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

research/p104-flag0-tail-owner-host/CERTIFICATE.json

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+{
+  "schema_version": 1,
+  "claim_id": "p104-flag0-tail-owner-host",
+  "pinned_main": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "answers": "CrocSwap#3669 OQ2",
+  "flag_index": 0,
+  "source": 0,
+  "target": 34,
+  "source_register": "X0",
+  "target_register": "Y34",
+  "promote_event": 5758,
+  "add_event": 5759,
+  "restore_event": 5807,
+  "coefficient": "-1/2",
+  "host_chart": [1, 2, 4, 8, 16, 32, 64, 128, 256],
+  "channel_final_x0": [1, 2, 4, 8, 16, 32, 64, 128, 256],
+  "channel_final_y34": [499, 23, 232, 32, 112, 15, 7, 2],
+  "source_initial": [232],
+  "target_initial": [],
+  "schedule_id": "S0",
+  "owner": "X0",
+  "owner_kind": "self",
+  "unique_owner_among_event_named_registers": true,
+  "dirty_helper_touches_in_window": 0,
+  "x0_destination_events_after_channel": 0,
+  "x0_last_destination_event": 1486,
+  "endpoint_repay_x0_to_initial": false,
+  "endpoint_repay_y34_to_initial": false,
+  "x0_frame_after_restore": [1, 2, 4, 8, 16, 32, 64, 128, 256],
+  "y34_frame_after_restore": [499, 23, 232, 32, 112, 15, 7, 2],
+  "y34_tail_transports": [5758, 5807],
+  "window_add_count": 48,
+  "pre_read_x0_restoration_blocks_common_chart": true,
+  "selected_kappa": "0.001672660197076918",
+  "no_new_kappa": true
+}

research/p104-flag0-tail-owner-host/MASTER-HANDOFF.md

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+# Master handoff — `research/p104-flag0-tail-owner-host/`
+
+## Candidate
+
+- Branch: `cursor/flag0-tail-owner-host-60b9` (VictorLiwentao fork).
+- Content tip: `01cbbe345` (scientific package commit; parent = pinned base).
+- Packaging tip: branch HEAD (`git rev-parse HEAD` on this branch).
+- Package: `research/p104-flag0-tail-owner-host/`
+- Base: CrocSwap main `20ecf2891d80b5acf18d980b2164fb44ea7faa90`
+- Card: `p104-side-correction` (refined), priority revision 6
+- κ: unchanged at `0.001672660197076918`
+- Author and committer: Wentao Li `<wentaol4@illinois.edu>`, with no
+  `Co-authored-by: Victor Li` trailer (`git -c core.hooksPath=/dev/null commit`).
+- **Do not open a CrocSwap PR** — master publishes.
+
+## Claim
+
+On present-head flag 0, the published promote/add/restore at 5758/5759/5807
+admits self-owned host schedule S0 (`owner=X0` on `FULL`) for the `X0` read:
+unique among event-named registers, zero dirty-helper touches in the window,
+zero endpoint repayment toward initials, and pre-read `X0` restoration blocked
+by the published common-chart annotation. Answers #3669 OQ2. No new kappa.
+
+## Why this is not a chronology / repair-template reprint
+
+Headline is an owner/host **assignment** plus dirt and endpoint-repayment
+checks on the #2089 tail word. It does not reprint #3669's drop/arrive
+chronology, does not retarget the #3532/+2 head-span repair template, and does
+not price event-3369 co-hosting. Prior jwr404 packages show frames/coefficient
+and that no owner field is named; this package fills the owner gap with S0.
+
+## Evidence commands
+
+```sh
+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 markers:
+
+```text
+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`.
+Duplicate JSON keys are rejected. On-disk certificate / witness corruption is
+rejected in temp copies.
+
+## Soft overlap
+
+- Soft vs #3669 (chronology leave-alone): cites OQ2 only; no drop/arrive reprint.
+- Soft vs deferred `p104-flag0-head-span-schedule` / #3532: different cut
+  (5758/5759/5807 vs 3369 co-host repair); not a FLAG_INDEX retarget.
+- Soft vs jwr404 `p104-tail-flag0-*`: those are partial readings; this assigns
+  the schedule and adds dirt/repay/obstruction checks.
+- Leave-alones listed in the worker brief are untouched.
+
+## Disposition
+
+Fork branch for master publish decision. Do not open a CrocSwap PR from this
+worker.

research/p104-flag0-tail-owner-host/NOTICE.md

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+# Notice
+
+Copyright 2026 Wentao Li
+
+This directory is a scoped research certificate. It is licensed under the
+Apache License, Version 2.0, the same license as the surrounding project.
+
+The 4,058-event channel witness is the reviewed #1991 native channel. The
+augmented promote/add/restore tail word and correction rows are Cinna Davis's
+#2089 package at `research/p104-tail-side-correction-seed749717`. The prior
+unbound-owner receipt is jwr404's `research/p104-tail-flag0-owner`. The
+unrestored-endpoint census cited here is Wentao Li's #3349 package at
+`research/p104-channel-touch-restoration-audit`. Open #3669 states the OQ2
+this package answers.
+
+Those notices and files are unchanged. Prepared by Wentao Li with substantial
+AI assistance. No independent human or formal-kernel review is claimed.

research/p104-flag0-tail-owner-host/PROOF.md

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+# Proof: self-owned flag-0 tail host schedule without endpoint repayment
+
+## Claim
+
+On the published #2089 augmented witness, events 5758/5759/5807 form a
+promote/add/restore triple for target `Y34` with source read `X0` at
+coefficient `-1/2`. Schedule S0 assigns owner `X0` on host chart `FULL`. This
+schedule is legal for the published ADD, uniquely determined among registers
+named by that ADD, touches no dirty helper in the window, and leaves both
+endpoint frames at their unrestored channel finals. Restoring `X0` to its
+initial frame before the ADD conflicts with the published common-chart
+annotation. No new κ.
+
+## Inputs
+
+Pinned at CrocSwap main `20ecf2891d80b5acf18d980b2164fb44ea7faa90`:
+
+- `research/p104-native-channel/inputs/LOWRANK-WITNESS.json` (#1991 channel)
+- `research/p104-tail-side-correction-seed749717/AUGMENTED-WITNESS.json.gz` (#2089)
+- `research/p104-tail-side-correction-seed749717/CORRECTION-ROWS.json`
+- `research/p104-tail-flag0-owner/RESULT.json` (prior: no owner field)
+- `research/p104-channel-touch-restoration-audit/CERTIFICATE.json` (#3349)
+
+Hashes are in [SOURCES.json](SOURCES.json).
+
+## Setup
+
+Write `FULL = [1,2,4,8,16,32,64,128,256]` and
+`RANK8 = [499,23,232,32,112,15,7,2]`. The channel leaves `X0` at `FULL` and
+`Y34` at `RANK8`. Neither equals its initial (`[232]` and `[]`). #3349 records
+that this unrestored pattern holds for every endpoint; this package cites that
+census and rechecks only the flag-0 pair.
+
+The tail word's first 4,058 events equal the channel program. Event 5758 is
+`transport Y34: RANK8 → FULL` (rank 1). Event 5759 is
+`add Y34 X0 -1/2 FULL`. Event 5807 is `transport Y34: FULL → RANK8` (rank 1).
+Between them sit exactly 48 `Y34` adds.
+
+## Schedule S0
+
+Assign:
+
+- `owner(5759) = X0`
+- `host_chart(5759) = FULL`
+- no additional host register
+
+**Legality.** A forward frame walk from the tail initials reaches `X0 = FULL`
+and `Y34 = FULL` at event 5759, matching the ADD's chart field. The common-chart
+rule holds.
+
+**Uniqueness on the published word.** The ADD names exactly `{Y34, X0}`. The
+write target cannot own the source read. The only remaining named register is
+`X0`. So among event-named registers, S0 is the unique owner assignment. (A
+copied host using an unnamed helper would be a different word; see open
+questions.)
+
+**Dirt.** Scan events 5758 through 5807. No top-level field is a dirty helper
+name (`D*`, `G*`, `Q*`, or `C`). The channel's dirty-helper restorations are
+therefore undisturbed by this window. Arbitrary dirt that the channel already
+restored stays restored; S0 introduces no new dirty host.
+
+**Endpoint repayment.** After event 5807 the walk gives `X0 = FULL` and
+`Y34 = RANK8`. These equal the channel finals and differ from the initials.
+Define repayment as a transport that returns an endpoint to its initial frame.
+Neither endpoint is so returned. The promote/restore pair is a temporary lift
+of `Y34` that ends at the channel final, not at `[]`.
+
+**Coefficient.** `CORRECTION-ROWS.json` row 34, source 0, stores coefficient
+`-1/2`, matching the ADD.
+
+## Obstruction: pre-read X0 restoration
+
+Suppose one restores `X0` to `[232]` before event 5759 while keeping the
+published ADD, whose chart annotation is `FULL`. Then the live `X0` frame is
+not `FULL`, so the common-chart rule fails. Hence any schedule that repays
+`X0`'s unrestored endpoint before the read is incompatible with the published
+word. (Repayment after 5807 is outside this certificate and would cost
+positive descent rank from `FULL` toward `[232]`.)
+
+## What this does not prove
+
+- A global owner/host map for all 4,992 source reads
+- A copied-host construction or its rank-mass floor
+- Integration with the #1940 chronological schedule
+- A supplier admission or a new κ
+- Anything about the deferred #3669 OQ1 +2 head-span repair at event 3369
+
+## Independence
+
+`verify.py` walks frames in program order. `independent.py` builds per-register
+indexes and reconstructs frames from transport subsequences alone. Neither
+imports the other or the native checker. Both compare against
+[CERTIFICATE.json](CERTIFICATE.json). Temp-copy corruptions of that certificate
+and of the gzipped witness are rejected under `-O`.

research/p104-flag0-tail-owner-host/README.md

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+# Flag 0's published tail cut admits a self-owned X0 host schedule with zero endpoint repayment
+
+**Finite owner/host schedule certificate. No new exponent.**
+
+Open [#3669](https://github.com/CrocSwap/integer-mult-bounds/pull/3669) leaves
+as OQ2 whether the published promote/add/restore at events 5758/5759/5807 admits
+an owner/host schedule for the `X0` read that restores arbitrary dirt without
+repaying the unrestored channel endpoints. This package answers yes for that
+local cut.
+
+## Result
+
+Schedule **S0** assigns `owner = X0` (self) on the full host chart for the ADD
+at event 5759. On the published #2089 tail word:
+
+| Fact | Value |
+|---|---|
+| Promote / add / restore | 5758 / 5759 / 5807 |
+| Coefficient | `-1/2` (matches `CORRECTION-ROWS` row 34, source 0) |
+| Host chart at the ADD | `FULL = [1,…,256]` for both `X0` and `Y34` |
+| Unique source owner among registers named by the ADD | `X0` |
+| Dirty-helper (`D`/`G`/`Q`/`C`) touches in the window | **0** |
+| `X0` destination events after the 4,058-event channel | **0** (last write 1486) |
+| Endpoint repay of `X0`/`Y34` toward their initials | **false** / **false** |
+| Frames after restore | `X0=FULL`, `Y34=RANK8` (channel finals) |
+
+Dirt restoration: the window never touches a dirty helper, so the channel's
+already-restored 72 dirty helpers stay restored. Endpoint repayment: after 5807
+both registers sit at their channel finals, not at `[232]` / `[]`.
+
+**Obstruction.** Restoring `X0` to its initial frame `[232]` before event 5759
+while keeping the published ADD (annotated `FULL`) violates the common-chart
+rule. Endpoint repayment of `X0` cannot precede the read on this word.
+
+Selected κ stays `0.001672660197076918`. No global 104×104 owner map. Distinct
+from the deferred #3669 OQ1 +2 head-span repair and from open [#3532](https://github.com/CrocSwap/integer-mult-bounds/pull/3532).
+
+Details are in [PROOF.md](PROOF.md).
+
+## Reproduce
+
+```sh
+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
+```
+
+`verify.py` is read-only. Admission goes through `need()` and still fires under
+`-O`. `independent.py` imports neither `verify.py` nor the native checker.
+
+## Credit
+
+Credit #3669 for OQ2, Cinna Davis / #2089 for the tail word, jwr404's
+`p104-tail-flag0-*` readings for the unbound-owner gap and frame facts this
+package cites, #3349 for the unrestored-endpoint census, and the reviewed #1991
+channel. Prepared by Wentao Li with substantial AI assistance.
+
+## Open next questions
+
+1. Does the same self-owned zero-repay pattern hold for every target window?
+2. What host rank mass does a copied-host alternative cost under unrestored
+   endpoints?
+
+[TASK.json](TASK.json) gives first steps and blockers.

research/p104-flag0-tail-owner-host/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "upstream": "CrocSwap/integer-mult-bounds",
+  "files": [
+    {
+      "path": "research/p104-native-channel/inputs/LOWRANK-WITNESS.json",
+      "usage": "input",
+      "git_blob": "86beaf424e9f0f800ae3a62797d94ec9386b7706",
+      "sha256": "0f541bef7f19fdeffd67157684e9f03d785f42c89973632f508fc1a0452b580e",
+      "credit": "Reviewed #1991 native channel witness (Chafik Boukhalfa / Rohan Arun #1972)"
+    },
+    {
+      "path": "research/p104-tail-side-correction-seed749717/AUGMENTED-WITNESS.json.gz",
+      "usage": "input",
+      "git_blob": "7e248e2d263fc6b1b578350a7bbc6d4ad725b106",
+      "sha256": "fa7487b0b0b4e8fb6bdb1bed1171498a4ed487a1efeb8bb93897e379200000a0",
+      "credit": "Cinna Davis / #2089 terminal promote/add/restore tail word"
+    },
+    {
+      "path": "research/p104-tail-side-correction-seed749717/CORRECTION-ROWS.json",
+      "usage": "input",
+      "git_blob": "bbb46b132c0f5093fedf2269b24fd7b0b4b87af2",
+      "sha256": "59c145194ba070fda338619e890f25a4a8ae7f37facf3689c1c8c89f79e8bd36",
+      "credit": "Cinna Davis / #2089 sparse I-G/2 correction rows"
+    },
+    {
+      "path": "research/p104-tail-flag0-owner/RESULT.json",
+      "usage": "input",
+      "git_blob": "d84b02599cd8388b0fa9a5d9c058ee2c03c03f3b",
+      "sha256": "0a7aafbc0fc004eb21eef1fefea049b2831ba2f62cfae3389181afb295c3368b",
+      "credit": "jwr404 prior: event 5759 names no owner field"
+    },
+    {
+      "path": "research/p104-channel-touch-restoration-audit/CERTIFICATE.json",
+      "usage": "input",
+      "git_blob": "a3f80bb15f85598c3dfe138239f9343077068c49",
+      "sha256": "aa8fbc62f4238f8395c7ca5dc0763105a559106178e9c94264579e0b701da4d5",
+      "credit": "Wentao Li / #3349: 0/208 endpoint frames restored; flag0 unrestored"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0",
+      "pin": "base_commit:docs/research/agent-task-catalog.json",
+      "credit": "Priority revision 6 task catalogue"
+    }
+  ]
+}