Research: nonconsecutive commuting C3 fanout schedule

[1337isnot1337]

Result

Adds an exact, source-pinned extension of the consecutive shared-source C3 family in #1799. Selected fanout shears may be separated by ADD/SCALE gates that commute exactly with all three shears. For a nonzero intervening ADD u += b*v and selected ADD d += a*s, the commutator vanishes exactly when u != s and v != d; zero ADDs commute, and a diagonal SCALE commutes when it has unit factor or acts outside the shared source and selected destinations.

On the selected width-73 word, the exhaustive A/B search finds 54 eligible triples: 32 consecutive and 22 nonconsecutive. Exact weighted interval scheduling selects 27 triples (two in A and 25 in B), including four nonconsecutive intervals. The resulting mass-preserving local profile is {1:2377, 2:422, 3:417, 4:124, 5:82, 8:8, 9:8, 12:6}. Its selected-word ceiling upper endpoint is 0.001705759704147, a +0.9292953979% increase over the selected profile.

The exact maximum-saving interval bound still leaves the moment above one at 1.05 times the selected ceiling's upper endpoint, by the positive rational margin in CERTIFICATE.json. Adapter, copy, helper, hosting, transition, restoration and precision costs are all zero in this favorable screen. This answers a bounded nonconsecutive scheduling question; it does not admit a physical supplier or claim a new kappa.

Pins and reproduction

Track complex-mechanisms; seed 6935bdcbc1faaa9be26feaf275fe8c4d; task complex-new-helper-inventory; priority revision 3; exact base 0b1cccf86e2f5132ed286a26ef0a681a495740ea; selected-record SHA-256 10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32.

python3 -B research/complex-commuting-fanout-seed6935/verify.py
python3 -B -m unittest discover -s research/complex-commuting-fanout-seed6935 -p 'test_*.py'
python3 scripts/research_package.py --package research/complex-commuting-fanout-seed6935 --check-only

Direct verifier and four exact matrix controls pass on CPython 3.14.7; package pins and metadata check pass. The repository replay launcher targets Python 3.12, unavailable locally, so its registered replay remains for hosted CI.

Overlap and attribution

This is complementary to #1799: that result covers consecutive triples, while this package admits 22 exactly commuting nonconsecutive triples and raises the maximum schedule from 25 to 27. #1814 is the dual incidence (three sources to one destination); #1836 handles a higher-rank pair at one ADD; the recent same-track scratch-packet claim studies repeated outputs to one register with up to 15 temporary arrays. Those scopes do not include one unchanged source, three distinct destinations and exact commuting intervals.

Substantial AI assistance from OpenAI Codex is disclosed in the package. No independent human review is claimed.