Add P104 flag 0 coefficient transport audit

research/p104-flag0-coefficient-transport/README.md

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+# P104 flag 0: coefficient and sign through the native word
+
+**Scoped exact row audit. No new kappa, correction program, supplier, or cost claim.**
+
+## Question and result
+
+For the first record of PR #2981's 208-flag collection, does the exact
+coefficient for source `X0` reach target `Y34` through the cited 4,058-event
+native word, and what sign does the complementary `I-G/2` term require?
+
+Flag 0 is `(X0, Y34)` with basis head `232`. The source and target roots have
+dot product `4` in the fixture's doubled E8 coordinates (root norm `8`). Thus
+the native `G/2` coefficient is `4/8 = +1/2`, while the off-diagonal
+coefficient required from `I-G/2` is `-1/2`.
+
+The exact one-hot row replay sets `x0=z`, all other source and dirty
+coefficients to zero, and the `y34` baseline to zero. It follows the scalar
+rows through the pinned word: transports retain rows, additions use their
+literal `Fraction` coefficient, and private zero/copy/erase events update the
+row as specified by the native-channel proof. The `Y34` additions carrying
+`z` occur at events 2815 (`+z/2`), 2998 (`-z/2`, canceling it), and 3369
+(`+z/2`). The final native row is therefore `z/2`; the required side term is
+`-z/2`.
+
+The zero-based event order is `Y34` first touched at 129, `X0` first touched at
+591, `Y34` last touched at 3500, and `X0` last touched at 3954. PR #3242's
+whole-word scan reports no X/Y pair sharing an event; this check confirms that
+`X0` and `Y34` do not share one. The one-hot replay shows that first-touch
+ordering alone does not rule out later relay delivery in this native word:
+`Y34` gets its nonzero `X0` coefficient after event 591. These are
+native-channel additions, not an executable side correction.
+
+## Scope and limits
+
+This checks one exact coefficient row for one named flag. It uses the
+independent linear-row invariant already proved for the pinned native
+realization; it does not rerun that package's Clifford or all-column proof.
+The dirty coordinates are zero in this one-hot coefficient slice. The audit
+does not deliver the opposite side term, restore arbitrary dirty inputs,
+certify frame availability for a correction, or price correction/idle/hosting
+work. The newer pooled support audits (#3259, #3803, and #3810) concern whether
+fixed-cover correction coefficients have support; this package checks the
+opposite-sign native row for one actual word path and does not extend those
+support claims.
+
+Reproduce the bounded check from the repository root:
+
+```sh
+python3 scripts/research_package.py --package research/p104-flag0-coefficient-transport --check-only
+python3.12 scripts/research_package.py --package research/p104-flag0-coefficient-transport
+```
+
+## Open next questions
+
+Can an added correction deliver `-z/2` to `Y34` at a legal common-frame cut
+while restoring all dirty inputs? This matters because the native word
+delivers `+z/2`, and the opposite sign is required for this off-diagonal entry.
+The next step is to name a legal source/target frame cut and an explicit
+correction writer, then test its full dirty row. A complete bill and the
+correction construction remain outstanding.
+
+## Credit
+
+Credit Nick Petalas / PR #2981 for the static flag certificate; Rohan Arun / PR
+#1972 and Chafik Boukhalfa / PR #1991 for the low-rank channel and native row
+invariant; and jwr404 / PR #3242 for the event-index chronology that motivated
+this flag-0 check. The coefficient trace and sign comparison here are new.
+The pooled support lineage remains credited to PR #3182, #3259, #3803, and
+#3810. Prepared by OpenAI Codex, laptop-03 session; no independent human or
+formal-kernel review is claimed. New work is Apache-2.0.

research/p104-flag0-coefficient-transport/RESULT.json

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+{
+  "status": "PASS_P104_FLAG0_COEFFICIENT_TRANSPORT",
+  "flag0": {
+    "source": "X0",
+    "target": "Y34",
+    "basis_head": 232
+  },
+  "events": {
+    "target_first": 129,
+    "source_first": 591,
+    "target_last": 3500,
+    "source_last": 3954,
+    "X0_Y34_joint_events": 0
+  },
+  "raw_doubled_root_dot": 4,
+  "native_G_over_2_coefficient": "1/2",
+  "required_I_minus_G_over_2_coefficient": "-1/2",
+  "target_additions": [
+    {
+      "event": 2815,
+      "source": "D17",
+      "scale": "-1/4",
+      "source_coefficient": "-2",
+      "delta": "1/2",
+      "after": "1/2"
+    },
+    {
+      "event": 2998,
+      "source": "D13",
+      "scale": "1/4",
+      "source_coefficient": "-2",
+      "delta": "-1/2",
+      "after": "0"
+    },
+    {
+      "event": 3369,
+      "source": "D23",
+      "scale": "1/4",
+      "source_coefficient": "2",
+      "delta": "1/2",
+      "after": "1/2"
+    }
+  ],
+  "one_hot_fixture": "x0=z; other x and dirty coefficients zero; y34=0",
+  "controls": [
+    {
+      "z": "1",
+      "native_y34": "1/2",
+      "required_side_addition": "-1/2"
+    },
+    {
+      "z": "7/11",
+      "native_y34": "7/22",
+      "required_side_addition": "-7/22"
+    },
+    {
+      "z": "-3/5",
+      "native_y34": "-3/10",
+      "required_side_addition": "3/10"
+    }
+  ],
+  "no_correction_program_or_cost_claim": true
+}

research/p104-flag0-coefficient-transport/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "67f085acd86acd7d4e03922d9cf4b26bca66fed5",
+      "sha256": "47b42433f5a85809a3aadd29c2c339da2c6ed728e4f7762df6b88bccb7874cf0"
+    },
+    {
+      "path": "research/p104-joint-unit-flags/CERTIFICATE.json",
+      "usage": "input",
+      "git_blob": "0fa7d2d40566e92f3ea1539723abf438ba65adb8",
+      "sha256": "a98126428a8da6eae91c50afcc42e014a284c82b554ef77e5b3a34fc6d228128"
+    },
+    {
+      "path": "research/p104-native-channel/inputs/LOWRANK-WITNESS.json",
+      "usage": "input",
+      "git_blob": "86beaf424e9f0f800ae3a62797d94ec9386b7706",
+      "sha256": "0f541bef7f19fdeffd67157684e9f03d785f42c89973632f508fc1a0452b580e"
+    },
+    {
+      "path": "research/p104-native-channel/inputs/P104-FIXTURE.json",
+      "usage": "input",
+      "git_blob": "2e16f99b295bb386fd13bd8fbd57b42ef54143a9",
+      "sha256": "516c06f6ec3cb84be588c546108de897650288576dd5fbf5fe44b9c5546ad8a4"
+    },
+    {
+      "path": "research/p104-endpoint-geometric-budget/geometry.py",
+      "usage": "input",
+      "git_blob": "f49752bcfc321a6129186d4daa774b2c3fdb84f1",
+      "sha256": "1a2792189beaf15aa8180136ca007cd2301992a62e77ba72edea99b298e4148f"
+    },
+    {
+      "path": "research/p104-native-channel/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "a69311b74f74a2f8e8f411c1451baacd9bacddce",
+      "sha256": "5d743145d389ffdfaffc66096fa7e32c7155b18f73d74755403151d0435bb94c"
+    },
+    {
+      "path": "research/p104-flag-channel-schedule/RESULT.json",
+      "usage": "provenance",
+      "git_blob": "c2d7443350e7a8fdb77910689df75516b789b55d",
+      "sha256": "4ba6fd7555d8907ce28d52d8de5087133e3649431f8ef0617a8961ebcbb73e16"
+    }
+  ]
+}

research/p104-flag0-coefficient-transport/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "p104-side-correction",
+  "priority_revision": 6,
+  "base_commit": "20ecf2891d80b5acf18d980b2164fb44ea7faa90",
+  "original_card": {
+    "id": "p104-side-correction",
+    "question": "Can the proposed P104 joint endpoint flags be realized by a chronological correction program with coefficients, dirty restoration and an affordable complete bill?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "research/p104-native-channel/README.md",
+      "research/p104-native-channel/PROOF.md",
+      "docs/research/community-efficient1000-review.md",
+      "research/p104-joint-unit-flags/README.md"
+    ],
+    "methods": [
+      "Construct one side-correction word at an explicit chronological cut with the needed frames still available.",
+      "Derive a lower bound on the side correction and hosting costs that decides whether this channel can beat the selected budget."
+    ],
+    "acceptance_gate": "An exact arbitrary-input identity, source/target frame availability and restoration at the chosen cut, plus the complete channel+correction+idle/hosting bill or an explicit favorable bound. The native channel alone is not a supplier. A scoped local result may be retained without a complete supplier. Expanding it into further construction rounds requires the family-level budget and obligation gate in research-family-status.md; an optimistic passing relaxation alone is not acceptance.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read the revision-6 family record and #2981 static joint flags, alongside the reviewed #1991 channel. #2981 is an author-checked source archive, not an independently validated executable correction or a refutation of program-level lifetime floors.",
+      "scope": "Source-bound orientation only. Read the named package and review before relying on its local evidence; this command is not its replay or supplier admission."
+    },
+    "first_experiment": "After checking live handoffs, pin one named collection from #2981 and attach acquisition/delivery times, source dependencies and coefficient requirements. Test legal access and arbitrary dirty restoration; price any completion against the full channel/endpoint/hosting allowance. Stop with the exact missing implication or a scoped counterexample rather than expanding the static cover census.",
+    "bottleneck_link": "Completing an already realized changed channel tests a concrete construction opportunity, instead of refining the incumbent packing. A positive local result still needs global and all-size admission.",
+    "allowed_variations": [
+      "One correction factorization, one chronological cut, or one explicit hosting obstruction.",
+      "A changed correction schedule with an updated full bill and native frame contract."
+    ],
+    "scope_change_triggers": [
+      "Recompiling the already certified low-rank channel without closing a new obligation.",
+      "Treating a pending ancestor, local histogram or unpriced side correction as an admitted global supplier.",
+      "Repeating a correction or physical conversion already supplied by a pending follow-up without adding independent coverage or a different unresolved obligation.",
+      "Repeating the 208-flag static matching or calling a static nested cover a chronological correction program. Independent audit of that certificate is distinct and remains useful."
+    ],
+    "overlap_terms": [
+      "P104",
+      "I-G/2",
+      "side correction",
+      "native channel",
+      "1972",
+      "1991",
+      "2586",
+      "endpoint transport",
+      "physical dual",
+      "relay composition",
+      "2981",
+      "joint unit flags",
+      "acquisition delivery",
+      "static nesting"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #2981 reports static joint endpoint flags and a matching of 208 departure and arrival flags; archival intake is not independent verification.",
+        "evidence": "research/p104-joint-unit-flags/README.md",
+        "remaining": "Independent flag check and a chronological coefficient program with dirty restoration and a complete cost.",
+        "status": "author-checked",
+        "source_commit": "3d24b92d8ba057b57cb2d480170ec407520e6882",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "For PR #2981 flag 0 (X0 -> Y34), exact-check the native G/2 coefficient and opposite I-G/2 side sign through the PR #1991 4,058-event scalar word using a one-hot x0=z row. Record event chronology; do not construct the side correction.",
+  "scope_change_reason": "Live overlap already covers static flag schedules and pooled correction support: PR #3242 reports flag-0 event order; PR #3259 and #3803 audit fixed-cover support, and open PR #3810 further checks that support model and coefficient signs. This scope complements them by tracing one actual native coefficient through the original chronological word.",
+  "bottleneck_link": "The changed channel needs its complementary I-G/2 row to cancel the native G/2 contribution. An exact one-entry sign trace checks this interface obligation; it does not supply the correction or improve the selected exponent.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after reproducing flag 0's exact one-hot coefficient, sign, and event trace. Do not expand to other flags, correction construction, lifetime floors, or hosting prices; those are separate live scopes and the family gate requires a complete boundary ledger before another construction round.",
+  "outcome": "partial",
+  "evidence": "Exact Fraction replay of one formal source coordinate through all 4,058 scalar events gives native Y34 coefficient +1/2; root pairing requires side coefficient -1/2. The target is first touched before X0's first event, then receives +1/2, -1/2, +1/2 at events 2815, 2998, 3369 and finishes at +1/2.",
+  "author": "OpenAI Codex (laptop-03)",
+  "ai_assistance": "Substantial OpenAI Codex assistance. No independent human review or formal-kernel proof is claimed.",
+  "open_questions": [
+    {
+      "question": "Can a correction program add -z/2 to Y34 at a legal common-frame cut while restoring every arbitrary dirty role?",
+      "why_it_matters": "The native word contributes +z/2 at this entry, so the complementary side term must be delivered with the opposite sign before the channel can meet its exact row contract.",
+      "first_step": "Name one cut with source and target frames available, then trace the correction on the X0 and every dirty basis coordinate through the full word.",
+      "blocked_by": "No correction word or complete dirty-restoration/interface invoice is established here; construction and lifetime/hosting work remains separate."
+    }
+  ]
+}

research/p104-flag0-coefficient-transport/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/p104-endpoint-geometric-budget/geometry.py",
+    "research/p104-joint-unit-flags/CERTIFICATE.json",
+    "research/p104-native-channel/inputs/LOWRANK-WITNESS.json",
+    "research/p104-native-channel/inputs/P104-FIXTURE.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Exact port/root pairing, source-bound flag 0, zero-based event cut, exact Fraction one-hot row replay, three relay contributions, opposite-side sign controls, and explicit no-correction scope."
+    }
+  ]
+}