Research: present-head I−G/2 full-row forcing census — 144/144 need +2 (no new kappa)

[VictorLiwentao]

Change and mathematical scope

Bounded follow-up under priority revision 6, card p104-side-correction. Open #3614 proved that an 18-entry sample of present-head strict I − G/2 entries (primary + 5 extras per flag among {1,9,43}) need non-private floor +2, and left OQ1: whether the same floor holds for every off-diagonal nonzero Gram source on those three target rows (~48 per row).

This package answers that OQ on the published native-channel word: all 144 off-diagonal nonzero Gram entries on Y7/Y23/Y59 have every insertion-class zero-mass placement obstructed. Under the inherited class-Z + even nested-transport convention, that is a non-private lower bound of +2. No counterexample. The #3614 18-entry sample is a named subset (in_pr3614_sample); the remaining 126 sources are new coverage.

Primary feeders unchanged from #3614: X7:387, X58:333, X12:131.

Scoped obstruction census. No correction words. No new kappa. Selected κ stays 0.001672660197076918.

Task and overlap

• Package: research/p104-present-head-side-correction-full-row-census/
• Tip: b37f6aef686c940a7613db3e04c6234e472399cf
• Content tip: 42e62a310eb3a4cf80488506ff6baff1d53addd6
• Base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90
• Scope: refined — full-row extension of Research: present-head I−G/2 forcing census — 18/18 checked entries need +2 (no new kappa) #3614's census

Closest priors: #3614 (18-entry sample + OQ1; leave-alone — in_pr3614_sample is a named subset with byte-faithful feeder/class/obstruction match), #3618/#3610/#3601 (bills leave-alone). Soft-overlap with #3614 is intentional scale-up (verify≈0.87, independent≈0.93, test≈0.97); scientific novelty is the row-complete 144/144 theorem with independent recomputation of all 126 new obstruction tables, not a new obstruction method or a certificate reprint. Bound: published word only; non-private floor only. Does not reopen deferred flag-9 head-step repair. Not a supplier.

Validation

python3.12 -I -B research/p104-present-head-side-correction-full-row-census/verify.py
python3.12 -I -O -Werror -B research/p104-present-head-side-correction-full-row-census/verify.py
python3.12 -I -O -Werror -B research/p104-present-head-side-correction-full-row-census/independent.py
python3.12 -I -O -Werror -B research/p104-present-head-side-correction-full-row-census/test_package.py
python3.12 -B scripts/research_package.py --package research/p104-present-head-side-correction-full-row-census

Expected:

PASS_P104_PRESENT_HEAD_SIDE_CORRECTION_FULL_ROW_CENSUS flags={1,9,43} entries=144/144 need_plus_two primary_feeders=X7:387,X58:333,X12:131 no_new_kappa
PASS_P104_PRESENT_HEAD_SIDE_CORRECTION_FULL_ROW_CENSUS_INDEPENDENT flags={1,9,43} entries=144/144 need_plus_two primary_feeders=X7:387,X58:333,X12:131 no_new_kappa
PASS_P104_PRESENT_HEAD_SIDE_CORRECTION_FULL_ROW_CENSUS_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/p104-present-head-side-correction-full-row-census outcome=completed

Default verify is read-only. Admission uses need() and still fires under -O.

Credit

Credit #3614, #3618, #3610, #3601, Nick Petalas / #2981, and Chafik Boukhalfa. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.

Open next questions

1. Private-copy / co-hosted discount on any of the 126 non-primary full-row entries.
2. Same row-complete floor for present-head flag 0 once the cascade commits a cut.