Improve conditional κ to 0.001697060296258836 with coherent handoffs and retimed hosting

[Vlado-V]

Change and mathematical scope

This finite construction certifies conditional κ = 1697060296258836/10^18 = 0.001697060296258836, exceeding the pinned PR2312 claim by approximately 1.69229e-7. It composes that supplier's width exchange and existing kernels with a new coherent four-helper change and two jointly legal owner exchanges. It does not change the maintainer-selected record.

Twelve preparation ADDs move to their first source acquisition. Four high roles 619/621/622/623 are simultaneously replaced by retired source fields 1/4/6/12 through rank-zero Clifford handoffs at a common rank-four chart. This avoids intermediate rank-five visits. Complete arbitrary-dirt, forward/dual, cleanup and physical-phase checks pass. Helpers decrease 438→434, with 46 handoffs and all 78 proper-ended buffers retained. PR2312's actual frame choices and pivot-518/506 kernels are inherited unchanged.

Two compatible rank-seven/rank-nine exchanges use an actual jointly acyclic invocation order. All 1332 windows, owner capacities, physical families and offsets are independently reconstructed.

The complete profile is {1:1576979,2:340992,3:292195,4:79937,5:27958,7:87,8:5328,12:1,21:1,48:24545}: 666 calls, 289044 hosted roles, dimension 73, live count 66304, rank mass 4816512 and deficit 23680. Physical stock is 66748; all 78 zero buffers fit inside the priced 434-field reserve. The exact native endpoint lies between 0.0016970602962588368950279736213908681182 and …1183; the published rational lies below the complete fine-prime outer ledger. The fixed-local-profile packing cap is below 0.001720061111244974 (about 98.66% realized).

README, proof, claim, complete owner/word generators, source manifests and bound execution receipts are included.

Inherited all-size/compiler, common-label/mutable-source realization, whole-call hosting, semantic precision/fixed tapes, exact recovery, analytic transfer, PR559 recurrence correction and bit H1–H5 obligations remain. Fine-prime precision and PR1758 accretive/per-visit interfaces remain proof inputs. No unconditional result, complete Lean multiplication theorem or practical cutoff is claimed.

Task and overlap

Scope is changed against the nearest catalogue category, complex-rank-shape-decoder: the user explicitly assigned incremental κ improvement toward 0.002; no random card was drawn and no claim is made to meet its five-percent planning gate.

Base main: 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2. Exact adopted supplier: PR2312 head fb76f799ccf078f51780076ebed3fd26b1db11c0, manifest c545968fb8cf6e550b82ba631e92fd756484db75e621aee211347749cff55313. Parent baseline: PR2288 head 614c74a63b0f6d4a24c7740d7ddb90d37861b3c7. Both complete source inventories are authenticated by Git-blob and SHA256 pins.

The width exchange, new exact fill and frame re-solve are Jeremy Kothe's PR2312 work. That source already contains the PR2302 kernels; they are not inserted twice. Dugongue's PR2309 is concurrent independent single-alias/repacking work. Our addition is the simultaneous four-role producer change and its own complete owner/schedule certificate. Fresh canonical-main and bounded live-overlap checks are recorded in the package; they are not an exhaustive novelty proof.

Validation

python3 scripts/research_package.py --package research/t74-joint-owner-hillclimb --check-only
python3.12 scripts/research_package.py --package research/t74-joint-owner-hillclimb

The registered standard-library hook independently checks actual owner geometry, complete paid profile, directed moment and packing cap, publication bindings and semantic failure controls. Full cold reproduction uses fetch_suppliers.py for both explicit source roots and cold_replay.py; commands and exact Python/C++17/Boost requirements are in the README.

Full evidence includes both orientations/all 658 arbitrary columns; native Clifford phases, wrappers and restoration; Lemma G labels; complete changed controller and invoice; 114 admission, 12 bit, eight independent owner and six geometry controls; and the final fine-prime outer's 63 inequalities, 17 rejecting controls and independent checker. The baseline reuse binder covers all 1181 artifacts/four native chains; changed native reuse binds all 17 required artifacts plus the complete immutable source inventory. Deliberate phase/recipe/wrapper/source/word corruption and hosted owner time/digest mutations are rejected. Original input SPEC and regenerated frozen SPEC are distinguished with complete effective-input equivalence.

MacOS/CPython 3.14.7 execution and bounded CPython 3.12.14 execution are distinguished from hosted CI and a fresh single-process cold run without caches. Native and baseline runs were completed separately, authenticated reuse was checked, and changed controller/invoice/outer admission was rerun. Immutable source bytes stay pinned; regenerated gzip equality compares complete canonical payloads.

Credit

Cinna Davis (1337isnot1337), PR2226: anticipatory dirty borrowing and K_G/free-operator/cleanup interface. Jeremy Kothe, PR2288/PR2302/PR2312: adopted supplier, width exchange, frame re-solve, exact fill, donor kernels and ledger lineage; mdumitrean/PR1625: kernel shape; WildIdeas: preceding frame-refit work; Rohan Arun: T74 ownership. The unchanged outer retains Chafik Boukhalfa/PR1786, Tim Trudgian's prime estimate, PR1673/PR1758, Jeremy Kothe/PR2044 and dataisfire/PR2161/PR2180. Hosted binding checks address Josie Elliston/PR1959 and Aaron Wang/PR2301. Source-specific notices and licenses remain intact, including superseded work. New work is Apache-2.0 with substantial AI assistance; no independent human review is claimed.

Open next questions

The README and structured TASK metadata identify another coherent producer/basis change as the next useful step: emit one complete changed block, price every native and hosted cost, then validate phases and outer transfer. The scoped fixed-profile cap rules out reaching 0.002 through further packing alone; a larger gain requires changing the supplier or controller.