Research: seed-7 H2-sem matching dominates #1805 F/ADD invoice

[VictorLiwentao]

Change and scope

Answers open question 1 of #1805: under the H2-sem replacement interface, can a different disjoint helper-sharing matching lower forward envelope F while keeping most of the ADD saving?

Yes. The same PR848 ADD-greedy rule with shuffle seed 7 (instead of the published seed 42) produces a disjoint matching that strictly dominates the #1805 seed-42 invoice on ADD count (−14), F (−1,576), and B (−8,612). Paid profile mass 5,129 is unchanged; dirty F2 boundaries and semantic N are unchanged; local/nine-stage guards remain strict. Package is freestanding (research/h2sem-matching-f-invoice/) and does not reopen #1805 / #2033 objects.

Priced finite invoice; no new kappa.

Result

word	pairs	ADDs	F	B
seed-42 matching (#1805)	205	18,074	75,381	1,196,402
seed-7 matching (this)	208	18,060	73,805	1,187,790
seed-7 minus seed-42	+3	−14	−1,576	−8,612

A bounded ADD-greedy shuffle screen over seeds 0..255 found no point that beats seed-7 on both ADD saving and F simultaneously (not a claim of optimality outside that screen).

Package: research/h2sem-matching-f-invoice/.
Tip: 2f79aebb959aa9e528c5c7d5f1314b685190e11f.

Validation

python3.12 -I -B research/h2sem-matching-f-invoice/verify.py
python3.12 -I -O -B research/h2sem-matching-f-invoice/verify.py
python3.12 -I -B research/h2sem-matching-f-invoice/test_package.py
python3.12 -B scripts/research_package.py --package research/h2sem-matching-f-invoice

Expected:

PASS_H2SEM_MATCHING_F_INVOICE seed42_pairs=205 adds=24305->18074 F=75381 seed7_pairs=208 adds=24305->18060 F=73805 delta_adds=-14 delta_F=-1576 profile_mass=5129 columns=661 controls=7 no_new_kappa
PASS_H2SEM_MATCHING_F_INVOICE_PACKAGE_CONTROLS relocation=1 corruptions=5
PASS_REGISTERED_RESEARCH_PACKAGE research/h2sem-matching-f-invoice outcome=completed

Default verify is read-only. Admission uses need() (not assert); -O also passes. Full make verify, selected cold replay, Lean, and multiplication-theorem obligations were not rerun for this isolated invoice package.

Overlap and credit

Closest prior: #1805 seed-42 priced invoice (OQ1 open; this answers it with a full re-invoice; #1805 is now merged). #2033 already answers #1805 OQ2 and is left alone. Leave-alone tooling through #2433 was not reopened. No competing open PR on this freestanding matching-F invoice package at refresh.

Credit the #1805 / PR848 / H2-sem lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.