Conditional κ = 0.00162536523418317: jp8-heavy dispatch with an exact integer owner map on the PR604 cold witness (+0.692% over PR601)

[DreamingOfClouds]

Conditional κ = 0.00162536523418317, +0.252% over #604 and +0.692% over #601. The conservative model gives 0.001625365231365566. The value comes from ASSEMBLY.json of the strict verify.py run on this package's literal owner map. The complex side binds; the bit value (#543, 0.0016538) does not, so κ is the same capped and uncapped.

Stacked on #604 (and through it on #601). The diff includes those commits until they merge. This PR adds one commit to research/complex-571-cold14/.

What changes relative to #604

The ck and jp8 provider words, every verifier script and every remaining build step of #604 stay the same. Only the dispatch and the literal owner map change (data/PLAN.json, data/OWNERS.json.gz), plus the recorded expected values in data/SPEC.json.

• Dispatch moves to jp8: jp8 ×71 + ck ×1, from Conditional κ = 0.00162128508944984: cold factory-scratch helpers end at 4-dimensional frames on the PR601 witness (+0.439%) #604's ck ×44, atm3 ×22, jp8 ×6. The cold jp8 word's widths tile the idle children exactly, so 8, 9 + 7, 8 + 8 and 5 + 9 + 9 + 9 fill rank-8, rank-16 and rank-32 children. In the all-jp8 solution the only idle remainders are whole rank-48 children.
• Exact integer owner map:
  • A per-owner-group CP-SAT pattern model with one helper per port per call, expanded literally by bipartite edge colouring (Kőnig); the verifier re-admits the map independently.
  • For the all-jp8 dispatch the integer optimum equals its LP bound.
  • The single ck call (the audit requires at least two dispatched providers) is added by a warm-started repair. It costs about 0.02% of b and is not proved optimal.
• atm3 removed: atm3 is no longer dispatched, so its build chain and recipes are removed.

Checks

• Strict global chain: PASS through bind, emit, the audit (23 controller mutants), invoice, assemble, 114 assembly controls, phase-timing and generated-identity.
• Pins: verify.py --check-pins on a fresh git archive gives PINS OK.
• Fresh archive: strict verify.py from a fresh git archive, with no baseline reuse, passes (40/40 stages; κ 0.00162536523418317).
• Independent review (a separate Claude agent's re-implementation): it re-derived the paid profile from the words and OWNERS, and price104.b_exact reproduces the conservative κ. The owner map passes an independent checker (one helper per call, widths/ranks, windows, distinct families, prefix cells), and 11/11 mutant maps are rejected. It also confirmed that the all-jp8 integer optimum equals the LP bound exactly.

Future optimization / research

• Remaining gap: ≈ 0.026 pt to the free-dispatch LP ceiling.
• Cold units, analysed (not shipped as an artifact) within scope (monotone frames, rank-0 premix, a fixed forward word with 46 hyperplane ends): at most 14 dim-4 ends per provider word, each unit forced, and no residual capacity at dim 5/6.
• Open items: the last 2 entering ends ("e2", ≈ +0.010% b) and extras at dim 7/8 (none positive found; the bound is not closed).
• Lineage providers (Conditional κ = 0.001593667716067094: two compatible cold kernels in all 72 calls #567–Conditional κ = 0.001602278921983212: two gate-move frame coalescences on PR584 #588, Conditional κ = 0.001600067494703216: width-seven providers and whole-owner packing #569/Conditional κ = 0.001600682403612293: joint-prefix kernels and structural bounds #571 words): they carry the same 14 units and none more. Adding them to the dispatch menu moves the joint LP by ≤ +0.008%. Small residual levers (≈ +0.06%) are left for future work.

Credits:

• Conditional κ = 0.00162128508944984: cold factory-scratch helpers end at 4-dimensional frames on the PR601 witness (+0.439%) #604 (DreamingOfClouds) is the base.
• jeremykothe2: Conditional κ = 0.001609915765452068: hyperplane-ended helpers on the PR588 witness #591, Conditional κ = 0.001612719427075359: hyperplane-ended helpers with ck/atm3 dispatch #592, [Lean] Hyperplane-ended helpers: Lemma A with an arbitrary terminal frame (no κ claim) #593, Conditional κ = 0.0016127213726553: improved owner map for the PR592 hyperplane-ended witness #596, Conditional κ = 0.001612722852614221: improved owner map for the PR596 hyperplane-ended witness #600 and Conditional κ = 0.001614202339036103: 46 hyperplane-ended helpers per call via commuting-prefix cleanup #601 (the hyperplane-end mechanism, verifier, Lean and base packages).
• icekylinx: Direct delivery with 504 helpers for conditional κ = 0.001517760977820331 #531 and Post-center rank-four kernels for conditional κ = 0.001584931111785787 #535.
• DreamingOfClouds: Lemma G of #484: clean proof and Lean 4 formalisation of its core #509, Lemma A of #484: the realization of paid wrappers and spectators, proved in Lean 4 #516 and [Lean] Hyperplane-end helpers: multi-gate cleanup tails and the cold specialisation (stacked on #593, no κ claim) #599 (Lean).
• The pinned Conditional κ = 0.001596133352130093: seven more cold-kernel helpers on PR564 #568, Conditional κ = 0.001600067494703216: width-seven providers and whole-owner packing #569, Conditional κ = 0.001600682403612293: joint-prefix kernels and structural bounds #571, Conditional κ = 0.001600770286423653: joint prefixes in all 72 complex calls #575 and Conditional κ = 0.001601661522127798: six paid-frame coalescences in the added-kernel provider #583 packages are listed in NOTICE.md.

DreamingOfClouds with Claude Opus 5.5 (Anthropic), via Claude Code.

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