Exclude the generalized non-Fano five-target invoice saving

[flyingviper]

Change and mathematical scope

The q=4 generalized non-Fano identity supplies six rational queries for five fixed P112 canonical targets, but its specified split-reader assignment cannot lower the complete physical-group invoice. Five ordinary targets cost at least 32 versus baseline 30; repeated paired roles, J targets and the residual line are covered by a written case proof. The two ordinary hub copies must use the two different displayed readers. Other reader assignments are outside scope.

This rules out one explicit literature construction without a coefficient or embedding sweep. It supplies no decoder below 334, no cost296 witness and no changed multiplication bound.

Task and overlap

Base: canonical main 20ecf28, refreshed before submission. TASK.json records changed scope from coverage-law-change to the donor-assigned rational-decoder goal and literature audit. Only research/p112-generalized-nonfano-invoice/ is added.

This is separate from #3684: the present mechanism uses six queries for five targets and is excluded by dense physical source spans, not the five-term triple classification. Canonical target geometry and the existing canonical-span proof are exact pinned inputs. The earlier repository non-Fano and hub mechanisms retain their distinct scope in PROOF.md. Discussions remain unavailable with HTTP406; overlap coverage is therefore incomplete.

Validation

The registered replay, committed-byte and source-history checks passed. A committed Git-free export reproduced RESULT.json exactly in 0.203 seconds with all 11 extracted files unchanged. The verifier checks 100 rational endpoint entries, rejects 73 nonzero-coefficient mutations, and proves the fixed pair/J/foreign-triad dimension premises by exact annihilator calculations. A separate AI-agent mathematical and portability audit found no blocker.

python3.12 -I -O -Werror -B research/p112-generalized-nonfano-invoice/verify.py
python3.12 -B scripts/research_package.py --package research/p112-generalized-nonfano-invoice

The analytic inequalities are in PROOF.md. The hub-J case explicitly uses the pinned canonical-span theorem; it is not reproved here. No human or formal-kernel review, native construction, or full supplier replay is claimed.

Credit

The coding identity is from N. Das and B. K. Rai, Generalized Fano and non-Fano networks, Section IV, Lemma5 and the scalar code following equation(44): https://arxiv.org/pdf/1609.05815. The new contribution is the split-reader adaptation and physical invoice obstruction. No third-party paper text is vendored.

Prepared by flyingviper with substantial OpenAI Codex assistance, including a literature agent and separate mathematical audit. Repository predecessor attribution is retained through SOURCES.json. New work is Apache-2.0.

Open next questions

README.md and TASK.json ask for a different sparse characteristic-dependent query identity: derive its exact whole-group supports and annihilator benefit before optimizing placement. No cheaper construction or native supplier is supplied.