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Research: six-source universal dirty-connector boundary, f(6)=16 (no new kappa) - #1185
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…new kappa) Extends PR943 (Ross Richardson) one source further: two independent exhaustive censuses exclude universal restored source words of length 12 and 14 on six labels (max coverage 49/64 and 59/64); a Gray-cycle word of length 16 covers all 64 masks. The all-63-row batch has exact unit-cost optimum 142 queries. For general n, 2^((n+1)/2) <= f(n) <= 2^ceil(n/2) + 2^floor(n/2); 18 <= f(7) <= 24. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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100-PR batch review at Merged to Reviewed scope: Exact f(6)=16 universal dirty-connector census, 142-query full batch and general square-root-exponential bounds; n=7 heuristic failure is not an exclusion. The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions. Batch review, attribution and evidence. Thank you for the contribution. |
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… kappa)
Add one new complete call type DUO_{j,k}: z += B_j x_j + B_k x_k to the frozen
universal-connector alphabet (the only changed premise is 'no combined
queries'; the call is charged in full). Exact finite result: the five-source
universal source word has unique Pareto profile (10 calls, 12 toggle-adds)
versus the frozen (12, 12), so the all-31-row batch runs 72 root queries at 74
toggle-adds instead of 74 at 74 - the support bound 72, unattainable in the
singleton alphabet, is attained exactly here. k=9 is excluded by a complete
zero-cover census of all 7,888,725 nine-point sets; W>=12 by parity plus the
reproduced 945-pairing control. n=3 (5,6) and an n=4 (6,8) side row included.
Predecessor credit: Ross Richardson's research/universal-connector-boundary
(#943 / #934).
Comparison: #1340 and
#1370 mutable-source shear (Arham Tahir),
discussion 1352; #1185 f(6)=16. Prepared by
Navinor with help from opencode. Apache-2.0.
This was referenced Oct 15, 2026
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Extends merged PR943 (Ross Richardson,
research/universal-connector-boundary) one source further. The model and alphabet are unchanged.Result
Reproduce (stdlib, ~35 s):
python3 -I -B research/universal-connector-six-source/verify.py→
PASS_SIX_SOURCE_CONNECTOR f(6)=16 max14=59/64 max12=49/64 batch63=142 f(7) in [18,24]Checks: both censuses agree on counts, histograms and SHA256 of the sorted records. As a positive control, both reproduce PR943's five-source histogram exactly. A dense F2 replay of the full 142-query program runs at d = 1, 2, 3, forward and reversed, on dirty states. Four mutation controls are rejected.
test_research_assignment.pypasses.Not checked / scope: this is a finite exclusion plus a construction inside PR943's abstract interface. It has no supplier instantiation and no new kappa. PR943's remaining obligations (common-label realization, frames, owners, full-row charging, compiler/tape, precision, analytic) are unchanged. Other alphabets are out of scope, and f(7) is open. No selected record, shared generator or upstream file changes. No discussion claim was posted. The local task card and overlap check are in
CLAIM.md.Credit: Ross Richardson (PR943, PR934) and the lineage in the retained notice. This was prepared with substantial Anthropic Claude assistance; see
NOTICE.md.🤖 Generated with Claude Code