Research: flag-43 head-step repair co-hosts at update 3364 with no added channel mass (no new kappa)

[VictorLiwentao]

Change and scope

Bounded follow-up under priority revision 6, card p104-side-correction. #3456 shows that on present-head flag 43 (X21 → Y59, head 15) no published Y59 update co-hosts the basis head. This package answers its open repair question with a concrete changed schedule R0 and an exact channel bill.

R0. Keep every published event in order with the same ADDs and coefficients. Retarget nine transports of Y59, D17, Y103 and D28 (each changed frame = published frame plus 15). Then event 3364 (Y59 += D17/4) — the ADD that settles Y59's final X21 coefficient 1/2 — runs in chart [95,447,6,32,20,15] while X21 is still live. The published check_native.validate() passes on the repaired word (eight native edges swapped for eight newly lowered ones; 280 framed rows, 72 dirty-helper restorations, 208 endpoint adapters hold).

Bill. Events (4,058), ADDs (2,624), transport occurrences (1,410), rank mass (2,368) and distinct native edges (740) are unchanged. Paid profile delta -3H1 + 5H2 - H3 - H4. Published ranks of the changed transports majorize the repaired ranks, so the delta is ≤ 0 under any convex per-rank price and exactly 0 under any affine one. Under a strictly concave per-rank price the same profile delta can be positive; that case is left symbolic.

Obstruction (same class). Among repairs that keep event order and ADDs, keep endpoint frames and add no rank mass (inserted refinements allowed), 14 of 15 Y59 updates are blocked; only 3364 is admissible and it forces exactly the four registers above. Comparison schedule R1 (reorder + one rank-1 lift) also validates natively at +1 transport.

Scoped repair bill. No new kappa. Selected κ stays 0.001672660197076918. Does not reprint drop/arrive chronologies of #3456/#3451/#3443. Does not supply the I − G/2 side correction (still open).

Result

Package: research/p104-flag43-head-step-repair/.
Tip: 69b13ac1f39d647c9375582541c5a30bc6419354.
Content tip: cc77db2b62d1eaa6a1f7b9ffec7e694a910bba54.
Base: 6f100d4bb5083f8c35d96fd95a539811c62f245c.

Validation

python3.12 -I -B research/p104-flag43-head-step-repair/verify.py
python3.12 -I -O -Werror -B research/p104-flag43-head-step-repair/verify.py
python3.12 -I -O -Werror -B research/p104-flag43-head-step-repair/independent.py
python3.12 -I -O -Werror -B research/p104-flag43-head-step-repair/test_package.py
python3.12 -B scripts/research_package.py --package research/p104-flag43-head-step-repair

Expected:

PASS_P104_FLAG43_HEAD_STEP_REPAIR flag=43 head=15 repaired_update=3364 added_events=0 added_adds=0 added_transports=0 added_rank_mass=0 retargeted_transports=9 forced_registers=4 profile_delta=-3H1+5H2-H3-H4 native_validate=PASS earlier_updates_obstructed=14/14 no_new_kappa
PASS_P104_FLAG43_HEAD_STEP_REPAIR_INDEPENDENT … rows_equal=280/280 earlier_updates_obstructed=14/14 no_new_kappa
PASS_P104_FLAG43_HEAD_STEP_REPAIR_TESTS cases=14 clean_read_only=1 scanners=2
PASS_REGISTERED_RESEARCH_PACKAGE research/p104-flag43-head-step-repair outcome=completed

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

Overlap and credit

Closest prior: #3456 (flag 43 published obstruction; this answers its repair OQ). Cites #3451/#3443/#3392/#3349 only. Soft-overlap checked against open #3363 (relay census / coefficient convention reused; event-level delivery split recomputed only for co-hosting). Does not reopen #3441/#3436/#3421/#3411, deferred peeled-leaf/rho=0/V45, or the merged readout series through #2883.

Credit Nick Petalas / #2981, Chafik Boukhalfa (witness/checker/compiler), #3456, and #3363. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.