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Improve kappa with an eight-replica rank-seven construction #3468

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Merged
Mister-Meeseeks merged 3 commits into from
Oct 18, 2026
Merged

Improve kappa with an eight-replica rank-seven construction #3468

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e47d1dd
Compose rank-seven supplier with T16 for improved conditional kappa
hexapode Oct 18, 2026
52c8434
Improve T16 allocation with bounded omitted full-bin patterns
hexapode Oct 18, 2026
dbeac6c
Compose current rank-seven supplier on eight replicas for improved kappa
hexapode Oct 18, 2026
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7 changes: 7 additions & 0 deletions research/t8-rank7-provider-composition/BOUNDED-DOMAIN.md
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# Bounded replication experiment

The changed parameter is replica count: fixed T8 instead of PR3465's T16. Source words, nine-stage per-replica events and native interfaces remain unchanged. Chronology is the exact projection of PR3413 onto replicas 0 through 7. The candidate dictionary combines the inherited PR3465 patterns with active patterns from a chronology-free T8 relaxation; the latter is a necessary-cost screen, not an owner construction.

One chronological integer model was allowed at most 120 seconds. It returned an integer solution after approximately 43.3 seconds, yielding 106 allocations and 645 nonzero flows. Floating optimization status is not used in scientific verification. Exact conservation, deterministic coloring, both native owner audits and complete modern admission establish the retained candidate. No further allocation search was run after freezing it, and no global or chronological optimum is claimed.

Potential future work must name a different replica architecture or interface, first show a favorable complete cost bound, then retain actual source-event windows and physical/private-buffer bills. The existing attained 480-helper envelope is not a bound for this 408-helper supplier.
2,625 changes: 2,625 additions & 0 deletions research/t8-rank7-provider-composition/CANONICAL-INPUTS.json
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12 changes: 12 additions & 0 deletions research/t8-rank7-provider-composition/CAP-RATIO.json
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{
"scope": "Complex endpoint divided by the same current-word packing cap; not a T8 optimality claim.",
"candidate": "27015506985863611979/15625000000000000000000",
"cap_root_lower": "1729777494678597011886903656817803609/1000000000000000000000000000000000000000",
"cap_root_upper": "17297774946785970118869036568178036091/10000000000000000000000000000000000000000",
"ratio_lower": "17289924470952711666560000000000000000/17297774946785970118869036568178036091",
"ratio_upper": "1728992447095271166656000000000000000/1729777494678597011886903656817803609",
"source_pr": 3361,
"source_head": "f9de2024916a347d939ed256a7a2e9e68d633684",
"source_path": "research/coupled-cap740-grid35/RESULT.json",
"source_sha256": "d4193c7f5f1a0dbc1d9287ce547fc6b354a700bf2e694d00f8f246768593c2ef"
}
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