Research: rule out one arity-four connector bundle

[1337isnot1337]

Summary

Adds a precisely priced arity-four source-bundle operation Q_S: z += Σ_{j∈S} B_j x_j and rules out its minimal paired-readout profiles on five and six sources. The six-source census is complete over 756,000 normalized words; none covers all 63 nonzero masks, and the exact maximum is 41. No supplier or κ change is claimed.

The n=5 pivot covers all 15,120 normalized words and has maximum coverage 25/31. The earlier scratch count included mask zero and was corrected in the coordination comment and package.

Cost conclusion

With arbitrary dirty connector state and even output-map multiplicities:

• 9 source transitions have at most 45 boundary pairs, forcing at least 162 output reads; the bill is at least (171 root calls, 174 additions).
• The exact 11-transition census leaves at least 22 output masks without a two-read representation, forcing at least 170 output reads; the bill is at least (181,184).
• The next parity-allowed source length is 13 transitions, with at least 16 source additions; even the minimum two reads per output gives (139,142), componentwise above the current six-source TRIO profile (138,140) in the uniform positive (o,p) model.

Any Q4 implementation, staging, child-price difference, scratch, hosting, precision, restoration, or interface surcharge only raises those bills. This excludes the one-Q4 six-source family in the stated model; it is not a barrier for other arities or output contracts.

Reproduction

python3 -I -B research/connector-quad-six-seedde3f84/verify.py
python3 scripts/research_package.py --package research/connector-quad-six-seedde3f84 --check-only

Both pass locally under Python 3.14.7. The registered package replay requests Python 3.12, which is not installed locally; hosted CI will run that hook.

The package pins exact base 0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2, selector seed de3f84ac54d98bf098a9e9bab973b212, priority revision 4 and the selected record. The live claim is Discussion #1166.

Predecessors and attribution

The nearest source-call profiles are PR #2128 (DUO) and PR #2146 (TRIO); PR #2134 studies a wider TRIO readout profile. PR #2182 addresses fixed-port/two-root boundaries. PR #2098's order-four typed echo and PR #2116's A4 group-algebra target use different interfaces and are distinguished in the package.

Prepared by Cinna Davis with substantial OpenAI Codex assistance in scope selection, derivation, exact search, implementation, debugging and packaging. No independent human review, physical Q4 implementation, selected supplier admission or new κ is claimed.