Research: flag-0 tail self-owned X0 host schedule S0 at 5758/5759/5807 (answers #3669 OQ2; no new kappa)

[VictorLiwentao]

Change and mathematical scope

Bounded follow-up under priority revision 6 answering #3669 OQ2: does the published promote/add/restore at 5758/5759/5807 admit an owner/host schedule for the X0 read that restores arbitrary dirt without repaying the unrestored channel endpoints?

On present-head flag 0, that cut admits self-owned host schedule S0 (owner=X0 on FULL):

• Unique among registers named by ADD 5759 (unique_owner=1)
• Zero dirty-helper touches in the window (dirty_helper_touches=0)
• Zero endpoint repayment toward initials (endpoint_repay=0)
• Pre-read X0 restoration blocked by the published common-chart annotation (pre_read_restore_blocks=1)

S0 is an interpretive owner/host assignment on the published #2089 word; compatible with jwr404 p104-tail-flag0-owner (owner_assigned=False / owner_field=False). “Arbitrary dirt restoration” here means zero dirty-helper touches in 5758–5807 (channel dirt undisturbed), not a new dirt-restore construction. Uniqueness holds only among registers named by ADD 5759; copied-host alternatives and a global 104×104 map remain open. Pre-read obstruction is the static chart conflict [232] ≠ FULL, not a priced post-5807 repay bill.

Does not answer #3669 OQ1 or retarget #3532.

No new kappa. Selected κ stays 0.001672660197076918.

Task and overlap

• Package: research/p104-flag0-tail-owner-host/
• Tip: 9a53c8ad9ac5ba8ad1a77907f66ac2529c947829
• Content tip: 01cbbe3450d00afd57fbd529d8d9c7f6cc3d776c
• Base: 20ecf2891d80b5acf18d980b2164fb44ea7faa90
• Scope: changed — S0 owner/host assignment + dirt/repay/obstruction on the published tail cut

Closest priors: #3669 (leave alone; OQ2 answered), jwr404 p104-tail-flag0-* (soft-overlap ≈0.20–0.28; complementary gap-fill), deferred p104-flag0-head-span-schedule / #3532 (different cut; soft-overlap ≈0.08). Side-correction and present-head chronology leave-alones untouched.

Validation

python3.12 -I -B research/p104-flag0-tail-owner-host/verify.py
python3.12 -I -O -Werror -B research/p104-flag0-tail-owner-host/verify.py
python3.12 -I -O -Werror -B research/p104-flag0-tail-owner-host/independent.py
python3.12 -I -O -Werror -B research/p104-flag0-tail-owner-host/test_package.py
python3.12 -B scripts/research_package.py --package research/p104-flag0-tail-owner-host

Expected:

PASS_P104_FLAG0_TAIL_OWNER_HOST flag=0 owner=X0 promote=5758 add=5759 restore=5807 dirty_helper_touches=0 endpoint_repay=0 pre_read_restore_blocks=1 unique_owner=1 no_new_kappa
PASS_P104_FLAG0_TAIL_OWNER_HOST_INDEPENDENT flag=0 owner=X0 promote=5758 add=5759 restore=5807 dirty_helper_touches=0 endpoint_repay=0 pre_read_restore_blocks=1 unique_owner=1 no_new_kappa
PASS_P104_FLAG0_TAIL_OWNER_HOST_TESTS groups=6
PASS_REGISTERED_RESEARCH_PACKAGE research/p104-flag0-tail-owner-host outcome=completed

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

Credit

Credit #3669 OQ2, #2089 / Cinna Davis, jwr404 p104-tail-flag0-*, #3349, and the retained P104 present-head lineage. Prepared by Wentao Li (VictorLiwentao, @Is__Victor) with substantial AI assistance, under Apache-2.0.

Open next questions

1. Does any non-self / copied-host alternative among event-named registers also achieve zero dirt-helper touches and zero endpoint repayment on this cut?
2. Can arbitrary dirt be restored under S0 without enlarging the published promote/add/restore window (constructed dirt-restore program)?

[VictorLiwentao]

OQ1 co-chart census (recorded; no separate PR)

Fork package research/p104-flag0-tail-copied-host/ on VictorLiwentao:cursor/flag0-tail-copied-host-60b9 @ 90cd61fa6 counts interpretive co-chart hosts on this cut:

• 47 window-named non-X0 ADD sources (exemplar X5) hold FULL at ADD/after restore with zero post-channel destinations.
• Broader all-X nonself co-chart count 103.
• Shares dirty_helper_touches=0 / zero endpoint repayment; ADD-5759 uniqueness of X0 retained.

Gates PASS. A separate CrocSwap PR is deferred for soft-overlap / weak-need vs this PR (verify≈0.672): the census is largely a corollary of channel-wide X→FULL finals plus the window dirt=0 already certified here — not a vector-equal / dirty-helper copied-host certificate. Prefer folding a stronger construction (vector-equal host or priced dirty-helper floor) into this thread, or treating this comment as the interpretive census record.

κ unchanged. Does not close OQ2 (constructed dirt-restore). Prepared by Wentao Li with substantial AI assistance.

[VictorLiwentao]

OQ1/OQ2 follow-up attempt (deferred; both OQs still open)

A candidate package research/p104-flag0-tail-vector-equal-host/ @ 2769913eb built a five-event outside-window splice so dirty helper D0 is copy-rule / value-id equal to X0 at the ADD, with displaced-dirt save/restore and window_len=50 / zero in-window dirty touches (+5 events).

Soft-overlap / OQ-misclaim deferred vs this PR:

• OQ1 asks for a non-self host among event-named registers on this cut; the splice leaves the cut and hosts on D0 (not named by ADD 5759), while the ADD still reads X0.
• OQ2 asks for arbitrary dirt restore under S0 without enlarging the published window; this uses S_D0, adds +5 schedule events, and restores only the singular dirt it displaced.

No separate CrocSwap PR opened. OQ1 and OQ2 remain open.