research: audit minimal joint-output connector charge

[1337isnot1337]

Minimal joint-output connector charge

Summary

Refines the connector-alphabet-change card to the smallest nonzero instance
of one output-side operation:

J_ik: (y_i, y_k) += (A_i z, A_k z)

With one source, one arbitrarily dirty connector and two arbitrarily dirty
targets, J_ik, B, J_ik, B computes both requested outputs and restores the
connector for arbitrary fixed F_2-linear maps. A dimension-independent
additivity proof accompanies an exhaustive check of all 1,048,576 combinations
of 2x2 maps and data states, plus three failure controls.

The complete bill charges both output-map evaluations and both targets on
every J_ik. If D is one root dispatch and phi is the extra joint-routing
and fusion overhead, the original schedule costs
2c_B+2c_i+2c_k+6D, while the extended schedule costs
2c_B+2c_i+2c_k+4D+2phi. The operation improves the completed bill exactly
when phi<D; leaf map work is unchanged. The package does not claim a physical
one-record implementation or supplier benefit.

Verification

python3 scripts/research_package.py --package research/joint-output-connector-minimal-charge-247794 --check-only
python3.12 scripts/research_package.py --package research/joint-output-connector-minimal-charge-247794
python3 scripts/check_research_commit.py --package research/joint-output-connector-minimal-charge-247794 --check-source-history

Results: PASS_PACKAGE_METADATA_AND_PINS;
PASS_JOINT_OUTPUT_CONNECTOR_MINIMAL cases=1048576 controls=3 records=6_to_4 leaves_equal delta=2*(phi-D);
PASS_REGISTERED_RESEARCH_PACKAGE outcome=completed;
PASS_RESEARCH_COMMIT_BYTES (9 package/input files).

Source and scope

Base 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6.
The package is research/joint-output-connector-minimal-charge-247794/; exact
source blobs and SHA256 hashes are recorded in SOURCES.json.

The source-side pair operation is already covered by PR #2056, including dirty
replay and charged accesses. PR #3604's specialized P112 co-delivery is
adjacent but distinct: it shares tetrad products with a fused port and source
correction, and this package neither re-audits nor claims that factorization.
The live PR #3779 addresses a six-window restoration bill. No selected result,
supplier, or frontier changes here; there is no new κ.

Credit the fixed-alphabet and pair-source connector predecessors. Prepared by
OpenAI Codex with substantial assistance. No independent human or formal
proof-kernel review is claimed.

Publication validation

python3.12 scripts/research_package.py --package research/joint-output-connector-minimal-charge-247794 passed on CPython 3.12.3, and python3.12 scripts/check_research_commit.py --package research/joint-output-connector-minimal-charge-247794 --check-source-history passed. The registered replay left the worktree clean. This supersedes any earlier pending note above for the registered package replay; separate full selected cold-replay limits remain as stated.