Shared completed cores and physical frames: conditional κ = 1.23988197806e-4

[eumemic]

κ = 1.23988197806e-4 = 61994098903/500000000000000.

κ ≈ 123988197806/10¹⁵ > 2⁻¹³.

Under the retained stopped-product, endpoint, analytic and fixed-tape interfaces, this finite witness supports T(n) = O(n(log n)^(1−κ)). This value is 0.72152% above PR #128's pinned κ = 1.2310001053253e-4. The complex saving is 1.25008315e-4; the unchanged round-seven stopped bit saving 1.240189553e-4 now limits the assembly.

The construction combines per-operation frame compression with an664's PR128 completed-core sharing, on PR117's immutable 91,770-addition DAG. Every scalar addition, carrier link and rational decoder coefficient is retained. Each add/copy occurrence gets a nondegenerate frame nested between the previous and next frames of both incident roles. Exact geometric checks validate 19,323 changed operation frames. The search uses PR114's saturated frames as guidance; the selected word sets all auxiliary source gauges to zero and has no deferred old-value reads.

A completed core restores every logical scratch coordinate for arbitrary dirty inputs. With zero source gauges, its physical pre-exterior residual is exactly C_A in both orientations, including the reflected source inverse. PR128's explicit signed orthogonal partition covers all 2,024 outer triples with 83 groups of 24 and four groups of eight. Each group runs whole cores consecutively on shared original scratch. Full groups need no auxiliary exterior; each partial group pays the signed width-384 complement on every shared role.

Complex supplier	Previous PR114	Shared physical frames
scalar additions / carrier links	91,770 / 71,185	same
local auxiliary roles	28,705	same
original streams W	124,390,992	13,187,822
total recursive rank	71,647,349,312	7,594,323,392
largest child	574	529
strict complex saving	1.09305097e-4	1.25008315e-4

Every internal transition, copied-center transform, source/target front, data projector and endpoint correction is retained. Only the separately audited unshared auxiliary exteriors are replaced by the complete group-complement ledger. The rank deficit remains 1,862,080.

Validation: the finite compiler reconstructs the pinned DAG, maximum matching, physical operation frames and exact source/target map. The independent scalar/reflection audit checks integer fresh-source coefficients, the signed rational old-readout transpose, dirty cancellation, the literal inverse/sign-negate/bank-swap word and complemented frame incidences. Numerators as large as 55/42 are split into bounded same-frame shears, and every extra shear is charged. The signed-partition checker verifies all group Gram entries, explicit complement bases, actual quadratic phases and stage-two signs. The full shared histogram, exact moments, all 47 strict constraints, seven margins, and the next bit/complex/κ grid exclusions are recomputed.

The scalar/semantic guard is G = 166402563655360. This includes the larger expanded-readout bill and a separate 64m² paid wrapper-atom reserve per group-role in each orientation. Binary basis atoms remain ordinary-bit adapter calls under the inherited interface; they are not constant-time tape instructions. All three row stocks are paid, with row degree 22,000. Completed-core Gaussian-dyadic returns preserve the inherited exact odd grid.

The complete local read-only verifier passes, including regeneration of both suppliers, signed partition phases, the shared profile, exact certificate, literal reflection audit and all 23 controls. All 39 CI jobs passed on the submitted head 77227550987a49eec5f335b61ab233fc5c93dbe8, including the focused verifier on Python 3.11, 3.13 and 3.14.

python3 research/cyclic-deferred/verify.py
make verify

research/cyclic-deferred/SHARING.md gives the operator and allocation argument. Source manifests bind the immutable DAG, round-seven bit inputs and PR128's signed partition. Verification writes only to a temporary copy. The general normal-form, transparent-core, stopped-bit, binary-adapter, semantic precision, streaming, routing, analytic, prime and recovery interfaces remain conditional assumptions; the finite checks do not prove them.

Credit: an664 for PR128's completed-core allocation, signed partition and phase checks, with OpenAI Codex assistance; Xiande Zhang and Gennian Ge for the underlying resolvable packing (JCD 18 (2010), 209–223, DOI 10.1002/jcd.20234); eumemic with Anthropic Claude assistance for PR117's producer; Avi Eisenberg / ikeboy for PR110's compiler; Swapnil Jain for round seven, lifted frames, V leaves and deferred readouts; icekylinx, Zhihao Chen, Rohan Arun, Aurel Prosz, RaD and all inherited contributors. Concurrent physical-frame work in DanieleCorso's #126 and GamingPuzzled's #125 is credited. Earlier PR114 contributions and imported notices remain preserved. This optimizer, composition and independent scalar/frame audit were prepared for eumemic with OpenAI Codex assistance.

[Mister-Meeseeks]

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

Contribution: Completed-core sharing with full pre-exterior accounting.

Review and limits: Exact-head CI evidence; current head differs from obsolete PR-body narrative. No silent zeroing of auxiliary input.

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: 77227550987a49eec5f335b61ab233fc5c93dbe8. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.