Mister-Meeseeks · Oct 21, 2026 · Oct 21, 2026
diff --git a/research/p104-fiber-tag-orientation-check/README.md b/research/p104-fiber-tag-orientation-check/README.md
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+# #4154's P104 fiber-tag seam, checked in its sources' orientation
+
+**Claim type: an independent finite check with a correction. No new κ.** The
+selected conditional κ stays `0.001672660197076918`.
+
+## Object
+
+[PR #4154](https://github.com/CrocSwap/integer-mult-bounds/pull/4154)
+(unpaidmoon, merged, `research/p104-fiber-tag-seam`) compares #3966's row tag
+`z ⊗ q_j` with its column tag `r_i ⊗ z` on the 104 P104 labels, and pins
+#3954's witness. The `p104-side-correction` card lists it as still needing
+independent validation.
+
+**The orientation question.** The sources fix which tag is which:
+
+- **#3966** (`p104-phase-uniform-gauge/PROOF.md` §4) defines the row
+  correction as `z ⊗ q_j` and the column correction as `r_i ⊗ z`, with
+  `q_j = O p_j` for the row label and `r_i = O p_i` for the column label.
+- **#3954**'s witness lines are `386 ⊗ 386` (row port) and `405 ⊗ 386`
+  (donor port), decoded from its `RESULT.json`. Both lie in the row fiber
+  `q = 386`, so the pair is row 386, column 405, on the shared line
+  `r_i ⊗ q_j = 49 ⊗ 386`.
+
+#4154's README states that convention. Its code does not: `tags(row_image,
+column_image)` returns `z ⊗ column_image` as the row tag and
+`row_image ⊗ z` as the column tag. Those are the transposes.
+
+## Results
+
+**Confirmed: everything that does not depend on orientation.**
+
+| Claim | Result |
+| --- | --- |
+| Labels | `labels.json` equals `physical_labels` in #3966's source `RESULT.json` |
+| Gauge | `O` is an orthogonal involution with the weight law, on all of `F₂⁹` |
+| Label classes | 56 of class 1 and 48 of class 3; every image is class 3 |
+| Full address | no agreement in any of the 10,816 ordered pairs |
+| Shared line | 5,440 pairs agree and 5,376 disagree |
+| Uniform tag `a` | never a row tag or a column tag |
+| Minimum Hamming distance | 6, only at labels 4 and 32 |
+| Witness Hamming distance | 20 |
+
+**Corrected: the witness and one census sentence.** These are in #3966's
+orientation, at row 386 and column 405.
+
+| | #4154 | Source orientation |
+| --- | --- | --- |
+| Shared-line flips (row, column) | `(0, 1)` | `(1, 0)` |
+| Does `a` match the row tag on the shared line? | no | **yes** |
+| Separating cell | bit 11 = `(1, 2)` | bit 11 does not separate; bit 19 = `(2, 1)` does |
+| Helper matches the row tag on the shared line exactly when | the column label is class 3 | **the row label** is class 3 |
+
+The count is `104 · 48` ordered pairs either way.
+
+- **The full-address obstruction stands.** `a` is never a row tag, so a
+  helper carrying `a` still fails to match a row owner on the full 81-bit
+  address.
+- **The shared-line conclusion does not.** #4154 says that on the witness's
+  shared line "a helper carrying `a` does not match this row owner". In the
+  source orientation it does match there. That conclusion is the premise of
+  #4154's open question 2.
+
+**Control.** Evaluating #4154's transposed objects reproduces its numbers
+exactly: flips `0/1`, the helper mismatch and bit 11. The census is
+unchanged. The difference is therefore exactly the transpose. The verifier
+also checks the line in #4154's code that builds the row tag from the column
+image.
+
+**Provenance note.** #4154 says #3966's `RESULT.json` "is not a Git object on
+this base". It is on main, as
+`research/p104-phase-uniform-gauge/source/RESULT.json`, with the pinned SHA256
+`ce05a27e…`.
+
+## Method and independence
+
+The verifier imports nothing from #4154. It represents tensors as sets of
+`(α, β)` cells rather than packed integers. It reads the labels from #3966's
+file, not #4154's copy, and it reads the orientation from #3966's text and
+#3954's witness vectors.
+
+## Not covered
+
+- Native routing, owners, dirty return, precision and the inherited
+  44,096 excess, all of which #4154 also leaves open.
+- Which orientation a future P104 caller should use. This package only
+  matches the sources' definitions.
+
+## Reproduce
+
+```sh
+python3.12 -B research/p104-fiber-tag-orientation-check/verify.py
+```
+
+It prints `PASS_P104_FIBER_TAG_ORIENTATION_CHECK` in about 2 seconds, using
+only the standard library.
+
+## Open next questions
+
+1. **Revisit #4154's open question 2 in the source orientation.** At the
+   witness, the uniform tag already agrees with the row tag on the shared
+   line. The remaining question is only full-address agreement, which `a`
+   can never give.
+   - *First step:* restate the question for the full address alone.
+   - *Blocked by:* nothing.
+
+## Credit
+
+The seam comparison is unpaidmoon's (#4154). The labels, the gauge and the
+corrections are #3966's (ToikY); the witness is #3954's (Clear1nsight).
+Prepared by Ryanson Jonathan with substantial Claude Code (Claude Opus 5.5)
+assistance. Apache-2.0.
diff --git a/research/p104-fiber-tag-orientation-check/SOURCES.json b/research/p104-fiber-tag-orientation-check/SOURCES.json
@@ -0,0 +1,54 @@
+{
+  "schema_version": 1,
+  "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "b1fea0c94436b236cc2b7d41a7be032811b94c81",
+      "sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "64bfc5af6709ed9811171e0a2108f05e1219cb65",
+      "sha256": "352a6184713b8843d96fd2c2071eb7aeaa655906b7c51d45ad444912666c8a96"
+    },
+    {
+      "path": "research/p104-fiber-tag-seam/README.md",
+      "usage": "input",
+      "git_blob": "149821201622a046742baa2df4563296cebe9800",
+      "sha256": "b0b493d9db3b7c99e8497a761678f11c0e331224d37bf8c9d56747517ff9c2a2"
+    },
+    {
+      "path": "research/p104-fiber-tag-seam/verify.py",
+      "usage": "input",
+      "git_blob": "836a547850b9d8740c99bf0f9f9eaa73afcbf2a2",
+      "sha256": "81e24ecc7aad4a504efadddb5afe99b371ca93289d2502efee2621208497777a"
+    },
+    {
+      "path": "research/p104-phase-uniform-gauge/PROOF.md",
+      "usage": "input",
+      "git_blob": "fd701d86feaead86d711fa8d25914c68ea70781c",
+      "sha256": "a0e72e6b48e75edf2948b455ebe59c7d912682204b34d916bfed804cea35c405"
+    },
+    {
+      "path": "research/p104-phase-uniform-gauge/source/RESULT.json",
+      "usage": "input",
+      "git_blob": "c7ed0ea02e8c462694762508b0bdd1dde2e116d0",
+      "sha256": "ce05a27ebc98677bec4febaa488fa03f5b6fc60216aa43b34298444d12f7ab6c"
+    },
+    {
+      "path": "research/p104-two-axis-compatibility/PROOF.md",
+      "usage": "input",
+      "git_blob": "1d84b2a1188eab6a5c38743cc1eed32d66446a3d",
+      "sha256": "bdc7d868e4411541a33179af683f48011e66d6446a45bef363f3f3dd5163f717"
+    },
+    {
+      "path": "research/p104-two-axis-compatibility/RESULT.json",
+      "usage": "input",
+      "git_blob": "c7ed0ea02e8c462694762508b0bdd1dde2e116d0",
+      "sha256": "ce05a27ebc98677bec4febaa488fa03f5b6fc60216aa43b34298444d12f7ab6c"
+    }
+  ]
+}
diff --git a/research/p104-fiber-tag-orientation-check/TASK.json b/research/p104-fiber-tag-orientation-check/TASK.json
@@ -0,0 +1,133 @@
+{
+  "schema_version": 1,
+  "task_id": "p104-side-correction",
+  "priority_revision": 7,
+  "base_commit": "12fa8c5c844be21bfefb38a19503fbd867a11244",
+  "original_card": {
+    "id": "p104-side-correction",
+    "question": "Can a changed P104 producer/consumer contract escape the scoped slot, chart and completion obstructions with a favorable full bill?",
+    "starting_points": [
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "research/p104-literal-slot-defect/README.md",
+      "research/p104-uniform-commutation-gap/README.md",
+      "research/p104-uniform-encoding-gap/README.md",
+      "research/p104-source-chart-shortcut/README.md",
+      "research/p104-fiber-tag-seam/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 named successor obstructions before extending #2981 static flags. Distinguish literal-slot action, commutation, uniform encoding, source-chart shortcut and fiber-tag seam scopes; none excludes all P104 mechanisms.",
+      "scope": "Source-binding orientation only; no scientific replay, theorem acceptance or supplier admission. Budget any heavy replay separately."
+    },
+    "first_experiment": "Name one hypothesis changed from these exact interfaces. Write a literal producer-to-consumer timeline and an arbitrary-dirty-input positive/control pair, then charge acquisition, coefficients, completion, hosting and restoration. Stop if the same slot/fiber mismatch persists or the favorable full budget already fails. A scoped independent audit remains useful; another static count is not a new completion.",
+    "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.",
+      "Repeating a static cover, source-chart shortcut or fiber-tag seam without changing the hypothesis responsible for its obstruction."
+    ],
+    "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",
+      "4133",
+      "4136",
+      "4140",
+      "4153",
+      "4154",
+      "p104-literal-slot-defect",
+      "p104-uniform-commutation-gap",
+      "p104-uniform-encoding-gap",
+      "p104-source-chart-shortcut",
+      "p104-fiber-tag-seam"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #4133: literal-slot defect",
+        "evidence": "research/p104-literal-slot-defect/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "88666f1dee93fbd85b31fd5d6f91a219e111b5f4",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4136: uniform commutation gap",
+        "evidence": "research/p104-uniform-commutation-gap/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "281ce601a8be9db470de630759179c23e1dfaa88",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4140: uniform encoding gap",
+        "evidence": "research/p104-uniform-encoding-gap/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "de25c6525aa866962309df5d107b32d55e6e5628",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4153: source-chart shortcut exhausts its optimistic allowance",
+        "evidence": "research/p104-source-chart-shortcut/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "9123241fea53df77e51ffe30d9aca1625d4bf3a8",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4154: fiber-tag seam mismatch",
+        "evidence": "research/p104-fiber-tag-seam/README.md",
+        "remaining": "Independently validate the stated scope or change its producer/consumer premise and pay the complete boundary.",
+        "status": "author-checked",
+        "source_commit": "4ffcdaee5d6255a9cea1fe53a5424435068089d0",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      }
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "Independently validate #4154's fiber-tag seam claims from #3966's labels and corrections and #3954's witness lines, in the sources' orientation.",
+  "scope_change_reason": "The card lists #4154 as needing independent validation of its stated scope; this does that and no new channel.",
+  "bottleneck_link": "#4154's helper-mismatch conclusion feeds the P104 side-correction channel; it must hold in the sources' convention before later work builds on it.",
+  "budget_minutes": 30,
+  "stop_rule": "Stop once every #4154 claim is confirmed or corrected in the source orientation.",
+  "outcome": "completed",
+  "evidence": "verify.py: labels equal #3966's source array; census 10,816 pairs, 0 full-address agreements, shared line 5,440/5,376, min Hamming 6 at labels 4 and 32, witness Hamming 20; in #3966's orientation the witness flips are (1,0), the uniform tag matches the row tag on the shared line, cell (2,1)=bit 19 separates; the helper match depends on the row label's class; the transposed control reproduces #4154's 0/1, helper mismatch and bit 11.",
+  "author": "Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance",
+  "ai_assistance": "Substantial Claude Code (Claude Opus 5.5) assistance in reading, verifier implementation and writing; no independent human or proof-kernel review.",
+  "open_questions": [
+    {
+      "question": "Restate #4154's open question 2 for the full address alone.",
+      "why_it_matters": "In the source orientation the uniform tag already agrees with the witness row tag on the shared line.",
+      "first_step": "Rewrite the question without the shared-line premise.",
+      "blocked_by": "None."
+    }
+  ]
+}
diff --git a/research/p104-fiber-tag-orientation-check/VERIFY.json b/research/p104-fiber-tag-orientation-check/VERIFY.json
@@ -0,0 +1,25 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/p104-fiber-tag-seam/README.md",
+    "research/p104-fiber-tag-seam/verify.py",
+    "research/p104-phase-uniform-gauge/PROOF.md",
+    "research/p104-phase-uniform-gauge/source/RESULT.json",
+    "research/p104-two-axis-compatibility/PROOF.md",
+    "research/p104-two-axis-compatibility/RESULT.json"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Pinned #3966 source RESULT.json and #4154 labels; #3966 correction text; #3954 witness lines decoded as 386(x)386 and 405(x)386; gauge facts on F2^9; orientation-free census; witness in source orientation; row-label helper rule; transposed control reproducing #4154's numbers; #4154 code line."
+    }
+  ]
+}