 1 and 2 dominated the complex moment, so it is cheaper to delay an increase and merge it into the next one.

Construction. One forward pass in chronological order considers the minimal span Lb_x = label(x) + Σ U_pred. It replaces U_x by Lb_x only when all of these hold:

• Lb_x is nondegenerate;
• Lb_x is strictly smaller than U_x;
• Lb_x lies in every successor frame;
• the local one-child cost of the role chains holding x drops.

Deferral candidates then use the shrunk start frames.

h=24 complex (PR117 DAG)	#114	this
roles / links	28,705 / 71,185	same
shrunk frames	—	16,031
deferred readouts	4,706	4,706
strict complex saving	109305097/10¹²	110616162/10¹²
κ	1.09281094468e-4	1.10591581647e-4

W, the rank mass 71,647,349,312 and the maximum child 574 are unchanged. Only the split of role chains into children changes. All of these stay paid:

• copied centres and exteriors;
• source and target fronts;
• data projectors and endpoint corrections;
• Shared completed cores and physical frames: conditional κ = 1.23988197806e-4 #114's expanded scalar charge;
• all three row reserves.

The bit supplier is unchanged: Swapnil Jain's round-seven word, with stopped saving 1240189553/10¹³.

Checks. Run python3 research/shrunk-frames/verify.py. It regenerates the package in a temporary tree, and it passes locally. It covers:

• the complex compiler, with pinned graph counts and the pinned shrink count (16,031);
• two arbitrary-scratch replays over Z/(2^61−1);
• exact F2 nesting and nondegeneracy of every role chain on the actual shrunk frames, plus every deferral frame and target chain;
• the independent literal reflection audit (inverse/sign-negate/bank swap, complemented incidences, bounded readout chunks, three mutations), which consumes the same shrunk frames;
• the exact certificate: both moments, next-grid rejections, 47 strict constraints, 7 margins and the next κ grid point;
• 17 controls. The new one shows that Shared completed cores and physical frames: conditional κ = 1.23988197806e-4 #114's frozen unshrunk profile contracts at Shared completed cores and physical frames: conditional κ = 1.23988197806e-4 #114's saving and fails at the new one.

Scope. This is a finite conditional witness. The finite checks show the shrunk frames meet #110's stated frame contract. They are not a new general argument. All inherited transfer hypotheses remain assumptions. No claim is made of global optimality or a practical speedup.

Orthogonality. The shrink step is independent of #124's dead-slot recycling and #122's terminal-accumulator elimination. Both of those change roles rather than frames, so a composition may give more. It has not been tested.

Credit: eumemic (#117 producer; #114 saturated placement, reflection audit and scalar charge); Avi Eisenberg/ikeboy (#110, #62); Rohan Arun (#111/#113/#116/#118); icekylinx (#104/#115); Swapnil Jain (round-seven words, lifted frames, deferred readouts); Zhihao Chen/jacklightChen; Aurel Prosz/Paureel; RaD/hipotures; Douglas Colkitt; OpenAI and all inherited contributors. Original licenses and notices remain. The shrunk-frame step was prepared by Joel Pulikkan with Anthropic Claude assistance.

🤖 Generated with Claude Code

[GamingPuzzled]

First-time contributor here, so upstream workflows are waiting for maintainer approval. The same workflows already ran on the fork at this head:

• ✅ Verify research artifacts: the full repository verification
• ✅ Verify shrunk-frame deferred witness: this PR's package on Python 3.11, 3.13 and 3.14
• ❌ Verify cyclic deferred witness: inherited from Shared completed cores and physical frames: conditional κ = 1.23988197806e-4 #114's package and untouched here. Shared completed cores and physical frames: conditional κ = 1.23988197806e-4 #114's own head 7dfa16e fails the same check upstream with Source hash mismatch: complex-profile.json.

Could a maintainer approve the workflow runs? Thanks.

[Mister-Meeseeks]

Thank you @GamingPuzzled. This contribution is now recorded on main in the scoped reconciliation review and contributor credits.

Contribution: Shrink to the minimal nondegenerate span inside a successor frame.

Review and limits: Exact-head CI evidence; recomputed profile and fixed target-frame boundaries required.

The complete original source, proof/research notes, notices and relevant replay/CI evidence are retained through the pinned source archive. The review distinguishes fresh runs, exact-head historical CI and prior integration evidence. Closing this historical PR as reconciled; its obsolete headline does not replace the current selected bound, and draft/retracted claims retain their explicit qualifications.

Reviewed head: dda535bdcfc321a13a1ebd3c2d70e2b5bb72368e. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.