Conditional κ = 0.001660666354374641: four entrance promotions, six dim-8 ends and a width-neutral B read exchange on the PR659 word

[jeremykothe2]

Summary

Conditional κ = 0.001660666354374641 (conservative 0.001660666351491326). This is +3.27×10⁻⁷ over PR685 (0.001660339298410333) and +1.35×10⁻⁶ over PR676. The complex side binds; PR589's bit supplier gives 0.0017334.

Construction on PR659's no-triangle layered word:

1. p6n (as in PR676): six dim-8 cold ends.
2. Four entrance-promotion groups (16 helpers, E4→E5), using a minimal deterministic recipe that changes frames only.
3. sw4, new here: a width-neutral B read exchange. For four entering-copy pairs (h, r) = (461,25), (581,89), (591,415), (603,431), the phase-B target reads of h and of its face register r are exchanged. Entrance pre-reads are deleted or inserted so that every register's value at the end of B is unchanged; the builder checks this mod p. Profile Δ {1:−24, 2:+16, 3:+8, 4:−8}, width unchanged at 3778.

Owner map: chafreaky's PR685 owner assignment. PR685's promoted word is the same word as our P6k4 base (identical widths, profile, windows and call order; different helper numbering). sw4 changes no widths, so the map transfers by a per-call width-matching relabel. Idle {48:2396, 44:1, 3:1, 1:1}.

Construction drivers: construction/promo/reproduce_promo.py --base p6n --k p6n-k4 and construction/sw4/reproduce_sw4.py (standard-library builder, 16-move recipe, four controls rejecting at pinned sites). All verifier code is byte-identical to PR676's reviewed set.

Independent reviews: both SOUND.

• Promotions: byte-identical rebuild of the k4 word, 11/11 promotion controls, and the reviewer's own mutants rejected by both audits. Its own strict run reproduces the tree's κ for the earlier map.
• sw4 on this word: rebuild d232183f, the four controls hit their pinned sites, an exact replay (0 bad rows, dyadic, no ended-helper reads), no collision with the fourth promotion group, and 11 extra mutants rejected (wrong r, missing or late pre-read, dropped read).
  The owner map is a data swap on that reviewed tree; the clean-clone replay below is the binding check for it.

Verification

From a fresh clone of commit 03e8d7c, with no reused artifacts (Windows, CPython 3.11.11):

• verify_manifest.py: PASS, 122 files
• reproduce.py, reproduce_notri.py, reproduce_np.py, reproduce_p6n.py: PR659/PR676 words rebuilt, with their controls
• reproduce_promo.py --base p6n --k p6n-k4: four-group promoted word rebuilt, with its controls
• reproduce_sw4.py: sw4 word rebuilt, with its controls
• audit_local.py: PASS_INDEPENDENT_EXACT_FORWARD_AND_DUAL_ENDPOINT_FRAMES_ENTRANCES_CONES
• verify_global.py: PASS invoice, assembly, admission-controls and bit-supplier-controls; PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY 0.001660666354374641

An exact packing relaxation on this word's window geometry finishes OPTIMAL at this idle distribution, so this map is packing-optimal for the word.

The rebuilt locals equal the strict locals except two seconds timing fields. Exact commands are in research/gauge44-promo-p6k4sw/README.md.

Scope

Conditional on PR645's premises and on PR589's bit-supplier assumptions. No unconditional theorem or Lean certification is claimed.

Credits

• chafreaky (PR685): the owner assignment used here, and the PR660 exact-flow packing approach.
• icekylinx (PR645): gauge44 construction, package and verifier.
• jeremydiviney (PR658), jaymosley07 (PR653), vectorsss (PR638): owner-search methods.
• PR589 lineage (bit supplier); the PR601/604/617/622/627/635 lineage and every upstream contributor credited in PR645.

Prepared with Claude Code (Anthropic).

[jeremykothe2]

Packing note: an exact packing relaxation over every owner assignment on this word's window geometry (144 windows, same per-(time, width) supply as PR685's P6k4 word; sw4 changes no widths or windows) finished OPTIMAL after 2400 s at objective = bound = 79.64706274042115, with idle {1:1, 3:1, 44:1, 48:2396}. That is exactly this PR's idle distribution, so this owner map is packing-optimal for this word and geometry. The all-rank-48 value (2397 × 48) is not attainable here. This is a statement about this fixed word, dispatch and window geometry only.

[Rohansguliani]

Scoped audit note at pinned head 03e8d7ca494a083e5053cd6b1228f66b98414479: README says the new data/PLAN.json and data/OWNERS.json.gz are search-only inputs that no verifier reads. verify_global.py passes PLAN to bind_providers_portable.py and OWNERS to emit_allcold.py; the resulting candidate data are consumed in the verifier path and checked by the global replay and independent owner/controller audit. Please clarify the wording to say the verifier reads and validates them. This is a documentation discrepancy, not evidence by itself of an unsound bound. I have not completed the independent global κ/owner replay, so this is not a whole-PR endorsement. Audit credit: Rohan Guliani (@Rohansguliani); substantial OpenAI GPT-6 Astra assistance through Mux.

[jeremykothe2]

Thanks @Rohansguliani, you're right. data/PLAN.json and data/OWNERS.json.gz are verifier inputs: verify_global.py passes PLAN to bind_providers_portable.py and OWNERS to emit_allcold.py, which validate them during admission. Only the search tools that produced them are outside admission. Fixed in f042731 (README wording plus the matching MANIFEST hash; no other file changed). A fresh clean-clone replay of f042731 passes every stage, including verify_manifest (122 files), all construction rebuilds, audit_local and verify_global: PASS_GAUGE44_NATIVE_EXACT_GLOBAL_ASSEMBLY 0.001660666354374641.

[Mister-Meeseeks]

100-PR batch review at f042731cb332359166e8215839f9a3da28c46c5b.

This remains open after scoped triage. Next review step: Changed cold-end/promoted/read-exchange construction and transferred owner map require source-bound delta admission.

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.