Price flag 9's head-step co-host at exactly +2 rank mass

[unpaidmoon]

Change and mathematical scope

Scoped head-step repair for present-head flag 9 (X4 → Y23, basis head 196) on the published #1991 word. No new κ and no selected-frontier change. Selected κ stays 0.001672660197076918.

Two natively validated schedules co-host 196 at the only update that delivers X4 into Y23 (published event 3124, carried coefficient -1/2):

• R0 (order-preserving) inserts one D28 return transport. Added rank mass is +2, all on D28. Profile delta -H1 + 2H2 + H4 - H5 (a + 2b for an affine price H(r) = a + br).
• R1 (relocation) moves that ADD into D28's full-chart window. No added event. Added rank mass is +2, all on Y23. Profile delta H7 - H5.

In the order-preserving class (published events kept in order, endpoint frames kept, nested rank-gap transports), added rank mass is even and zero is impossible, because keeping 196 on D28 through event 3126 forces it into Y28, whose final frame excludes it. R0 meets that floor. All nine Y23 updates are closure-obstructed.

The published literal source drop at event 500 does not remove 196 from the span: 64 XOR 132 = 196. All 21 events that name X4 span the head. The obstruction is target-side.

This is not an I−G/2 correction, a dirty-restoration program, or a supplier admission.

Task and overlap

• Base: bb4bccbf42844d2801487450727c2f63e10d1d0f (canonical CrocSwap/integer-mult-bounds main at submission; priority revision 6).
• Task: p104-side-correction, scope refined to flag 9's added rank mass. Card copied from the pinned catalogue.
• Dependencies: Research: certify joint P104 unit-step endpoint flags (no new kappa) #2981 flag matching, reviewed Native Clifford realization of the P104 low-rank channel (no new kappa) #1991 witness/checker, Research: present-head flag 9 hosts basis head only after source drop (no new kappa) #3443 literal chronology (cited, not rerun), Research: flag-43 head-step repair co-hosts at update 3364 with no added channel mass (no new kappa) #3508 method, Research: present-head flag 1 reaches target span only after its last update (no new kappa) #3451 span reading on flag 1.
• Not redone: open #3532 (flag 1's +2 repair; its open question 3 asks for this flag) and open #3618 (flag-9 I−G/2 end-cut, a different contract). Flag 43's zero-mass repair is Research: flag-43 head-step repair co-hosts at update 3364 with no added channel mass (no new kappa) #3508 and is already on main; flag 9 does not have that zero-mass result.
• The released flag-9 handoff is discussion comment 19036718. The finding for this session is posted on #2245 (an earlier CLAIM attempt from the agent integration was rejected with FORBIDDEN before any comment was created).

Validation

CPython 3.12. Registered replay:

python3.12 -B scripts/research_package.py --package research/p104-flag9-head-step-repair

Passed locally as PASS_REGISTERED_RESEARCH_PACKAGE research/p104-flag9-head-step-repair outcome=completed.

• verify.py runs published check_native.validate() on both repaired words (edges, 208 adapters, 280 framed rows).
• independent.py does not import that checker. It replays exact rational rows (280/280 equal), checks nested rank gaps, checks the six new native recipes with native_verify.py, and recomputes the closure.
• test_package.py: clean tree is byte-identical after both scanners; 10 mutations are rejected, including deletion of R0's return transport and an undercharged terminal rank.

Not run: a reordered zero-mass search, an I−G/2 word, a full selected cold replay, Lean, or Docker. The order-preserving floor is a written parity-and-closure argument, not an enumeration of every insertion.

Credit

Nick Petalas / #2981 for the flag match. Chafik Boukhalfa / #1991 for the witness, checker and compiler. #3443 (Wentao Li) for the literal flag-9 chronology. #3451 for the span reading on flag 1. #3508 for the head-step method. #3349 for the present-head census. #3532 for the flag-1 repair this package does not repeat. Prepared by unpaidmoon with substantial Cursor Grok assistance. No independent human or formal-kernel review is claimed. Apache-2.0. The selected frontier is unchanged.

Open next questions

1. Is there a zero-added-mass repair that reorders D28's reads so every final-excluding partner reads D28 before 196 enters? R1 still pays +2, so the exhibited relocation is not that schedule.
2. Can a side correction use R0's chart [447, 127, 192, 196] at repaired index 3124, or R1's full chart at 3633, and what does I−G/2 cost there?
3. Which of R0 and R1 is cheaper under the channel's actual per-rank weights? Affine prices prefer R1; H(r) = r^2 prefers R0.

Workflow feedback (optional)

The Cursor cloud agent's GitHub integration token could not write Discussions or open the upstream PR (Resource not accessible by integration); this PR was opened from the fork by the account owner and the finding was posted on #2245 afterwards. The overlap check was done with read-only GraphQL search before the package was written.