Research: flag-9 I−G/2 end-cut side correction attains +2 rank mass (no new kappa)

[VictorLiwentao]

Change and mathematical scope

Bounded follow-up under priority revision 6, card p104-side-correction. Open #3614 proved a non-private +2 lower bound for flag 9's primary entry on the published word (feeder X58:333 @ leave 745; 25/25 zero-mass) but constructed no attaining correction word. This package supplies that bill.

On the published native word, flag 9's I − G/2 entry (23,4) (G[23,4]=−1 ⇒ add +1/2·X4 into Y23) at end-cut 3489:

Word	Δ transports	Δ ADDs	Δ rank mass	Profile Δ
T (target lift A3→FULL, ADD, descend)	+1	+1	+2	H1 − H5 + H6
S (source detour FULL→F23→FULL)	+2	+1	+2	2H1
P (one private-copy lifetime; admissibility open)	+1	+1	+1	H1
T48 (whole row 23 on T's lift)	+1	+48	+2	(row becomes identity)

Native check_native.validate() passes each coefficient-0 word (three new recipes A3→FULL + FULL↔F23). Real words fail only at Y23's endpoint; only Y23 changes. Feeder/obstruction recomputed: X58:333 @ 745 blocks 25/25 zero-mass classes (and 7/7 early private deliveries), matching #3614. Strict non-private minimum exactly +2 (attained). No co-hosted repair (that path remains deferred).

Scoped bill. No new kappa. Selected κ stays 0.001672660197076918.

Task and overlap

• Package: research/p104-flag9-side-correction-bill/
• Tip: 0c4b73507ba7ed7b992e47b17f2cbcb6e362466b
• Content tip: f2c20bc4d82558bb4ff280a49814e70778816e96
• Base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90
• Scope: refined — flag-9 entry only, published end-cut

Closest priors: #3614 (feeder/floor leave-alone; obstruction recomputed, not imported — this closes its attaining-word OQ2), #3601 (flag-43 format prior; co-hosted cut — distinct obligation), #3610 (flag-1 format prior), #3443 (chronology cited only). Soft-overlap with #3601 is template-level (verify≈0.69, independent≈0.83, test≈0.93); scientific novelty is the flag-9 attaining end-cut words + P route on the published chronology, not a reprint of #3601's co-hosted bill or of #3614's lower-bound census. P (+1) uses the inherited private-copy discard contract; admissibility is open — strict non-private minimum remains +2. Does not reopen deferred flag-9 head-step repair; no co-host discount claimed. Not a supplier.

Validation

python3.12 -I -B research/p104-flag9-side-correction-bill/verify.py
python3.12 -I -O -Werror -B research/p104-flag9-side-correction-bill/verify.py
python3.12 -I -O -Werror -B research/p104-flag9-side-correction-bill/independent.py
python3.12 -I -O -Werror -B research/p104-flag9-side-correction-bill/test_package.py
python3.12 -B scripts/research_package.py --package research/p104-flag9-side-correction-bill

Expected:

PASS_P104_FLAG9_SIDE_CORRECTION_BILL flag=9 entry=(23,4) gram=-1 coefficient=+1/2 zero_mass_placements=0/25 forcing=X58(333)@leave745 strict_min_added_rank=2 … native_validate=4/4 published_end_cut no_new_kappa
PASS_P104_FLAG9_SIDE_CORRECTION_BILL_INDEPENDENT … forcing_head=333(X58)@leave745 T=+2rank S=+2rank P=+1rank T48=+2rank … new_recipes=3 no_new_kappa
PASS_P104_FLAG9_SIDE_CORRECTION_BILL_TESTS cases=14 clean_read_only=1 scanners=2
PASS_REGISTERED_RESEARCH_PACKAGE research/p104-flag9-side-correction-bill outcome=completed

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

Credit

Credit #3614, #3601, #3610, #3443, 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. Is private-copy P admissible, or must correction lifetimes be uncomputed?
2. If a co-hosted flag-9 repair later lands, does +2 discount?
3. Full-row (~48) forcing census on Y7/Y23/Y59 — Research: present-head I−G/2 forcing census — 18/18 checked entries need +2 (no new kappa) #3614 OQ1.