[petalas]

Summary

For the unsigned F3 complete-call connector of #4225 with five immutable sources and one arbitrarily dirty restored connector, I replace the 31 binary-mask rows with all 242 nonzero ternary coefficient rows. The exact optimum is 744 calls, three above the 741-call operator-count floor. This answers #4225's second open question. The claim type is a scoped proof backed by an exhaustive finite census. There is no new κ and no selected-frontier change. Only research/f3-ternary-demand-connector/ is added.

• Lower bound. Prove the exact 108-call unsigned F3 five-source connector optimum #4225's mod-three count argument puts every operator count in 3ℤ, each at least 3. A word below 744 must therefore sit exactly at 741, with a 15-event path and three readouts per row. That holds iff the triple sums of the path's boundary vectors cover F3^5 \ {0}. I enumerated all 1,401,400 such paths up to source relabeling. The maximum coverage is 241 (30 paths, each missing one row), so no 741-call word exists.
• Two 744-call constructions. (a) An 18-event path that uses one source six times covers all 242 rows with three readouts each. (b) A 15-event path covers 241 rows, and the missing row (1,2,0,1,2) takes six readouts.
• Tariff. For arbitrary positive source prices c_j and one common readout price α, the exact bill is 3Σc_j + 726α + 3·min(min_j c_j, α).
• Other source counts. The floor 3n + 3(3^n − 1) is attained for n = 1..4 (canonical census). It fails at n = 5 (this result), and fails by counting for every n ≥ 7. n = 6 is open.

Evidence and reproduction

The verifier uses only the standard library and writes no files. It runs the census and checks the canonical reduction against full labeled enumeration at n = 2, 3. It checks six literal 744-call words (five relabeled doubled-source words and one gap word) in two ways: a generic noncommuting coefficient ledger, and dense random F3 execution at L = 2, 3 with dirty registers. It also runs five rejection controls and four tariff fixtures. A positive control confirms that #4225's binary path covers 203 ternary rows.

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

Expected marker: PASS_F3_TERNARY_DEMAND_CONNECTOR calls=744 rows=242. All three pass locally. Each registered command (normal and -O, warnings as errors) takes about 37–38 s, dominated by the census. An independent C enumeration I wrote during development, not committed, gave the same canonical count and maximum.

Limitations

• This is the abstract unsigned complete-call interface over F3 only.
• Fixed prices must include complete primitive implementations. Admission, coefficient preparation, dispatch of the 744-record word and physical charges are additional and unknown.
• The exact envelope for row-dependent readout prices is not claimed. It needs every minimal missing set, and only the lone gaps are recorded.
• For n ≥ 7 only the lower bound (floor + 3) is proved, not the exact optimum.
• No consumer for ternary demand is identified.
• No proof-kernel certificate exists, and the selected cold replay was not run. This is not a complete multiplication theorem.

Open next questions

1. The exact envelope for unequal readout prices: compute the inclusion-minimal missing sets of all 15-event paths.
2. Six sources: is the 2202-call floor attained? This needs a compiled census of 190,590,400 canonical paths, or one reduced by rotation and reversal symmetry.
3. A concrete caller that needs coefficient-2 rows.

Related open work

• Prove the exact 108-call unsigned F3 five-source connector optimum #4225 (head 397025101d23195a5193c7912e6cd384eccdbf1c): binary-mask predecessor, with the same interface and count floor. Its 15-event path is used here as a control: it covers 203 of 242 ternary rows, checked numerically. Its 108-call binary optimum is a different demand.
• Bound the unsigned F3 connector floor for every source count: attained for n ≤ 6, impossible for n ≥ 14 (no new κ) #4232 (head 86ad339efc9f817846479431d8cc0f04edf95fb9): binary-mask floor for every source count. Its n = 5 value of 108 is consistent with binary attainment, while ternary demand fails at n = 5. The demand families differ, and no number overlaps.
• Classify the unsigned five-source connector in every characteristic (36c for c ≥ 3; no new κ) #4231: unsigned five-source binary-mask connector across characteristics. It is a different demand, with no overlapping ternary number.
• Research: exact F3 minimum for the one-source additive connector #4189: one-source unsigned F3 result (binary row only). Ternary one-source demand has two rows and attains its 9-call floor here.

Fresh overlap included the 100 most recent open PR titles, recent account PRs, the last 30 handoff comments, find_overlap.py for connector-alphabet-change and a PR title search for "ternary". Closed work and arbitrary diffs are incompletely covered.

CI notes

All hosted checks passed in run 39488529668: plan (2m39s) and the package replay (4m17s, both registered commands). No failed job or unrun registered check remains.

Merge danger

Two-way door. The blast radius is one new isolated package and its opt-in replay.

Produced by Nick Petalas. Credit to #4225 for the interface, count floor and triple-prefix identity; to Riquelme Soares's #4189; to Ross Richardson's #943/#934 lineage; and to ywz65's contract map. Independent human and formal proof-kernel review are unclaimed. Apache-2.0.

[rcfc-jreed]

Independent scoped audit of #4238 F3 ternary demand connector at 191a905d: 16/16

Code-disjoint checks; does not import package verify.py (local fork with patched PACKAGE/ROOT; full canonical-path census recomputed). Package bytes from head 191a905d7adba6695b079f744140a73e832787a8 via GitHub contents API. CLAIM.

No packaging defect in scope. Stdout receipt (no RESULT.json by design).

What passes:

1. Pins: base 12fa8c5c…; VERIFY ready; TASK completed; three SOURCES digests match.
2. Floor arithmetic 741 = 3·5 + 3·242; optimum 744 = 741+3.
3. Fork: PASS_F3_TERNARY_DEMAND_CONNECTOR calls=744 rows=242 with census path line; witnesses/controls/tariffs as printed.

Not covered: Lean formalization; new κ; merge/close.

This is a finite pin/seal/math replay, not a formal proof.

James Reed (@rcfc-jreed), with substantial AI assistance (Claude, in Cursor).