Conditional κ = 0.001651390457077212: PR648 complex supplier with the merged #589 bit supplier (outdated, independent)

[GamingPuzzled]

Outdated, independent composition. This was done concurrently with jeremykothe2's #649 (κ 0.001652528731617094: #589 bit supplier plus a dissolved owner map on gauge44) and #652 (κ 0.001652760598550299). Both are higher than this PR. It is submitted as an independent replay of the #589 bit swap applied to #648 alone: the owner map is unchanged. It makes no record claim over #649 or #652.

Summary

κ = 412847614269303/250000000000000000 = 0.001651390457077212, +0.01781% over #648 (0.001651096360425895). The complex side binds.

Why the swap is valid

• Conditional κ = 0.001651096360425895: repacked owner map on PR645's gauge44 construction #648 states its complex side certifies b = 0.0016541221, above Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543's bit c = 0.0016538270, so the bit side binds and κ is the Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543 cap. The outer assembly sets s = min(c, (1−β)·b), so a larger admissible c raises κ until the complex side binds.
• Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589 (DreamingOfClouds, c = 0.001733427039589844234749) is merged. It is preserved on main at research/e8-bit-p111-tuned/tune/EXPECTED.json (the same git blob, e293ddc5, as at Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589's head a5afc8c). Main's reviews cite Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543 only because their compositions were complex-limited. The hyperplane599 review says "Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589 is better bit headroom but is not needed by this complex-limited composition", and the family588 review calls Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555 "useful headroom". No dispute or retraction appears in the Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555 or Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589 threads.
• Retained bit premises (as in Punctured star bit unit: bit c = 0.00165947204563779652541 (+4.54% over #510) #545 and Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555): a v = 111 bit supplier in the outer assembly, and pooled-cell bit hosting. Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543 uses the same pooled-cell contract, and neither satisfies Conditional κ = 0.001274032589159993: complex kernel with paid residual adapters #458's stricter one-helper-per-family rule.
• Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555's own c (0.001733052823) gives the identical κ, since the complex side binds either way.

What changed (one commit on #648, research/gauge44-repack/ only)

• inputs/PR589-EXPECTED.json: main's Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589 receipt, byte for byte.
• code/assemble.py reads that receipt in place of inputs/PR543-EXPECTED.json. It then:
  • checks the receipt's git blob id, its c, and the word parameters (v = 111, R = 439, decoder constant 63 = 9·7);
  • replaces the literal bit deficit 9,984 (Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543's v = 120) with the nine-stage identity T(8v − 9·cst) = 32·321 = 10,272;
  • computes the binding side (complex) instead of hard-coding it;
  • records the supplier provenance.
• verify_global.py asserts the vendored receipt equals main's copy, and data/UPSTREAM-PINS.json pins main's copy by sha256.
• data/SPEC.json: only expected.kappa, kappa_decimal and conservative_kappa_decimal change. They were re-derived by the package's own discovery → code/freeze_spec.py → strict chain, and every other recorded value matched.
• README.md gains a header section, and MANIFEST.json is regenerated.

Unchanged: the owner map, PLAN, the construction, the invoice, both exact moment engines (the bit bad-residue surcharge is retained, and #589's profile is accepted at c and rejected at c + 10⁻²⁴ by both engines), the 47-inequality outer assembly, the outer controls (next_grid, zero_eta, zero_beta, unit_beta), and all 69 admission controls.

Verification

Run on macOS with CPython 3.11, from a fresh git archive of this commit:

• verify_manifest.py: PASS (87 files).
• construction/reproduce.py --until phases: PASS phases. It rebuilt the local supplier from Conditional κ = 0.001636241501576388: h4a plus PR627's two factored jp8 cold ends #635 (a6895a6); the construction files are unchanged from Conditional κ = 0.001651096360425895: repacked owner map on PR645's gauge44 construction #648.
• verify_global.py --main . --local <fresh local>: PASS for restore-parent, bind, emit, audit, invoice, assembly and admission-controls (69 rejected). It printed PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY 0.001651390457077212. The conservative (pre-Conditional kappa 0.001592517892053334: native complex moment on PR558 #559) complex charge passes at 0.00165139045419947.

git fetch https://github.com/CrocSwap/integer-mult-bounds.git a6895a69f8ad98ab45777b03e9e6f48888c39f6f
mkdir -p /tmp/gauge44-pr635 && git archive FETCH_HEAD research/complex-571-cold14-st2 | tar -x -C /tmp/gauge44-pr635
python -B research/gauge44-repack/verify_manifest.py
python -B research/gauge44-repack/construction/reproduce.py --main . --pr635 /tmp/gauge44-pr635 --out /tmp/g44b-local --until phases
python -B research/gauge44-repack/verify_global.py --main . --local /tmp/g44b-local/local --work /tmp/g44b-global

Scope

The same premises as #645 and #648 apply: the all-size compiler, common-label/mutable-source realization, normalized wrappers, whole-call hosting, precision/tape, exact recovery, analytic transfer and bit H1–H5. The #555/#545 bit premises above also apply. This is a conditional finite construction, with no unconditional theorem and no Lean certification.

Credits

• jeremykothe2: Conditional κ = 0.001651096360425895: repacked owner map on PR645's gauge44 construction #648's repacked owner map and package. The independent, higher Conditional κ = 0.001652528731617094: PR589 bit supplier and dissolved owner map on PR645's gauge44 construction #649 and Conditional κ = 0.001652760598550299: alternating dissolve/gap-merge owner map on the PR649 gauge44 + PR589 package #652 also come from jeremykothe2.
• icekylinx: Gauge44 factory and whole-family assignment for conditional κ = 0.001649483702558979 #645, the gauge44 factory, construction and verifier chain.
• DreamingOfClouds: Bit c = 0.001733427039589844: two A-section transports on #555's punctured R439 word (+0.0216%, κ unchanged) #589, the tuned punctured bit word and its receipt; Punctured star bit unit: bit c = 0.00165947204563779652541 (+4.54% over #510) #545, the punctured-star unit.
• eumemic: Bit c = 0.001733052823: #545's punctured unit on the R420 skeleton (111 live ports, +4.79% over #543) #555, the punctured R439 word; Conditional κ = 0.001587467473762886: an E8 bit word with 420 helpers, c = 0.001653826988 (+4.18% over #510) #543, the L3 skeleton and the previously cited bit supplier.
• vectorsss / Chi Zhao: Conditional κ = 0.001636456810414854: twenty-row owner improvement over PR637 #638 relocate_two.
• The Conditional κ = 0.001636241501576388: h4a plus PR627's two factored jp8 cold ends #635 lineage and every upstream contributor credited in Gauge44 factory and whole-family assignment for conditional κ = 0.001649483702558979 #645 and Conditional κ = 0.001651096360425895: repacked owner map on PR645's gauge44 construction #648.

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