Research: present-head I−G/2 forcing census — 18/18 checked entries need +2 (no new kappa)

[VictorLiwentao]

Change and mathematical scope

Bounded follow-up under priority revision 6, card p104-side-correction. Open #3601 and #3610 each price one present-head I − G/2 entry and leave OQ2: whether every present-head target row needs +2 for its strict side-correction entry.

This package answers that OQ for the primary present-head entries of flags {1,9,43} on the published native-channel word, plus a deterministic sample of five further off-diagonal nonzero Gram sources per target (18 checked entries total; each present-head row has ~48 nonzero sources). Every insertion class is zero-mass obstructed for all 18. Under the inherited class-Z + even nested-transport convention, that is a non-private lower bound of +2. No counterexample in the sample. No correction words are constructed (so flag 9 has no attaining +2 word here, unlike the leave-alone bills for flags 1 and 43).

Primary feeders:

Flag	Entry	Feeder	Head	Leave event	Insertion classes
1	(7,0)	X7	387	1074	19 (published order)
9	(23,4)	X58	333	745	25
43	(59,21)	X12	131	884	28

Flag-1 and flag-43 feeders match the leave-alone samples in #3610/#3601. Flag 9's feeder X58:333 at leave 745 on the published chronology (#3443) is new (outside_head_count=1 at that leave); the deferred flag-9 head-step repair is not reopened.

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

Task and overlap

• Package: research/p104-present-head-side-correction-forcing-census/
• Tip: a6c3ae20abe0a15d781ee952e717d489552c9c66
• Content tip: 293b90598af0e7632cdd398da7171c509091f17e
• Base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90
• Scope: refined — cross-entry obstruction census on the published word only

Closest priors: #3610, #3601 (cite samples X7:387 / X12:131; bills leave-alone), #3443 (flag-9 published chronology; no feeder reuse), #3532/#3508 (repairs leave-alone). Soft-overlap with #3601/#3610 verify builders is negligible (seq ≈0.03–0.04); independent scanners share frame/need idiom only (≈0.15–0.17). Obstruction tables are recomputed from pinned witness/Gram, not imported from those bills. Does not reopen deferred flag-9 repair / pinned-late / peeled-leaf / rho=0 / V45.

Validation

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

Expected:

PASS_P104_PRESENT_HEAD_SIDE_CORRECTION_FORCING_CENSUS flags={1,9,43} entries=18/18 need_plus_two primary_feeders=X7:387,X58:333,X12:131 no_new_kappa
PASS_P104_PRESENT_HEAD_SIDE_CORRECTION_FORCING_CENSUS_INDEPENDENT flags={1,9,43} entries=18/18 need_plus_two primary_feeders=X7:387,X58:333,X12:131 no_new_kappa
PASS_P104_PRESENT_HEAD_SIDE_CORRECTION_FORCING_CENSUS_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/p104-present-head-side-correction-forcing-census outcome=completed

Default verify is read-only. Admission uses need() and still fires under -O. Duplicate JSON keys and temp-copy certificate/pin corruption are rejected.

Credit

Credit #3610, #3601, #3443, #3532, #3508, 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. Full-row extension beyond the 18-entry sample on Y7/Y23/Y59 (~48 off-diagonal nonzero sources per row).
2. Flag-9 end-cut side-correction bill / private-copy discount on the published word (no co-hosted repair; would also give an attaining +2 word).