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…it hosting assumption
….001265848755025708
…s and revised exact assembly
rohanarun
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… runtime receipts
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Conditional κ = 0.001265848755025709, 0.1966% above #445 at
40ab91daf2b5e87fc4071dedae1699d5d7e7cecc, under the same additional PR442 idle-data hosting assumption. The complex supplier binds.Combine our PR434 rank147 kernel (123 pivots,118 donor slots) with PR445's eleven compressed stages and dimension78. Frozen ownership hosts all65,120 helper occurrences:9,600 live/9,609 physical families, zero helper banks, deficit3264. Bit lower
0.001267514693114214441041; complex lower0.001267453159029119461392. Keeping the full certified complex endpoint improves the initial draft's last κ grid digit from708 to709; this final tick is a precision-only change, not a stronger supplier.Verification: uninterrupted full Python3.11.15 and3.14.8 runs passed at the708 endpoint, including complete parent reconstruction and all complex phases. Exact receipts/logs/manifests are in
research/e8-eleven-hosting-selected-validation/python311/andpython314/. The only subsequent executable change is two lines in the assembly (retain the full rational endpoint and compare it to the inherited weaker bound). Both runtimes reran both exact moments, refreshed invoices, six bootstrap levels,47 strict inequalities and adjacent-grid/parameter controls against their fully verified suppliers. Seeprecision/for the exact diff, input hashes and receipts. No fresh uninterrupted full wrapper of the revised manifest is claimed; CI remains pending.The unchanged full supplier checks cover all9,340 unbanked scalar columns; signed ten-wire identity and24 omitted-shear controls;1,320 geometry routes; complete1,740,288-instruction digest; every hosted owner and22 mutation controls; three-level halving,514-bit coefficient charged1024 and complete row bound19431<20161. The earlier disk-exhaustion failure and corrected missing-dependency setup logs remain preserved. SSD cleanup freed7.4GiB before the successful full runs.
Reproduce: install
sympy, thenpython -B research/e8-eleven-hosting-selected/verify.py /absolute/new/output. Subsequent unsuccessful complex-side retiming, hosting and partition screens are retained under the validation package'sresearch/to avoid duplicate work.All inherited all-size compiler, dirty-helper/compressed-window, restored-work, tape/common-grid, precision, row-divisor and analytic assumptions remain. Finite audits do not prove the hosting operator extension. No unconditional multiplication theorem, earlier-assumption record, or new Lean proof is claimed.
Prepared by Rohan Arun with substantial OpenAI Codex assistance. Eleven-stage geometry and row argument: chafreaky #445 (OpenAI Codex assistance). Credit #443/#444/#417/#439, eumemic #436/#440/#441, DaysSky #442 (Anthropic Claude assistance), icekylinx #433 and all retained earlier authors. Exact pins, licenses and source notices are preserved.