Record the P104 fiber-tag mismatch on one row/column pair.

research/p104-fiber-tag-seam/README.md

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+# P104 fiber-tag seam on one row/column pair
+
+**Finite obstruction; no new supplier and no κ.** On the 104 published P104
+labels, the phase-uniform row tag `z ⊗ q_j` and column tag `r_i ⊗ z` are never
+the same 81-bit translation. A mixed weight-class pair also disagrees on the
+one-dimensional shared line. The published witness `(386, 405)` is such a pair.
+Selected conditional κ stays `0.001672660197076918`.
+
+## Scope and evidence
+
+Original card: `p104-side-correction`, scope **refined**. The card allows one
+chronological cut or one hosting obstruction. Discussion #1166 comment 19034676
+asks for one actual row/column pair and a reconciliation of the fiber-dependent
+tags `z ⊗ q_j` and `r_i ⊗ z` on shared owners. This package does that comparison
+for every ordered pair of the retained labels, and pins the witness already
+named by PR #3954. It does not build a caller, clear the inherited excess
+44,096, or admit a physical owner.
+
+The labels are `physical_labels` from the `RESULT.json` exported by PR #3966
+at `3e2d70630fde46847c8938564576d78da48d101d`, origin PR #3954 head
+`f1e2839819959cd0534d008be91ed5b79ec55a6a`. That file's SHA-256 is
+`ce05a27ebc98677bec4febaa488fa03f5b6fc60216aa43b34298444d12f7ab6c`. It is not a
+Git object on this base. `labels.json` is the vendored array; `verify.py`
+checks its SHA-256
+`7227a7d6bdb49f36b6e401478034cc542eb887979890c8deda924b8ac0844209`.
+
+### Conventions
+
+`z = 420`, support `{2, 5, 7, 8}`. `O x = x + (x · z) z`. Bit `9α+β` of
+`u ⊗ v` is `u_α v_β`. The row image is `q_j = O p_j` and the column image is
+`r_i = O p_i`. The row tag is `z ⊗ q_j`. The column tag is `r_i ⊗ z`. The
+shared line is `span(r_i ⊗ q_j)`, read by the dot product with that vector.
+The uniform completion tag is `a = z ⊗ 511 + 511 ⊗ z`.
+
+### Proof
+
+`z · z = 0` and `wt(z) = 4`, so `O` is an orthogonal involution and `Oz = z`.
+Hence `z · (O p) = z · p`. The checker tests the involution, the orthogonality
+identity, and `q(Ox) = q(x) + 2(x · z) (mod 4)` on all of `F_2^9`.
+
+Every retained label is odd, 56 of weight class 1 and 48 of class 3. Every
+image has weight class 3, so every image is odd, and none equals `z`. The
+weight law then forces `z · p = 1` exactly on class 1.
+
+**Full address.** Summing a matrix over its second index in `F_2`:
+
+- the row tag contributes `z_α (q · 1) = z_α`, because `q` is odd;
+- the column tag contributes `r_α (z · 1) = 0`, because `z` is even.
+
+`z ≠ 0`, so the tags differ for every odd `q` and every `r`. All 10,816
+ordered pairs therefore have distinct full-address translations. The oddness
+hypothesis is necessary: both tags are zero when `q = r = 0`.
+
+**Shared line.** Both images are odd, so `b = r ⊗ q` satisfies `b · b = 1`.
+The two tags flip that line by `z · r = z · p_i` and `z · q = z · p_j`. The
+flips agree if and only if the labels have the same weight class. That is
+5,440 ordered pairs. The other 5,376 disagree.
+
+**Uniform helper.** Write `a = z ⊗ 511 + 511 ⊗ z`. Its column sum, summing
+the first factor, is `z`. The column sum of a row tag `z ⊗ q` is `0` because
+`z` is even, so `a` is never a row tag. Its row sum, summing the second
+factor, is also `z`. The row sum of a column tag `r ⊗ z` is `0`, so `a` is
+never a column tag either. On the shared line, `a` matches the row tag exactly
+when the column label is class 3.
+
+**Distance.** The minimum Hamming distance between a row tag and a column tag
+is 6, attained only by the ordered pairs of labels `32` and `4` (list indices
+19 and 75, both class 1, images 388 and 416). Even the two diagonal pairs
+differ. No shared-line agreement is a full-address agreement.
+
+### Pinned witness
+
+PR #3954's witness names `p_row = 386` and `p_donor = 405`. In
+`physical_labels` those are indices 0 and 8. The field `donor_port = 2` is not
+an index into that list.
+
+| | row 386 | column 405 |
+|---|---:|---:|
+| weight class mod 4 | 3 | 1 |
+| image under `O` | 386 | 49 |
+| shared-line flip | 0 | 1 |
+| Hamming distance of the tags | 20 | |
+| separating coordinate | bit 11, which is `(α, β) = (1, 2)` | |
+
+`χ` at that bit takes values `+1` and `-1` on the two translations, so they
+differ as operators on arbitrary functions. The uniform tag flips the same
+shared line and the row tag does not, so a helper carrying `a` does not match
+this row owner.
+
+## What this does not establish
+
+Nothing here clears the scaffold excess 44,096 from PR #3966, which already
+grants every gauge and tag for free. Same-class pairs still need a correction
+on at least six address bits before the full translations agree. Native
+routing, owners, dirty return, precision, and a changed favorable bill are
+open. This is not a multiplication theorem.
+
+## Reproduce
+
+From the repository root, CPython 3.12, standard library only:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-fiber-tag-seam --check-only
+python3.12 -B scripts/research_package.py --package research/p104-fiber-tag-seam
+python3.12 -B research/p104-fiber-tag-seam/verify.py
+```
+
+Expected marker:
+
+```text
+PASS_P104_FIBER_TAG_SEAM pairs=10816 full_equal=0 mixed_shared_disagree=5376 same_shared_agree=5440 min_hamming=6 witness=386/405 shared_flips=0/1 ham=20 helper_disagrees_on_witness=true no_new_kappa
+```
+
+The same command under `-O` is registered. A forced claim that the witness tags
+are equal is rejected. The zero-vector pair shows that an even image can agree.
+
+`python3 -B scripts/research_baseline.py` returned
+`PASS_RESEARCH_BASELINE_BINDINGS_ONLY`. That check binds the selected record.
+It is not this certificate.
+
+Not run: the PR #3954 and PR #3966 executables, Lean, Docker, and the selected
+cold replay.
+
+## Open next questions
+
+1. For one same-class pair, such as label 32 against itself, can a paid
+   correction of the six disagreeing bits be hosted without repaying the
+   inherited excess 44,096? The shared line already agrees, so only the
+   complementary address bits are in play. Blocked by a physical owner and a
+   changed bill; the free-tag scaffold is still over capacity.
+2. Does any non-orthogonal address change make the witness pair `(386, 405)`
+   share one translation on both the full address and the helper tag `a`?
+   This orthogonal gauge cannot. A different gauge needs its own defect
+   calculation before it is treated as a caller.
+
+## Credit
+
+Chris R / Clear1nsight for PR #3954 and PR #3966, including the labels, the
+witness, the gauge `z = 420`, and the open fiber-tag question. The orthogonal
+gauge and the uniform tag `a` are theirs. The comparison of `z ⊗ q_j` with
+`r_i ⊗ z` on these labels is new.
+
+Prepared by unpaidmoon with substantial Cursor Grok assistance. No independent
+human or formal-kernel review is claimed. New work is Apache-2.0.

research/p104-fiber-tag-seam/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f",
+  "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"
+    }
+  ]
+}

research/p104-fiber-tag-seam/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "p104-side-correction",
+  "priority_revision": 6,
+  "base_commit": "bb4bccbf42844d2801487450727c2f63e10d1d0f",
+  "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": "One chronological row/column pair of the 104 published P104 labels: the fiber tags z\u2297q_j and r_i\u2297z never agree as 81-bit translations, and they disagree on the shared line exactly for mixed weight classes. The published witness is (386, 405).",
+  "scope_change_reason": "Handoff comment 19034676 asks for one row/column pair and a reconciliation of the fiber-dependent tags. The card's chronological correction program is not constructed; this is the tag obstruction at that cut.",
+  "bottleneck_link": "A side-correction caller that reuses one translation on a shared row/column owner cannot use these phase-uniform fiber tags. The inherited scaffold excess 44096 remains, so the obstruction stops this gauge rather than improving kappa.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop after every ordered pair of the 104 labels and the one published witness. Do not search another gauge or price a correction of the six-bit minimum while the free-tag scaffold stays over capacity.",
+  "outcome": "negative-result",
+  "evidence": "README states the marginal-sum proof. verify.py checks O on all 512 vectors and all 10816 pairs, including shared-line flips, Hamming distance, the witness character at bit 11, and the uniform helper tag.",
+  "author": "unpaidmoon",
+  "ai_assistance": "Substantial Cursor Grok assistance in the proof, checker, and write-up. Not independent human or formal-kernel review.",
+  "open_questions": [
+    {
+      "question": "Can a paid correction of the six disagreeing bits on a same-class pair, such as label 32 against itself, be hosted without repaying the inherited excess 44096?",
+      "why_it_matters": "Same-class pairs already agree on the shared line, so only the complementary address bits block one common translation.",
+      "first_step": "Freeze label 32, list the six bits where z\u2297388 differs from 388\u2297z, and price one owner that sees those bits against the unchanged scaffold capacity.",
+      "blocked_by": "No physical owner model is fixed here, and PR #3966 already rejects the scaffold when every tag is free."
+    },
+    {
+      "question": "Does a non-orthogonal address change make the witness pair (386, 405) share one translation on the full address and on the helper tag a?",
+      "why_it_matters": "The orthogonal phase-uniform gauge cannot reconcile this mixed-class pair, but the handoff still allows a different encoding.",
+      "first_step": "Name one address map other than O\u2297O and recompute both fiber tags and a on labels 386 and 405.",
+      "blocked_by": "Any new defect has to be derived before the map is treated as a caller. This package does not supply one."
+    }
+  ]
+}

research/p104-fiber-tag-seam/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [],
+  "commands": [
+    {
+      "argv": ["{python}", "-B", "{package}/verify.py"],
+      "timeout_seconds": 120,
+      "checks": "All 512 gauge vectors, all 10816 label pairs, the pinned witness 386/405, and the even-image control"
+    },
+    {
+      "argv": ["{python}", "-O", "-B", "{package}/verify.py"],
+      "timeout_seconds": 120,
+      "checks": "Same certificate with assertions removed, so the explicit exceptions still fire"
+    }
+  ]
+}

research/p104-fiber-tag-seam/labels.json

@@ -0,0 +1 @@
+[386,391,431,426,127,122,82,87,405,445,440,351,304,290,295,309,346,357,31,32,79,93,88,74,37,26,224,223,176,162,167,181,218,229,261,494,385,406,446,425,454,468,289,310,345,331,358,372,283,94,73,38,52,25,11,100,115,134,148,251,236,196,211,188,174,161,182,217,203,230,244,155,140,121,107,4,19,59,44,67,81,262,276,379,324,339,316,302,475,460,419,433,398,481,502,301,434,397,482,501,487,392,439,296]