[petalas]

Summary

Prove the exact 108 complete-call optimum for the unsigned F3 connector with five immutable sources, all 31 nonzero binary-mask outputs, and one arbitrarily dirty restored connector. This answers Riquelme Soares's explicit batch handoff in #4189. The claim is a scoped proof with a finite certificate, uniform in row length and arbitrary compatible F3-linear maps. No new kappa or selected-frontier change.

3 calls per source + 3 calls per output
= 15 source calls + 93 readouts
= 108 complete calls, attaining every operator count floor

The same literal schedule minimizes every independently positive fixed complete-call tariff: 3 sum_j c_Bj + 3 sum_m c_Am. Its unsigned reverse is a 108-call inverse. Only research/f3-five-source-connector/ is added.

Evidence

Before this result, #4189 supplied the six-call one-source result and left this batch open. The new certificate supplies all 31 three-prefix representations and a literal attaining word; the mod-three count argument excludes every shorter generic legal word, without a search cap.

Local CPython 3.12 checks pass: 816 prefix triples, 231 dense dirty-bank inputs, 462 forward/reverse comparisons, 462 roundtrips, eight semantic controls, and the 108/270 tariff fixtures. Both registered normal/optimized commands pass with warnings as errors, each about 0.12 seconds. The seven-file committed-byte/source-history preflight passes. Both commands also pass from the official Git-free export in 0.114/0.116 seconds with all eight exported files unchanged; on-disk readout and source corruptions are rejected.

Exact reproduction from the worktree root:

/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -B research/f3-five-source-connector/verify.py
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/f3-five-source-connector
/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/f3-five-source-connector --check-source-history

Expected marker: PASS_F3_FIVE_SOURCE_CONNECTOR calls=108 masks=31. Generated scientific receipt SHA256: 455a5ee5951fffb97ac1cc1123b2ecb5516338bc30efecdf355e87cf152a0b34, bound to all six package files and the live predecessor README.

The card's first working #943 command and selected baseline binding command also pass. Main remains 12fa8c5c844be21bfefb38a19503fbd867a11244, priority revision 7. Source and provenance pins are in SOURCES.json; no unmerged executable dependency is imported.

Limitations

This is the unsigned, immutable-source, unobserved-output complete-call interface over F3. Signed calls, additional connectors, source mutation and free frame changes are excluded. Fixed call prices must include their complete implementation. Input admission, coefficient preparation, instruction work and word-dependent physical charges remain additional. A concrete supplier consumer, physical/native admission, precision and outer transfer remain open. The selected cold replay and proof-kernel build were not run. This does not prove a complete multiplication theorem.

Open next questions

• Identify a concrete compatible consumer and charge all 36 primitives plus admission and dispatch before pursuing a recursive saving.
• Decide whether full ternary demand has a useful consumer, then test whether 15 source calls and three readouts per row can serve all 242 nonzero ternary rows. This different demand is not resolved here.

Related open work

• Research: exact F3 minimum for the one-source additive connector #4189, head 5fb3936dfc8082f438f21c72dd6ca49ff4366ae7: predecessor unsigned F3 one-source result; this closes its five-source handoff. All five singleton projections of the new word have length six and belong to its published six-word witness list, checked directly. No independent replay of its census is claimed.
• Add five-source arity-four connector cost bound #3909, head 0133b60ee8cba7512ef88c0261984adca65977f3: same five-source binary demand over F2 with an added paid arity-four operation. Its 74-call original-alphabet baseline agrees with the unchanged Research: sharp four/five-source dirty-connector boundary (no new kappa) #943 replay here. Its enlarged-alphabet cost and this F3 108-call cost concern different contracts.
• Prove the exact unequal-price five-source binary connector envelope #4226 (closed as a duplicate of merged Research: exact five-source connector optimum for all 36 positive tariffs #2063, research/connector-all-tariff-optimum, which proves the same envelope), head f3a717b2040076ce69e7b569fd57d0cf411b35b3: same five-source/all-31-mask/single-dirty-connector interface over F2 with arbitrary positive operator prices. At unit prices its formula gives 2*36+2=74, agreeing with the F2 baseline cited here; this F3 certificate gives 3*36=108, checked numerically. The two field-specific optima differ.

Fresh overlap included 336 open/draft PR bodies and 2,963 Discussion records, the recent account PRs and the latest handoff comments. Broader closed-work/diff coverage is incomplete. Concurrent F2 unequal-tariff and signed-characteristic claims have different fields or alphabets.

CI notes

All hosted checks passed in run 39483250732: plan and the package replay. Both hosted normal/optimized scientific receipts match the local/export digest above. The hosted unchanged-input check also passed. No failed job or unrun registered check remains.

Merge danger

Two-way door. Blast radius is the new isolated research package and its opt-in replay. No shared generator, frozen evidence, selected frontier or predecessor credit is changed.

Produced by Nick Petalas. Credit Ross Richardson's #943/#934 lineage, Riquelme Soares's #4189 handoff, Sagar Thakrar's distinct #1349 comparison and ywz65's contract map. Independent human and formal proof-kernel review are unclaimed. Apache-2.0.

[rcfc-jreed]

Independent scoped audit of #4225 F3 five-source connector at 39702510: 8/8

Code-disjoint checks; local fork with nested HERE/root. Head 397025101d23195a5193c7912e6cd384eccdbf1c. CLAIM.

No packaging defect. PASS_F3_FIVE_SOURCE_CONNECTOR calls=108 masks=31. Certificate package; SOURCES pins match.

Finite replay ≠ formal proof. James Reed (@rcfc-jreed), with substantial AI assistance (Claude, in Cursor).