Conditional κ = 0.001734770557111513160495: R438 bit supplier with #3190's idle-remainder donors (complex binds again, +0.0775%)

[rohanarun]

Conditional κ = 0.001734770557111513160495 − 10⁻⁴⁶ − 10⁻⁷⁰. This is +1.3435e-6 (+0.0775%) over #3190, +4.58e-6 over #3184 and +4.99e-6 over #3148.

	complex endpoint	bit endpoint	binds	κ
#3190	0.0017347705571115131604951	#589 0.001733427039589844234749	bit	0.001733427039589844234749 − …
this	0.0017347705571115131604951	R438 0.001734846264120199151475	complex	0.001734770557111513160495 − …

Idea

#3190's idle-remainder exchanges pushed the complex root above the #589 bit saving, which capped κ at the bit value. A stronger certified bit supplier is already on main: R438. That is Ali Romman's #1043 word, plus Sagar Thakrar's #2423 transport and re-hosting, with a complete native and hosted replay in research/r438-native-rehost. Its endpoint, 0.001734846264120199151475, sits above the new complex root, so with R438 the complex side binds again.

This PR stacks on #3190 (rank7-idle-remainder-donors-t740 is included). It also carries the registration fix for #3190's failing replay job: TASK/SOURCES/VERIFY schema, open questions, and a read-only verifier.

Verification

research/rank7-idle-donors-r438-bit/verify.py uses only the standard library and runs in about 1 s. It checks three things, each with its own interval arithmetic:

1. It recomputes Conditional κ = 0.001733427039589844234749 (bit-bound): idle-remainder donors on #3148's T740 fill (+0.187% over #3184) #3190's complex root bracket on its complete profile.
2. It re-derives the R438 endpoint from the certificate's own bit profile (m = 64, live = 28,416, including the 10⁻¹⁶·32m² fallback envelope): accepted at c, rejected at c + 10⁻²⁴.
3. It checks κ = min(floor₂₄(complex), floor₂₄(bit)) − 10⁻⁴⁶ − 10⁻⁷⁰ against CLAIM.json, gated above Realize the coupled-carrier T740 packing cap: κ ≈ 0.001729777494678597 #3148, Conditional κ = 0.001730189061233850760095: idle rank-48 star exchanges on #3148's T740 fill (+0.0238%) #3184 and Conditional κ = 0.001733427039589844234749 (bit-bound): idle-remainder donors on #3148's T740 fill (+0.187% over #3184) #3190.

Three mutation controls are rejected. scripts/research_package.py passes locally with Python 3.12 for this package and for rank7-idle-remainder-donors-t740.

Scope

This is conditional on #3190 and its stack (#3148, #3133, and the hosted-remainder donor hypothesis), and on R438, whose source PR #1043 is open; r438-native-rehost does not promote a selected supplier.

R438's bill fits the inherited bounds: row coefficient 18,355 < 20,161, and maxchild 42. The T74 outer ledger pins the #589 constant and only asserts complex < bit. That assertion holds with R438, but the constant still needs re-pinning in a release.

All inherited obligations remain.

Credits

• Ali Romman (Finite BIT construction: R438 source boundary with full hosted invoice #1043)
• Sagar Thakrar (Bit construction (no κ; conditional on #1043): R438 + one transport + optimal window-respecting re-hosting → c = 0.0017348463 (+0.082% vs #589); fixes two #1345 atlas crashes #2423)
• commdata2338 (Research: certify exact pending projectors for PR #2423's R438 rehosting #2653)
• the r438-native-rehost authors
• the Conditional κ = 0.001733427039589844234749 (bit-bound): idle-remainder donors on #3148's T740 fill (+0.187% over #3184) #3190/Conditional κ = 0.001730189061233850760095: idle rank-48 star exchanges on #3148's T740 fill (+0.0238%) #3184 credits: Gonzalo-Mier Idle pair exchanges improve the #1094 κ candidate #1252, Guéorgui Maissouradze, Jeremy Diviney Realize the coupled-carrier T740 packing cap: κ ≈ 0.001729777494678597 #3148, dcharb78 research(rank7-coupled-586-588-carrier-fold): lower helpers 586 & 588 via coupled B+restore carrier folds (κ = 0.0017297760894) #3133, Marius-Paul Dumitrean Conditional κ ≈ 0.0017290339826465: joint rank-7 end frames, five paired extractions and #2957's rewrites on #2942's words (+5.00e-6 over #2969) #2979
• DreamingOfClouds and eumemic (Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589/Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555)

Prepared by Rohan Arun. Done with help from OpenCode (Space bunny free), with Anthropic Claude assistance.

🤖 Generated with Claude Code

https://claude.ai/code/session_011S35E2acyQDaVRjPRw4TDy

[rohanarun]

Retracted. This PR reuses #3190's idle-remainder donations, and #3296 (merged, independently confirmed by #3311) shows those change the exact eight-stream physical operator. No operator-preserving replacement exists in this move class at any owner replica: 0 of 266,732 single-axis transfers survive, and the multi-copy search has found none. The full explanation is in #3251. Closing this together with #3184, #3190, #3200 and #3251.