Under review (split-residual interface): #493's R489 bit word with #448's cross-copy complex supplier; computed κ = 0.001435468764627892 not established

[higherbeing]

Conditional κ = 358867191156973/(2.5·10¹⁷) = 0.001435468764627892, complex-bound, +4.63 % over #480 (1.3725502·10⁻³). This composes two published suppliers without constructing anything new on either side: eumemic's #493 R489 bit word (bit c = 1.565442·10⁻³, whole-residual hosting, eleven stages, no cross-copy slot on the bit side) and #448's cross-copy hosted #433 complex word (b = 1.437532·10⁻³).

It is the pairing #493's own assembly prices as "information only". Here the complex supplier is rebuilt and audited rather than cited: #442's complete verifier rebuilds #434 and the #433 word with its Gaussian phases, the cross-copy generator re-hosts it, and an independent audit (seven mutation controls) checks every piece, window, remainder and the deficit before the assembly. #493's package is vendored byte for byte and its verify.sh is run unchanged, including its controls that reproduce #472's and #445's published bit savings; the bit root is asserted equal to #493's receipt.

supplier	saving	hosting	source
bit, m = 78, R = 489, eleven stages, 8 replicas	1.565442·10⁻³	whole residuals (#442)	#493, rebuilt
complex, m = 73, R = 560, nine stages	1.437532·10⁻³ (binds)	cross-copy (#448)	#448, rebuilt and audited

Assembly: #493's bit half (#472's eleven-stage invoice with R = 489: three-level halving, physical prefix charged to the next 64-bit block, complete row bound < 20,161) with #448's complex half (#442's invoice with the hosted stock), then the #434/#315 outer assembly: six bootstrap levels, all 47 strict inequalities, next-grid and zero-η/zero-β/unit-β controls rejected.

With the bit side at 1.5654·10⁻³ the complex supplier is now the constraint by 9 %, so the next gains are on the complex side (an eleven-stage layout with cross-copy hosting, a complex response kernel as in #466/#484).

Validation

python3 -B research/r489-cross-copy-complex/verify.py /absolute/new/output runs #493's verify.sh unchanged, #442's complete verify.py, the cross-copy complex generator, its independent audit and the exact assembly, and compares every value, the emitted-program digest and the complex template hash with EXPECTED.json. Local run: macOS, Python 3.14. CI is not claimed before it runs.

Scope

Conditional like its parents. Review points: #448's cross-copy slot, here on the complex side only (the dispute is on #451's thread, with the exact two-family check in #448 §7), and #493's own points (mutable-source bit word, carrier structure, relaxed checker). All inherited interfaces remain assumptions. No Lean proof and no unconditional integer-multiplication theorem is claimed.

Credits and AI disclosure

eumemic (#493 word and pipeline adaptation), DaysSky (#442), chafreaky (#443–#445, #472 pipeline, #451 review), icekylinx (#433), Zhihao Chen (#425/#386), Rohan Arun (#434), Dylan Crow (#370), Jacob Sussman, and all source-pinned authors. This branch is #480's branch plus #493's package vendored unchanged and one new directory, research/r489-cross-copy-complex/. The composition, complex audit and assembly were prepared by higherbeing with substantial Claude (Anthropic) assistance.

🤖 Generated with Claude Code

[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.