Conditional κ = 0.001675658002271934: two source-holder fusions on #1148's joint-entrance k8 word

[mdumitrean]

Change and mathematical scope

This proposes the conditional finite witness κ = 0.001675658002271934, +9.705×10⁻⁸ (0.00579%) over #1148's
joint-entrance witness 0.001675560947524449. It is also above that word's fixed-family all-replica grid ceiling,
0.001675568675201533, which this crosses by changing the local word. That ceiling is the value #1169 attains with T37
packing, the highest open claim when this was submitted.

Depends on #1148. The branch starts from #1148's current head e7d0d016 and reuses its joint-entrance word, frozen T16 owners,
k8-eight-ends-t16 parent and run_global.py unchanged. Until #1148 merges, this PR also shows #1148's commits; the new
content is only research/k8-source-holder-fusions/.

Two of the k8 word's seven triangle-hybrid slots (#987/#1018, sites X=439 and X=444) use a two-donation form. Each is
replaced by:

• the slot's own source-holder donation (holder 10, resp. 34), with its FULL-cleanup restore;
• the full read-set exchange of the slot's copy pair (584, 439), resp. (590, 444), in place of the second-holder
  donation (74, resp. 98) and its early tail.

The other five slots and every entrance and end frame are unchanged, as are helper widths, rank mass and #1148's owners.
All A, B and tail frames are refitted exactly. The local paid profile changes from {1:2364,2:498,3:412,4:130,5:82,8:8} to
{1:2358,2:504,3:408,4:134,5:80,8:8}, exactly {1:−3,2:+3,3:−2,4:+2,5:−1} per site. The idle profile
{1:360,24:1,48:4918} and the 69,120 whole-helper roles in 144 calls are reused verbatim.

Start review at research/k8-source-holder-fusions/README.md, PROOF.md, CLAIM.json and verify.py.

Validation

The complete package wrapper passed on macOS (Python 3.14, NumPy/SymPy/SciPy, no C++ or Boost needed). It ran cold,
rebuilding #1148's parent geometry and the native chain:

• Parent: Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's k8-eight-ends-t16 replay rebuilt from the seven-slot base and checked against all 16 parent pins.
• Build: the word built from Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's word by a standard-library literal patch, with every removed element checked.
• Local audit: Gauge44 factory and whole-family assignment for conditional κ = 0.001649483702558979 #645's independent audit_local.py, i.e. exact forward and dual replay of all 704 columns, frames,
  entrances and cones.
• Controls: 10/10 fusion negative controls rejected; at each site: dropped restore, dropped donation, flipped
  donation sign, kept fused read, and dropped donation and restore.
• Native: fresh PR635 native local chain, five stages including all phase edges, with semantic identities equal to the
  rebound PLAN.
• Strict T16 admission: Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's unchanged run_global.py. 69 admission, 12 bit-supplier, 15 controller and six
  independent T16 controls, both exact moment engines and all 47 strict outer inequalities.
• Final line: PASS_K8_SOURCE_HOLDER_FUSIONS_COMPLETE_ADMISSION 0.001675658002271934.

PLAN.json.gz is #1148's PLAN with only the word-dependent fields rebound: provider hashes, semantic identities, program
hashes and the paid profile. SPEC.json was re-derived by the engines' discovery → freeze protocol before the strict run.

python -B research/k8-source-holder-fusions/verify.py --base "$BASE" --work /absolute/new/output-directory

BASE is the R480 k8 + seven-slot word pinned in research/k8-eight-ends/RECIPE.json. --parent-from and
--native-from reuse completed replays.

The same two-site change was also strictly admitted on earlier hosts, recorded in SEARCH.json and not separate claims:

• 0.001672756914849856 on Conditional kappa 0.001672660197076918: rare-pattern T16 exchanges #1094's T16 owners;
• 0.001674194854569677 on Conditional κ = 0.001674097969905390: an attaining T37 construction and fixed R480 owner optimum #1129's T37 owners;
• 0.001675218651386511 on Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's three-demotion word.

Search and attribution

The sites come from an exhaustive exact sweep of read fusions with enlarged-reader repairs:

• on the pre-slot k8 word, 2,405 fusions, with exactly these two gains;
• on the seven-slot word, 2,217 fusions, with none.

The tools are in the companion tooling PR #1186 and are not needed for verification.

The change is width-neutral, so it also applies to #1169's T37 owners for the same joint-entrance word (idle
{1:834,48:11374}). There it is priced exactly at 0.001675665730846312; that is not strictly replayed here and not
claimed. #1152's word was not rebuilt. Fresh open PRs were checked for overlap before
submission; none uses this exchange variant at these sites.

Built on:

• Thomas DiFiore's Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148, with seslly/shipstuff's PR1111 lead;
• Jeremy Kothe's mutable-leaver k8 and seven-slot words (Conditional κ = 0.001664233607446043: mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1004/Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005/Conditional κ = 0.00167166528321877: seven triangle-hybrid slots (PR987 search) on the k8 leaver word #1018);
• Rohan Arun's Conditional κ = 0.001662039077758742 — U10 (two new triangle-hybrid slots) on PR942's T37 owners #987 slot search, NewBArch's Conditional κ = 0.001661948695165034: eight triangle-hybrid B deliveries in block 0 on PR799's word #869 triangle-hybrid delivery and BRoute's SW4 read-set exchange;
• Hao Yan's Research: T16 owner concentration raises conditional κ to 0.001661642255531641 #858 T16 controller and checker, and the PR870/PR1074 admission engines;
• icekylinx's Gauge44 factory and whole-family assignment for conditional κ = 0.001649483702558979 #645 and audit_local.py, PR635's native chain, PR559, and DreamingOfClouds' PR589 bit supplier on
  eumemic's PR555.

Full credit is in NOTICE.md.

All-size compiler, common-label/mutable-source realization, whole-call hosting, precision/tape, exact recovery,
analytic-transfer and bit H1–H5 assumptions remain. This is not an unconditional multiplication theorem or a Lean
certification. The selected repository certificate is unchanged.

Prepared by Marius-Paul Dumitrean with substantial AI assistance (Anthropic Claude, via Claude Code), under Apache-2.0.

[Mister-Meeseeks]

100-PR batch review at cc1b023b123622abba467c7933f3759f8034c753.

This remains open after scoped triage. Next review step: Whole-head supplier review remains open for research/k8-coordinated-owners, research/k8-eight-ends-t16, research/k8-eight-ends, research/k8-joint-entrances, research/k8-source-holder-fusions, research/k8-three-demotions. Bind its exact native providers, physical owner allocation and admission evidence, then reconcile changed predecessor blobs before merge. Path overlap with a replayed descendant does not establish complete coverage; see SUPPLIER-FAMILIES.json.

This is a specific continuation point, not a rejection or a request to redo already recorded checks. Completed local evidence is retained separately from outstanding whole-head obligations.

Batch review, attribution and evidence. Thank you for the contribution.

[mdumitrean]

Whole-head supplier data for the continuation point above, now at head 99a8a424.

Predecessor reconciliation. #1195 was branched from #1148's e7d0d016. #1148's head is now 506ea08d, which changes
only records in research/k8-joint-entrances:

Path in research/k8-joint-entrances	e7d0d016	506ea08d	Consumed by #1195
MANIFEST.json	001cb880	f17eecce	no
README.md	504aae69	c6156654	no
evidence/REPOSITORY-VERIFICATION.json and three repository-*.log.gz	absent	added	no

I merged 506ea08d with merge commit 6447ac74; no history was rewritten.

• The five inherited directories now have exactly Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's tree ids: k8-coordinated-owners 95810919, k8-eight-ends
bb118a1c, k8-eight-ends-t16 1772764e, k8-three-demotions 0471df8e, k8-joint-entrances 0e567f6d.
• git diff 506ea08d 99a8a424 touches only research/k8-source-holder-fusions/, 29 files.
• The eight consumed predecessor files in SOURCE-PINS.json hash identically at Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's f1d8dc59, e7d0d016 and
  506ea08d.

Binding. evidence/WHOLE-HEAD-BINDING.json
was written by the new standard-library binding.py from a fresh verify.py run on this head. The run rebuilt the parent
geometry, ran the native chain and ran the strict T16 admission. A second, independent fresh run and a run reusing
completed replays reproduce its stable section (binding.py --check).

• Native provider.
  • The word payload bd8a8dc5… equals both FULL-WORD.json.gz and the recipe output.
  • The PR635 chain ran native, ledgers, local replay, wrappers and phases.
  • The seven semantic identities equal those in PLAN.json.gz.
  • Content hashes of all ten native artifacts and of the bound providers/gauge44 directory are recorded.
  • Paid profile {1:2358,2:504,3:408,4:134,5:80,8:8}.
• Physical owner allocation.
  • Owners: Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148's k8-joint-entrances/OWNERS.json.gz 7755af41…, copied unchanged. PLAN payload 4a9e68c0…, and
    SPEC.json.
  • T=16, M=73, live 14336, deficit 5120.
  • The independent owner/profile audit passes: 69,120 hosted residuals, 704 owners per call, rank mass 1,041,408,
    physical width 14826.
  • The hosting template is 9a77a95a…, a canonical hash that excludes async_schedule.source_plan_sha256. That field is
    the runtime PLAN hash. It binds CLIFFORD-REVIEW.json's elapsed seconds, so it changes on every run.
• Admission. PASS_CHANGED_LOCAL_INTERFACES_STRICT_T16_ADMISSION with κ = 837829001135967/500000000000000000 =
  0.001675658002271934. The receipt also records:
  • the complex and bit endpoints;
  • 69 admission, 12 bit-supplier, 6 independent-T16 and 15 controller controls rejected;
  • 10 fusion controls and 47 strict outer inequalities;
  • every stage log hash.

Not covered. The five inherited packages' own claims remain part of #1148's whole-head review. This verifier runs
three of #1148's scripts:

• k8-eight-ends-t16/verify.py, completely, for the parent geometry;
• k8-eight-ends/replay_native.py, on this word;
• k8-three-demotions/run_global.py, with k8-joint-entrances' owners.

k8-joint-entrances/verify.py needs a C++ compiler and Boost and was not rerun here. #1195 should be merged after #1148,
or together with it.

Prepared with substantial AI assistance (Claude Code).