Late compensation and joint frame refinement: conditional κ = 4.24830828577e-4

[eumemic]

κ ≈ 4.24830828577 × 10⁻⁴.

Delay old-value compensation reads until their actual dependencies require them, reuse the newly available scratch banks, and jointly optimize the physical operation frames. This improves the retained h22 sequential-cover construction in #142 by about 1.11%, with the same inherited multiplication interfaces.

The literal scalar DAG stays fixed. A read deadline precedes both the recipient's first workspace gate and every strictly larger gauge read on its reached targets. A donor may be reused only after its last actual workspace use and before that correction. This adds 780 disjoint handoffs to the existing 1,703, reducing persistent local scratch from 21,274 to 20,494 slots. Omitted and prematurely executed corrections are rejected by numerical controls and exact chronology checks.

The additional frame search moves connected groups of equal operation frames, prioritizes compatible donor dimensions, adjusts source gauges while respecting the exact read deadlines, and allows handoff frames to change inside their verified containment bounds. Those deterministic searches select the word; the independent literal audit and exact moments validate it. Scalar coefficients, root interfaces and actual inverse chronology remain fully checked.

Per three-vertex complex cell	Value
Local / ambient dimension	22 / 66
Persistent roles	70,722
Recursive rank	4,662,570
Deficit	5,082
Largest child	57
Complete local copies	9
Paid width-two data finishes	9,240

The exact complex-side saving is 4.25192098 × 10⁻⁴. The retained weighted bit supplier supports 4.5060418316 × 10⁻⁴, including its full fallback and atom conversion. The complete finite group stock, virtual-role scalar reserve, routers, auxiliary adapters, data finishes and row budget are paid. The independent audit counts all 7,075,117 scalar operations per stage. Final assembly uses positive rational slack and checks all 47 strict constraints, seven margins and rejection of the next grid point.

Validation: a fresh deterministic reconstruction from the original pinned PR117 witness reproduces the restricted DAG, operation frames, gauges, pairs and read deadlines. Its full literal forward/reflected audit passes, including arbitrary dirty scratch restoration. Geometry checks all 1,540 ports and 246 physical source-frame types. All 46 corruption controls pass. The repaired full frozen aggregate passes, including byte-identical regenerated receipts and the unchanged-source check. All 45 CI checks pass on repaired head 803b28a5e373442974385396e9d4d3f6e75fd5e7.

Receipt repair: the first frozen receipt included an authoring-only reproduction field that the audit CLI never emits. The CLI receipt has replaced it, its dependent geometry/certificate hashes and source manifest were regenerated, and the existing canonical-receipt control now rejects that field. The compiler output, mathematical checks and claimed saving are unchanged. All 46 publication controls and the complete aggregate pass on the repaired head.

python3 research/cover-local-reuse/verify.py

The verifier rebuilds the source closure in a temporary copy, requires byte-identical generated profiles and receipts, and requires the frozen package to remain unchanged. The focused CI matrix uses Python 3.11, 3.13 and 3.14. LATE-REUSE.md, REFINEMENT.md, PADDED-GEOMETRY.md and BIT-PADDED.md describe the finite construction beside its code.

This remains a conditional finite witness for T(n) = O(n(log n)^(1−κ)). General Clifford normal forms, common generic bases, uniform weighted local-ring compilation, restored row borrowing, analytic recovery and fixed-tape transfer remain explicit inherited contracts.

Credit: icekylinx with OpenAI GPT-6 Astra/Codex assistance for #130's cover and weighted interfaces; eumemic with Anthropic Claude assistance for #117's scalar DAG; James Chang/jamesyc for #124's compensated reuse; an664 for completed-core sharing; Avi Eisenberg/ikeboy, Zhihao Chen/jacklightChen, Swapnil Jain, Rohan Arun, Aurel Prosz, RaD and all inherited contributors. The late-read scheduler, frame refinement and independent verification were prepared for eumemic with OpenAI Codex assistance. Original licenses, source-specific notices and disclosures remain pinned.

[Th0rgal]

Technical Review & Comparison with Paired-Cube / Exact Bit-Subset Track (#144, #146)

We reviewed the commit chain in this PR (c205b7d $\to$ 2fc6cf5 $\to$ 376bb94 $\to$ 803b28a):

1. Padded $3h$-dimensional completed-core sharing (bit_padded.py, padded_checks.py):
   • Uses an order-$3$ block-cycling orthogonal permutation $\tau$ on $m = 3h$ coordinates ($m_c = 66$ for $h = 22$ on the complex side; $m_b = 69$ for $h = 23$ on the bit side) so right cosets of $\langle \tau \rangle$ have $3$ vertices per cell and $w = 6v + 3R = 3(2v + R)$ roles per cell ($2v + R$ per vertex), with rank-$2$ data-bank finishes ($6v$ children of width $2$ per $3$-vertex cell).
2. Restricted $h = 22$ complex cover with late compensation reads and joint frame refinement (gauge_deadlines.py, late_birth_weighted.py, refine_reuse.py):
   • Restricts the $h = 23$ DAG to $h = 22, v = 1,540$ (virtual_R = 22,977), applies $2,483$ compensated reuses ($1,703$ initial + $780$ late-birth pairs across $2,865$ delayed-read roles) to reach $R = 20,494$ physical roles, and refines plateaus/gauges/handoffs to certify $a_c = 425135147 / 10^{12} \approx 4.25135147 \times 10^{-4}$.
3. Relationship to Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144 and Use exact telescoping min-cut bit subset on paired-cube shared cores for kappa = 4.61028508707e-4 (4.61239827139e-4 at atom=1/2000) #146:
   • In this PR (Late compensation and joint frame refinement: conditional κ = 4.24830828577e-4 #143), the complex supplier ($a_c = 4.25135147 \times 10^{-4}$) is the binding side below the unpruned 69D bit supplier ($a_b = 21380424197 / 5\times 10^{13} \approx 4.2760848394 \times 10^{-4}$), yielding $\kappa = 424830828577 / 10^{15} \approx 4.24830828577 \times 10^{-4}$.
   • Note that on the 69D shared-core bit side (bit_padded.py), retaining all $11,565$ entrance gauges from PR Deferred endpoints and signed phase correction for a conditional 63965813/10^12 > 2^-14 bound #97 pays target-chain split costs on low-benefit slots; applying the exact telescoping submodular interval-$s$-$t$-min-cut reduction from Use exact telescoping min-cut bit subset on paired-cube shared cores for kappa = 4.61028508707e-4 (4.61239827139e-4 at atom=1/2000) #146 (retaining $9,730$ gauges and moving $1,835$ old-value reads to the initial zero frame) lifts the 69D shared-core bit supplier from $4.27608 \times 10^{-4}$ to $a_b = 461454009452021 / 10^{18} \approx 4.61454009452 \times 10^{-4}$ (coarse saving $a_0 = 461877426979 / 10^{15}$), which when paired with the $h = 24$ paired-cube complex supplier ($a_c = 4.856569 \times 10^{-4}$ in Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144) certifies $\kappa = 461028508707 / 10^{15} \approx 4.61028508707 \times 10^{-4}$ in Use exact telescoping min-cut bit subset on paired-cube shared cores for kappa = 4.61028508707e-4 (4.61239827139e-4 at atom=1/2000) #146.
   • Meanwhile, the late-birth compensation and joint plateau/gauge/handoff refinement techniques introduced here (gauge_deadlines.py, refine_reuse.py) are an independent local-word optimization on the physical-reuse track.

[Mister-Meeseeks]

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

Contribution: Late compensation before birth and target deadlines.

Review and limits: Exact-head CI evidence; donor finish, disjointness and complete chronology are checked.

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: 803b28a5e373442974385396e9d4d3f6e75fd5e7. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.