Under review (split-residual interface): cross-copy hosting on #472's R715 eleven-stage word; computed κ = 0.001372550159367980 not established

[higherbeing]

Conditional κ = 1372550159367980/10¹⁸ ≈ 1.372550159367980·10⁻³, bit-bound, +1.63 % over #469 (1.3505809·10⁻³) and +6.23 % over #472 (1.2920996·10⁻³). This is #448's cross-copy slot applied to #472's suppliers: chafreaky's R715 word with shared kernel, target mixing and retimings in eleven compressed stages on the bit side, and #448's cross-copy hosted #433 word on the complex side. Neither local word nor any schedule, isometry or bridge changes; only the owners of the helper residuals do.

Change

#472 hosts all 62,920 helper residual occurrences whole on idle data families (pooling the eight replicas), which leaves copies partly empty because widths 8/7/6 do not tile children of rank 7, 14, 28, 42 and 56; those remainders are paid. Here the pending sets of a child's 1,920 pooled copies form one tape, residuals are laid along it widest first, and a residual that straddles a copy boundary is owned by two copies of the same child, which share the window. The complete-program identity is #448 §2, family by family; the exact finite check of #448 §7 covers the two-family case in the model of #451's note. The concave cost makes the contiguous fill optimal: filled copies pay nothing and only the unfilled copies of the rank-56 final children pay.

supplier	parent saving	this saving	hosted residuals (split)	max child
bit, m = 78, R = 715, 11 stages, 8 replicas	1.293771·10⁻³ (#472)	1.374423·10⁻³	62,920 (14,612)	56
complex, m = 73, R = 560	1.437532·10⁻³ (#448)	1.437532·10⁻³	40,320 (13,720)	48

Accounting follows #472: eleven-stage invoice with three-level halving, complete row bound 19,431 < 20,161, the chronological physical prefix bound recomputed on the new owners (a split owner's two families both receive the update, a new accounting choice that is a review point of its own; 1,161 bits charged 1,216), one further route factor per helper selector for the split. Deficit 3,264 unchanged. The integer programme is frozen in SELECTION.json; any residual it leaves out is placed on an in-window child with room.

Validation

python3 -B research/cross-copy-hosting-r715/verify.py /absolute/new/output [--quick] runs #472's complete verifier (which rebuilds #458's complex supplier and the R715 composition), then both generators, an independent audit that shares no code with them (windows re-derived; one owner record per helper; pieces on copies of the named child, inside the pending set, widths summing to the residual width, disjoint per (child, copy), inside the window, off the active pair; owner families recomputed; unchanged template parts byte-identical to #472's; remainders, profile, stock, deficit, emitted-program digest and prefix bits recomputed; fifteen mutation controls rejected), and the exact assembly (two rational moment engines per supplier, both finite invoices, six bootstrap levels, all 47 strict outer inequalities; next-grid and η/β controls rejected). Local run: macOS, Python 3.14, quick mode (skips only #443's inherited exhaustive controls); every value, the emitted digest and the complex template hash match EXPECTED.json. CI is not claimed before it runs.

Scope

Conditional like its parents. The review point is #448's cross-copy slot, on which #450, #453, #464 and #469 also rest; #451's trace note and the replies on that thread describe the disagreement. #472's own review points and all inherited interfaces remain assumptions. No Lean proof and no unconditional integer-multiplication theorem is claimed.

Credits and AI disclosure

Builds on and runs unchanged: #472, #467, #463 (R715 word: DreamingOfClouds), #458, #454, #451, #443–#445 (chafreaky), #442 (DaysSky), #450 (target mixing), #441/#440/#436 (eumemic), #434 (Rohan Arun), #433 (icekylinx), #425/#386 (Zhihao Chen), #370 (Dylan Crow), Jacob Sussman's E8 unit and interfaces. This branch is #472's branch plus one new directory, research/cross-copy-hosting-r715/; no inherited file is changed. The cross-copy generators, audit and assembly were prepared by higherbeing with substantial Claude (Anthropic) assistance.

🤖 Generated with Claude Code

[hipotures]

Independent replay: at the pinned head 668c7dd0, verify.py passes from a fresh worktree and reproduces κ = 0.001372550159 exactly.

An independent ledger of the produced bit template finds consistent coordinate accounting, with no overlaps and windows that match the schedule. It also finds 14612 of 62920 hosted residuals (23%) split across two copies. This κ therefore inherits #448's split-residual interface. Our note on that interface is on #448: #448 (comment). In a single-stream register model, the split is a program of the priced word only with one extra helper per split residual.

Report: https://github.com/hipotures/rad/blob/c6d971dabdde94e1c5ec1521c44ca63fd41debf9/research/integer-multiplication-bounds/campaigns/frontier-batch-20261011/report.md

---

This analysis was carried out by Claude Opus 5.5 (Anthropic) under human supervision.

[higherbeing]

Status: this κ inherits #448's cross-copy slot. hipotures' single-stream register model on #448 (#448) shows the split is a program of the priced word only with one extra helper per split residual, which costs more than the remainders it removes; the hub states no multi-stream register interface. The claimed gain is therefore not established. Retitled as under review; the package is left intact and reproducible.