Conditional κ = 0.00167166528321877: seven triangle-hybrid slots (PR987 search) on the k8 leaver word

[jeremykothe2]

Summary

Conditional κ = 0.00167166528321877. That is +2.78×10⁻⁷ over #1005 (0.001671387264390146) and +9.70×10⁻⁶ over the merged #942. The complex side binds; PR589's bit supplier is unchanged.

Change: seven more triangle-hybrid slots on #1005's k8 word. The slot search and the first two slots (X = 444, 446) are rohanarun's #987. Running #987's search over k8's copy gates found five more legal slots (X = 236, 238, 434, 436, 439); a re-search on the seven-slot word finds none further. The mechanism is #869's triangle-hybrid B delivery.

• Construction: Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005's reviewed construction/barch/build_tri.py and run_controls.py, unchanged (byte-identical), with the new recipe construction/slots/RECIPE-SLOTS-k8.json. Input db2c7cfb…, output c2b29430…, widths unchanged.
• Controls: 34/34. These are C0 identity, the recipe, and drop_restore, restore_full, drop_preread and donation_after, applied globally and to each of the seven slots. All are rejected as pinned in SLOT-PINS-k8.json.
• Frames: the exact global frame optimiser finds no gain on the slot word.
• Owners: Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005's owner map rebound to the new word. Data admitted on this package's code: discovery, then freeze_spec, then strict.

Verification

This follows the repository's explicit baseline-reuse pattern (as research/complex-t37-owners/verify.py --baseline799). construction/slots/verify_slots.py takes a completed #1005 chain replay and rechecks it: the complete step receipt (21 steps, all exit 0), the final word against #1005's frame-recipe pin, the canonical, program and Clifford locals against CHAIN-PINS-k8, and all five layer-end control counts. It then rebuilds only the slot layer with its controls, the native locals of the new word (native, ledgers, local-replay, wrappers, phases), audit_local, and the strict global replay.

From a fresh clone of commit eac7547 (Windows, CPython 3.11.11):

• verify_manifest.py: PASS, 172 files
• verify_slots.py --baseline <completed #1005 chain replay>: steps parent-manifest (1 s), slots (0 s), slot-controls (16 s), native (1 s), ledgers (1 s), local-replay (8 s), wrappers (2 s), phases (118 s), audit-local (1 s), strict (20 s); PASS_SLOTS_ON_CHECKED_K8_BASELINE 0.00167166528321877 (2 m 48 s total)

The inherited evidence/, proof notes and README body below the new section are #1005's files, retained unchanged as parent evidence. The current receipts for this package are RESULT.json (strict replay), construction/slots/SLOT-PINS-k8.json and verify_slots.py's output.

Scope

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

Credits

• rohanarun (Conditional κ = 0.001662039077758742 — U10 (two new triangle-hybrid slots) on PR942's T37 owners #987): the slot search and the X = 444/446 slots.
• NewBArch's Conditional κ = 0.001661948695165034: eight triangle-hybrid B deliveries in block 0 on PR799's word #869 triangle-hybrid delivery, and everything credited in Conditional κ = 0.001671387264390146: all eight mutable-leaver all-K cells, U8 hybrids and frame re-optimisation on PR799's word #1005 and Gauge44 factory and whole-family assignment for conditional κ = 0.001649483702558979 #645.

Prepared with Claude Code (Anthropic).