[petalas]

Summary

A finite construction certificate lowers the seven-source unsigned F3 dirty connector's full ternary upper bound from 6603 to 6600 complete calls, answering #4256 Open next question 2. All 2186 nonzero coefficient rows receive three readouts; a new restored source path uses 42 events instead of 45.

source word: 260536506545241601014125215430234634321306
source multiplicities: (6,6,6,6,6,6,6)
all boundary triple sums: F3^7
42 source calls + 3 * 2186 readouts = 6600 calls

The prefix identity proves the certified schedule works for arbitrary compatible F3-linear maps and dirty registers in every dimension. This is an upper bound, not an exact optimum or complete multiplication theorem. The cited #4244 lower bound leaves 6588 <= OPT_3(7) <= 6600. No new κ or selected-frontier change. Only research/f3-ternary-seven-source/ is added.

Evidence

Before: #4256 supplies a 45-source-event word with 6558 readouts, total 6603. After: the explicit 42-event word has every ternary row among its triple sums and emits a 6600-call legal schedule. Research stopped at the first improvement.

The verifier enumerates all 13244 boundary triples using packed arithmetic and a separate tuple computation, checks equality with all 2187 ternary rows including zero, and replays every literal call with generic noncommuting coefficients. Eight dense executions cover dimensions 1..4 with dirty arrays and explicit singular noncommuting maps. Six controls reject omitted source/readout calls, misrouting, source relabelling, an appended call and characteristic-six misuse. Its generated stdout receipt binds the counts to SHA256 hashes of all five package files. No hand-written receipt or replay output is committed.

Reproduce from the repository root with CPython 3.12:

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

Marker: PASS_F3_TERNARY_SEVEN_SOURCE, with calls=6600, rows=2186, source_calls=42, dense_cases=8, rejected_controls=6. All four commands pass locally. Registered normal/optimized commands were timed at 0.20/0.21 seconds; the package runner took 0.76 seconds. The final committed-byte/source-history check covers all five files and the public base ancestor. The card's source-bound positive control also passed with pairings=945 max_coverage=31 queries=74 leaves=182. These are replay timings, not a performance claim.

Limitations and unrun obligations

• Unsigned complete-call interface over F3 with immutable sources, one restored dirty connector, distinct dirty outputs and final-only observation. Unit prices only; other alphabets and observation contracts are outside scope.
• No shorter-word exclusion or exact optimum is claimed. The 6588 lower bound is cited from Prove the exact 2208-call F3 optimum for full ternary six-source demand (no new κ) #4244, not rechecked. No predecessor census is a deliverable or executable dependency.
• A concrete full-demand consumer, coefficient preparation, physical dispatch, stock, hosting, precision, tape and supplier admission remain unknown. Unknown costs are not zero.
• No proof-kernel build, independent human review or selected cold replay was run. Every registered check ran locally; no registered obligation is left to CI alone.
• The catalogue card asks for an alphabet extension. TASK.json records the changed scope explicitly: this retains the alphabet and improves one finite full-demand bound. The result ends this construction round.

Open next questions

1. Is the cited 6588 lower bound attained? Try a restored 30-event covering path, or a legal tradeoff between source events and extra readouts.
2. Can this finite palette lower the all-n leading constant? Any lifting must preserve triple decompositions and charge every positive source step.
3. Identify a concrete caller requiring all ternary rows and price its complete physical invoice before supplier expansion.

Related open work

• Prove the optimal full-coefficient connector overhead exponent in every finite characteristic (no new κ) #4256, head 6a95ef419f94e7b5c2fff710e34081520cc6aba2: immediate baseline and open question. The shared 2186 rows and 6558 readouts agree numerically; 45 + 6558 = 6603 versus 42 + 6558 = 6600 here.
• Prove the exact 2208-call F3 optimum for full ternary six-source demand (no new κ) #4244, head f436d2911351e5be2842208fe96b0b66442323a4: full ternary six-source theorem and larger-source handoff. Its seven-source lower bound 6588 is cited; 6588 <= 6600 is checked numerically. Its proof is not rerun.
• Prove the exact 744-call F3 optimum for full ternary five-source demand #4238, head 191a905d7adba6695b079f744140a73e832787a8: full ternary five-source predecessor. Its 242 rows equal 3^5 - 1 numerically; its five-source 744 optimum is a different quantity and is not rechecked.
• Prove the exact 108-call unsigned F3 five-source connector optimum #4225: five-source binary-mask F3 demand. Different output set and size; no overlapping optimum.
• Classify the unsigned five-source connector in every characteristic (36c for c ≥ 3; no new κ) #4231: unsigned interface across characteristics with five-source binary-mask demand. No overlapping full-ternary optimum.
• Bound the unsigned F3 connector floor for every source count: attained for n ≤ 6, impossible for n ≥ 14 (no new κ) #4232: binary-mask F3 demand for arbitrary source count. Its seven-source demand is 127 rows versus 2186 here, checked numerically; different bounds.
• Prove the seven-source F3 connector floor fails: optimum 405, floor attained exactly for n ≤ 6 (no new κ) #4250: exact seven-source binary-mask optimum 405. Different demand, no overlapping optimum.
• Prove the F3 connector excess grows with n: exact 795-call eight-source optimum (no new κ) #4264: binary-mask excess and exact eight-source optimum. Different demand, no overlapping optimum.
• Reach the unsigned connector floor for k ≤ 2c in every characteristic; 9 ≤ N(4) ≤ 21 (no new κ) #4248: binary-mask depth-block floor across characteristics. Different demand and construction; no overlapping optimum.
• Lower the characteristic-four connector floor bound to N(4) ≤ 20; the known nine-source walk does not extend (no new κ) #4255: binary-mask characteristic-four floor obstruction. Different characteristic and demand; no overlapping quantity.
• Prove N(4) ≤ 17 and classify optimal five-source depth-two blocks #4271: characteristic-four binary-mask floor and depth-two block classification. Different characteristic and demand; no overlapping quantity.
• Research: exact F3 minimum for the one-source additive connector #4189: one-source one-output unsigned F3 predecessor. Different output set; no overlapping optimum.
• Count optimal unsigned one-source connector words in every characteristic #4236: counts one-source one-output optimal words. This package serves every seven-source coefficient row; no overlapping word count.

Overlap checks included recent open/account PRs, relevant live PR bodies, latest handoffs and active discussions, main-tree searches for the formula/object and merged searches for full coefficients, ternary demand, seven-source bounds and 6600. The overlap cache reported 381 open PRs and 3156 Discussion records with complete pagination. Fresh pre-commit claims and PR titles had no competing full-ternary seven-source target. This is not exhaustive literature or unpublished-work coverage.

CI notes

Hosted CI is green on head 894fd12cd29946b9b0f6b32bb73bd33bc437158f in run 39524216265. plan passed in 2m37s and the package replay passed in 1m12s. Both hosted scientific modes printed receipts identical to the local committed replay, including all five package file hashes. All registered checks also pass locally, along with metadata, committed-byte/source-history and whitespace checks. No job failed and no registered obligation remains unrun. The selected cold replay and formal proof-kernel build remain outside scope and unrun.

Merge danger

Two-way door. Blast radius: isolated. Five new package files and an opt-in replay; no shared code, selected source or predecessor changes.

Produced by Nick Petalas. Credit #4256 and #4238/#4244, #4231, Riquelme Soares's #4189, Ross Richardson's #943/#934, conorholds's #2208 and ywz65's contract map. Independent human and formal proof-kernel review are unclaimed. Apache-2.0.