Conditional κ = 0.001168862033074029: R715 target factors in non-hosting banks

[eumemic]

κ = 0.001168862033074029

This conditional non-hosting construction improves our frozen R740 banked result (eumemic#3, κ = 0.001145834572824929) by approximately 2.01%. It composes the pinned R715 rank120 word and fourteen target-interval factors from #478 with #443's unchanged 32-replica whole-residual banks, nine stages and accounting engines, with a freshly recomputed finite invoice and the cited #433 complex supplier.

The R715 word uses 715 helpers instead of 740. There are 55,920 live families, 1,261,440 paid children, rank mass 3,568,896 and deficit 9,984. The exact bit lower bound is 1170229870339438219571/10^24; the cited complex lower bound remains 1183986549206329/10^18. This does not claim to exceed the higher reported whole-hosting or split cross-copy bounds in #473 or #480.

Verification reconstructs the final scalar word byte-for-byte from its pinned parent and selection, checks all 955 independent scalar columns and dirty restoration, both literal and reflected frame ledgers, copied-work closure, native C++ legality and five/nine-stage columns, nonvacuous record mutations, exact rational projectors, the full banked program, complete paid profiles, two rational moment engines, the finite invoice and all 47 strict outer inequalities. A separate audit constructs full64 coordinate routes for all 205,920 helper occurrences, verifies actual owner injection, and covers all 25,200 bank families without overlap or padding. Each route needs at most 56 coordinate transpositions within the existing paid allowance. The verifier also reruns the unchanged parent443/436 suite. The complex supplier is bound by its pinned receipt; its full phase suite is not rerun.

Both the complete worktree replay and a fresh replay from the committed Git archive passed on Python 3.12.13. All 139 package files matched the committed and archived bytes; the independent release review also passed. CI is included for Python 3.11 and 3.14; no CI success is claimed before it finishes.

This remains conditional on the inherited all-size compiler, routing, compressed geometry, restored work, precision/recovery and analytic interfaces. No complete Lean proof, unconditional multiplication theorem or global optimality is claimed. The local scalar word is inspectable UTF-8 JSON; upstream Git blob pins, licenses and AI disclosures are preserved.

Credits: DreamingOfClouds for the R715 carrier and overlap cancellation (#463); Rohan Arun for kernel selections and retiming (#467/#470/#473); Dugongue for the fourteen target factors (#478); chafreaky for the shared-kernel mechanism, banked routes and independent audit (#417/#443); eumemic and prior contributors for #436/#440/#441; icekylinx for #433 pricing and complex supply; Zhihao Chen and the wider integer-mult-bounds contributors for inherited geometry, compiler and assembly. The new non-hosting composition, source-bound packaging, explicit bank-route audit and review were prepared for eumemic with substantial OpenAI Codex assistance. All original notices are retained.