diff --git a/research/seed48-p120-orthogonal-shared-total/CLAIM.json b/research/seed48-p120-orthogonal-shared-total/CLAIM.json
new file mode 100644
index 0000000000..92ee99bb17
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/CLAIM.json
@@ -0,0 +1,44 @@
+{
+  "assignment_seed": 48,
+  "track": "structural decoder research",
+  "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "coordination": "No pinned sprint coordination issue was found; claim recorded locally. Refreshed overlap at 2026-10-13T23:43:55Z covered 847 open PRs and 94 discussions, complete pagination, no warnings. PR #1366 is the predecessor for one odd-pair pencil (e=L51,d0=L1). No claim for the seed-selected orthogonal pair e=L48,d0=L91 was found.",
+  "scope": "For the full P120 E8 root set and labels, set e=L_48 and choose d0=L_91 as the seed-selected 49th entry (zero-based index 48) of the sorted 63 orthogonal roots. Enumerate every target/nonzero F2^9 sink row in the calibrated one-row family, then every distinct-target pair with one shared d0 correction total.",
+  "changed_restriction": "Change the fixed relative geometry from PR #1366's odd pair <L_51,L_1>=2 to an orthogonal pair <L_48,L_91>=0, and use a separately implemented exact enumerator.",
+  "method": "Reconstruct the pinned root/label certificate independently; enumerate rows with exact Fraction arithmetic and bitset label supports; filter consistent rational calibrators and nonzero diagonals; test total availability, cross-target diagonal effects, and all row equations for every distinct-target pair.",
+  "optimistic_cost": "One rank-one shared total plus eight rank-eight coordinate totals costs 65 COPY-rank units in the complete local unit. This is seven below the P120 all-pairs floor 72, before claiming any full supplier or recursive improvement.",
+  "expected_deliverable": "A source-pinned research package with the independent exact P120 orthogonal-pencil census, proof of the pair obstruction or a fully checked exact witness, the P112 C.6 positive control, and mutation controls.",
+  "stop_rule": "Exhaust all 120 targets x 511 nonzero labels and all distinct-target pairs in the stated filtered family; stop after the exact census, control replays, and one final package check. Do not search other e,d0 geometries.",
+  "expected_finish_utc": "2026-10-14T00:15:00Z",
+  "preliminary_replay": "Using the predecessor's verifier functions as triage only for e=48,d0=91 found 65 nodes, 2,048 distinct-target pairs, 1,056 shared-total-available pairs, and zero exact pairs. Independent replay remains outstanding.",
+  "candidate_tasks": [
+    {
+      "task": "Orthogonal P120 pencil e=L48,d0=L91 with one shared total",
+      "decision": "chosen",
+      "reason": "This changes the root-pair geometry from the completed PR #1366 odd-pair case and has a fully priced local upside: 65 versus the 72-copy all-pairs P120 floor. The finite row/pair domain is small enough to exhaust exactly."
+    },
+    {
+      "task": "Global rank-eight masked rigidity on the P104 class of size 28",
+      "decision": "rejected",
+      "reason": "PR #1292 establishes only local rigidity and leaves this global question open, but classifying distant components is broader than the bounded session and the complete copy bill for a candidate component is not yet favorable."
+    },
+    {
+      "task": "Rank-nine single odd-entry completion on P104",
+      "decision": "rejected",
+      "reason": "The active claim #1360 studies arbitrary rank-nine factorizations of the corresponding P112 one-entry completion; PR #1320 and PR #1331 cover nearby P112 co-star and free-rectangle cases. This is too close to the active one-entry overcomplete line for this seed."
+    }
+  ],
+  "predecessors": [
+    "PR #1366 / discussion result: calibrated two-target diagonal obstruction for P120 e=L51,d0=L1, plus P112 C.6 positive control.",
+    "PR #968: P120 all-pairs copy-rank floor 72 and P104 frame-pair geometry.",
+    "PR #1292: local masked P104 rank-eight rigidity; global off-orbit cases remain open."
+  ],
+  "result": {
+    "status": "completed negative result",
+    "completed_utc": "2026-10-13T23:54:12Z",
+    "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/1386",
+    "package_commit": "41f06d17bd5693bcd7529eed18f96cae06f3e647",
+    "finding": "For the seed-selected orthogonal P120 pencil e=L48,d0=L91, every one of 1,056 shared-total-available calibrated row pairs cancels at least one target diagonal; the exact pair count is zero.",
+    "verification": "Independent exact replay passed, including PR1366 odd-pair regression, full P112 C.6 positive unit, total-source deletion control, label mutation control, source pins, and package metadata."
+  }
+}
diff --git a/research/seed48-p120-orthogonal-shared-total/LICENSE b/research/seed48-p120-orthogonal-shared-total/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/LICENSE
@@ -0,0 +1,201 @@
+                                 Apache License
+                           Version 2.0, January 2004
+                        http://www.apache.org/licenses/
+
+   TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+   1. Definitions.
+
+      "License" shall mean the terms and conditions for use, reproduction,
+      and distribution as defined by Sections 1 through 9 of this document.
+
+      "Licensor" shall mean the copyright owner or entity authorized by
+      the copyright owner that is granting the License.
+
+      "Legal Entity" shall mean the union of the acting entity and all
+      other entities that control, are controlled by, or are under common
+      control with that entity. For the purposes of this definition,
+      "control" means (i) the power, direct or indirect, to cause the
+      direction or management of such entity, whether by contract or
+      otherwise, or (ii) ownership of fifty percent (50%) or more of the
+      outstanding shares, or (iii) beneficial ownership of such entity.
+
+      "You" (or "Your") shall mean an individual or Legal Entity
+      exercising permissions granted by this License.
+
+      "Source" form shall mean the preferred form for making modifications,
+      including but not limited to software source code, documentation
+      source, and configuration files.
+
+      "Object" form shall mean any form resulting from mechanical
+      transformation or translation of a Source form, including but
+      not limited to compiled object code, generated documentation,
+      and conversions to other media types.
+
+      "Work" shall mean the work of authorship, whether in Source or
+      Object form, made available under the License, as indicated by a
+      copyright notice that is included in or attached to the work
+      (an example is provided in the Appendix below).
+
+      "Derivative Works" shall mean any work, whether in Source or Object
+      form, that is based on (or derived from) the Work and for which the
+      editorial revisions, annotations, elaborations, or other modifications
+      represent, as a whole, an original work of authorship. For the purposes
+      of this License, Derivative Works shall not include works that remain
+      separable from, or merely link (or bind by name) to the interfaces of,
+      the Work and Derivative Works thereof.
+
+      "Contribution" shall mean any work of authorship, including
+      the original version of the Work and any modifications or additions
+      to that Work or Derivative Works thereof, that is intentionally
+      submitted to Licensor for inclusion in the Work by the copyright owner
+      or by an individual or Legal Entity authorized to submit on behalf of
+      the copyright owner. For the purposes of this definition, "submitted"
+      means any form of electronic, verbal, or written communication sent
+      to the Licensor or its representatives, including but not limited to
+      communication on electronic mailing lists, source code control systems,
+      and issue tracking systems that are managed by, or on behalf of, the
+      Licensor for the purpose of discussing and improving the Work, but
+      excluding communication that is conspicuously marked or otherwise
+      designated in writing by the copyright owner as "Not a Contribution."
+
+      "Contributor" shall mean Licensor and any individual or Legal Entity
+      on behalf of whom a Contribution has been received by Licensor and
+      subsequently incorporated within the Work.
+
+   2. Grant of Copyright License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      copyright license to reproduce, prepare Derivative Works of,
+      publicly display, publicly perform, sublicense, and distribute the
+      Work and such Derivative Works in Source or Object form.
+
+   3. Grant of Patent License. Subject to the terms and conditions of
+      this License, each Contributor hereby grants to You a perpetual,
+      worldwide, non-exclusive, no-charge, royalty-free, irrevocable
+      (except as stated in this section) patent license to make, have made,
+      use, offer to sell, sell, import, and otherwise transfer the Work,
+      where such license applies only to those patent claims licensable
+      by such Contributor that are necessarily infringed by their
+      Contribution(s) alone or by combination of their Contribution(s)
+      with the Work to which such Contribution(s) was submitted. If You
+      institute patent litigation against any entity (including a
+      cross-claim or counterclaim in a lawsuit) alleging that the Work
+      or a Contribution incorporated within the Work constitutes direct
+      or contributory patent infringement, then any patent licenses
+      granted to You under this License for that Work shall terminate
+      as of the date such litigation is filed.
+
+   4. Redistribution. You may reproduce and distribute copies of the
+      Work or Derivative Works thereof in any medium, with or without
+      modifications, and in Source or Object form, provided that You
+      meet the following conditions:
+
+      (a) You must give any other recipients of the Work or
+          Derivative Works a copy of this License; and
+
+      (b) You must cause any modified files to carry prominent notices
+          stating that You changed the files; and
+
+      (c) You must retain, in the Source form of any Derivative Works
+          that You distribute, all copyright, patent, trademark, and
+          attribution notices from the Source form of the Work,
+          excluding those notices that do not pertain to any part of
+          the Derivative Works; and
+
+      (d) If the Work includes a "NOTICE" text file as part of its
+          distribution, then any Derivative Works that You distribute must
+          include a readable copy of the attribution notices contained
+          within such NOTICE file, excluding those notices that do not
+          pertain to any part of the Derivative Works, in at least one
+          of the following places: within a NOTICE text file distributed
+          as part of the Derivative Works; within the Source form or
+          documentation, if provided along with the Derivative Works; or,
+          within a display generated by the Derivative Works, if and
+          wherever such third-party notices normally appear. The contents
+          of the NOTICE file are for informational purposes only and
+          do not modify the License. You may add Your own attribution
+          notices within Derivative Works that You distribute, alongside
+          or as an addendum to the NOTICE text from the Work, provided
+          that such additional attribution notices cannot be construed
+          as modifying the License.
+
+      You may add Your own copyright statement to Your modifications and
+      may provide additional or different license terms and conditions
+      for use, reproduction, or distribution of Your modifications, or
+      for any such Derivative Works as a whole, provided Your use,
+      reproduction, and distribution of the Work otherwise complies with
+      the conditions stated in this License.
+
+   5. Submission of Contributions. Unless You explicitly state otherwise,
+      any Contribution intentionally submitted for inclusion in the Work
+      by You to the Licensor shall be under the terms and conditions of
+      this License, without any additional terms or conditions.
+      Notwithstanding the above, nothing herein shall supersede or modify
+      the terms of any separate license agreement you may have executed
+      with Licensor regarding such Contributions.
+
+   6. Trademarks. This License does not grant permission to use the trade
+      names, trademarks, service marks, or product names of the Licensor,
+      except as required for reasonable and customary use in describing the
+      origin of the Work and reproducing the content of the NOTICE file.
+
+   7. Disclaimer of Warranty. Unless required by applicable law or
+      agreed to in writing, Licensor provides the Work (and each
+      Contributor provides its Contributions) on an "AS IS" BASIS,
+      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or
+      implied, including, without limitation, any warranties or conditions
+      of TITLE, NON-INFRINGEMENT, MERCHANTABILITY, or FITNESS FOR A
+      PARTICULAR PURPOSE. You are solely responsible for determining the
+      appropriateness of using or redistributing the Work and assume any
+      risks associated with Your exercise of permissions under this License.
+
+   8. Limitation of Liability. In no event and under no legal theory,
+      whether in tort (including negligence), contract, or otherwise,
+      unless required by applicable law (such as deliberate and grossly
+      negligent acts) or agreed to in writing, shall any Contributor be
+      liable to You for damages, including any direct, indirect, special,
+      incidental, or consequential damages of any character arising as a
+      result of this License or out of the use or inability to use the
+      Work (including but not limited to damages for loss of goodwill,
+      work stoppage, computer failure or malfunction, or any and all
+      other commercial damages or losses), even if such Contributor
+      has been advised of the possibility of such damages.
+
+   9. Accepting Warranty or Additional Liability. While redistributing
+      the Work or Derivative Works thereof, You may choose to offer,
+      and charge a fee for, acceptance of support, warranty, indemnity,
+      or other liability obligations and/or rights consistent with this
+      License. However, in accepting such obligations, You may act only
+      on Your own behalf and on Your sole responsibility, not on behalf
+      of any other Contributor, and only if You agree to indemnify,
+      defend, and hold each Contributor harmless for any liability
+      incurred by, or claims asserted against, such Contributor by reason
+      of your accepting any such warranty or additional liability.
+
+   END OF TERMS AND CONDITIONS
+
+   APPENDIX: How to apply the Apache License to your work.
+
+      To apply the Apache License to your work, attach the following
+      boilerplate notice, with the fields enclosed by brackets "[]"
+      replaced with your own identifying information. (Don't include
+      the brackets!)  The text should be enclosed in the appropriate
+      comment syntax for the file format. We also recommend that a
+      file or class name and description of purpose be included on the
+      same "printed page" as the copyright notice for easier
+      identification within third-party archives.
+
+   Copyright [yyyy] [name of copyright owner]
+
+   Licensed under the Apache License, Version 2.0 (the "License");
+   you may not use this file except in compliance with the License.
+   You may obtain a copy of the License at
+
+       http://www.apache.org/licenses/LICENSE-2.0
+
+   Unless required by applicable law or agreed to in writing, software
+   distributed under the License is distributed on an "AS IS" BASIS,
+   WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+   See the License for the specific language governing permissions and
+   limitations under the License.
diff --git a/research/seed48-p120-orthogonal-shared-total/NOTICE.md b/research/seed48-p120-orthogonal-shared-total/NOTICE.md
new file mode 100644
index 0000000000..cd22d6b3c2
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/NOTICE.md
@@ -0,0 +1,9 @@
+`vendor/seed51/certificate.tsv` is copied from
+`CrocSwap/integer-mult-bounds` commit
+`21046cb8fa0d4f0e9b2f826ba71e01baaf9be02c`, the P120 root/label table used in
+PR #1366. Its Git blob and SHA-256 are recorded in `SOURCES.json`. The source
+contributor is Cinna Davis. The repository license and retained attribution
+apply; this new package is under Apache-2.0.
+
+Contributor: 1337isnot1337. Prepared with substantial OpenAI Codex assistance;
+no independent human review is claimed.
diff --git a/research/seed48-p120-orthogonal-shared-total/PROOF.md b/research/seed48-p120-orthogonal-shared-total/PROOF.md
new file mode 100644
index 0000000000..f8191af861
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/PROOF.md
@@ -0,0 +1,101 @@
+# Exact obstruction for the seed-selected orthogonal pencil
+
+## Fixed certificate and pencil
+
+The input is the source-pinned 120-row root/label table from PR #1366. The
+checker verifies 120 distinct integer roots of squared norm four, integral
+half-Gram entries in `{-1,0,1,2}`, diagonal Gram value two, and all 14,400
+label-pair identities
+
+\[
+  u_s\cdot u_t = 1 + G_{st}\pmod 2,\qquad G_{st}=\langle L_s,L_t\rangle/2.
+\]
+
+Set `e=L_48`. There are 63 indices `j` with `j != 48` and
+`<L_48,L_j>=0`. Sorting those source indices and taking index `48 mod 63`
+selects `d0=L_91`. The computed inner product is zero.
+
+For each port `s`, define the exact integers
+
+\[
+  p_e(s)=\langle L_s,e\rangle,\qquad
+  p_d(s)=\langle L_s,d0\rangle.
+\]
+
+## Row and total conditions
+
+For target `t` and nonzero sink word `w` in `F_2^9`, let
+
+\[
+  Z(t,w)=\{s:u_s\cdot w=1\pmod2\}.
+\]
+
+Keep rows with `t in Z(t,w)` and `w != u_t`. A calibrated row has one nonempty
+set of rational ratios
+
+\[
+  \left\{-p_d(s)/p_e(s): s\in Z(t,w),\ s\ne t,\ p_e(s)\ne0\right\}.
+\]
+
+Call its unique value `mu_t`, and require the uncorrected target diagonal
+`p_d(t)+mu_t p_e(t)` to be nonzero. The off-target coefficients that the
+`d0`-direction total must cancel are
+
+\[
+  E(t,w)=\{s\in Z(t,w):s\ne t,\ p_e(s)=0,\ p_d(s)\ne0\}.
+\]
+
+For two rows `a=(t_a,w_a)` and `b=(t_b,w_b)`, the single total has source set
+`Q=E_a union E_b`. It can be read at both sinks exactly when
+`E_a subset Z_b` and `E_b subset Z_a`. The modified row coefficient is
+
+\[
+  N_t(s)=p_d(s)+\mu_t p_e(s)-p_d(s)\,\mathbf 1_{s\in Q}.
+\]
+
+If `t_a in E_b`, then by definition `p_e(t_a)=0` and `p_d(t_a) != 0`; also
+`t_a in Q`. Hence
+
+\[
+  N_{t_a}(t_a)=p_d(t_a)+\mu_a\cdot0-p_d(t_a)=0,
+\]
+
+which violates the nonzero target-diagonal requirement. The same implication
+holds with `a` and `b` exchanged. Thus every available shared-total pair must
+avoid both cross-target memberships to be exact.
+
+## Complete finite census
+
+The checker tests all `120 * 511 = 61,320` target/word pairs and uses exact
+`Fraction` ratios. It finds:
+
+| Stage | Count |
+|---|---:|
+| Rows with target in sink support and nonbaseline sink word | 30,600 |
+| Rows with one nonempty rational calibrator | 190 |
+| Rows whose pre-total target diagonal is nonzero | 65 |
+| Distinct-target pairs among those rows | 2,048 |
+| Pairs for which the union total is available at both sinks | 1,056 |
+| Available pairs with both targets contaminated | 1,024 |
+| Available pairs with exactly one target contaminated | 32 |
+| Available pairs with no target contaminated | 0 |
+| Exact pairs | 0 |
+
+The script checks the source/target equations for every available pair in
+addition to the diagonal obstruction. Therefore the negative result is exact
+for this finite calibrated one-total family; it is not inferred from sampling.
+
+## Controls and boundaries
+
+The same implementation replays PR #1366's `e=L_51`, `d0=L_1` control: 27
+rows, 351 available pairs, all 351 with both target diagonals contaminated.
+It also finds the published P112 C.6 positive control (`e=L_0`, `d0=L_76`):
+targets 75 and 76, sink words 329 and 438, and a 24-source shared total. The
+checker verifies the full 112-by-112 unit and confirms that deleting one
+required total source breaks it. A mutated label is rejected by the pairing
+identity check.
+
+The result does not cover uncalibrated rows, other total vectors or scalars,
+more than one total, another orthogonal pair, rank-nine factorizations, other
+punctures, or the full complex supplier. The selected conditional κ remains
+unchanged.
diff --git a/research/seed48-p120-orthogonal-shared-total/README.md b/research/seed48-p120-orthogonal-shared-total/README.md
new file mode 100644
index 0000000000..c388e87979
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/README.md
@@ -0,0 +1,77 @@
+# Orthogonal P120 pencil: one shared total still loses a target diagonal
+
+**Status: scoped negative result. No exact decoder, supplier, or new κ is
+claimed.** This seed changes the relative root geometry in the calibrated
+two-target shared-total experiment of [PR #1366](https://github.com/CrocSwap/integer-mult-bounds/pull/1366).
+
+## Finding
+
+Using the pinned P120 root/label certificate, seed 48 selects `e = L_48` and
+`d0 = L_91`: `d0` is item 49 (zero-based index 48) in the sorted list of 63
+roots orthogonal to `e`. Thus `<e,d0> = 0`, while PR #1366's fixed pencil has
+`<L_51,L_1> = 2`.
+
+The exact census finds 65 calibrated, nonzero-diagonal row candidates and
+2,048 distinct-target pairs. Of those, 1,056 can read the union correction
+total at both sinks. Every available pair includes at least one target in the
+other row's correction set: 1,024 contaminate both target diagonals and 32
+contaminate one. That diagonal is then exactly zero. No pair in this finite
+family is an exact decoder.
+
+The geometry change matters because a successful pair would use one rank-one
+shared total plus eight rank-eight coordinate totals, an optimistic local bill
+of 65 COPY-rank units against the P120 all-pairs floor of 72. The census finds
+no such unit. This does not bound other orthogonal pencils, uncalibrated rows,
+different total directions, or multiple totals, and it does not change the
+selected κ.
+
+## Reproduce
+
+From the repository root, using Python 3.12+ and the standard library:
+
+```sh
+python3 -I -B research/seed48-p120-orthogonal-shared-total/verify.py
+```
+
+Expected final marker:
+
+```text
+PASS_P120_ORTHOGONAL_SHARED_TOTAL: no exact pair in the complete calibrated one-total family; no new kappa
+```
+
+The checker validates the pinned root, Gram, and label data; derives the
+seed-selected orthogonal pencil; exhausts all 120 targets and 511 nonzero
+sink labels; and checks every eligible pair exactly. It also replays PR #1366's
+odd-pair obstruction, the P112 C.6 exact positive control, and two negative
+controls. See [PROOF.md](PROOF.md) for the diagonal argument and scope.
+
+## Scope
+
+- **This pencil only.** The result is for `e=L_48`, `d0=L_91`, the 120-port
+  certificate, rows with one consistent nonempty rational calibrator, and a
+  single shared correction total equal to the `d0` direction.
+- **No complete supplier claim.** The 65-unit figure is only the favorable
+  local COPY bill that this family would have if an exact pair existed. No
+  pair exists here, and no recursive profile or κ is derived.
+
+## Open next questions
+
+- **Next question:** does any other orthogonal P120 pencil avoid the
+  cross-target diagonal obstruction? A first step is to orbit-classify ordered
+  orthogonal pairs under the E8 stabilizer, then replay one representative per
+  class. The blocker is a certified orbit reduction and a complete cost
+  argument for any surviving pair.
+- **Next question:** can two distinct correction totals preserve both target
+  diagonals? A first step is to specify their coefficients and source sets and
+  derive the exact cost before searching. The blocker is a bound on the number
+  and copy rank of those totals.
+
+## Attribution
+
+The P120 root/label table and calibrated row model come from Cinna Davis's
+PR #1366 (seed 51). That result covered `e=L_51`, `d0=L_1` with odd inner
+product; this note changes to a seed-selected orthogonal pair and uses an
+independently written enumerator. Credit PR #968 for the E8 frame-pair geometry
+and copy-rank floor, and the `format-limits` C.6 review for the 65-unit
+two-target cost convention. This package was prepared with substantial
+OpenAI Codex assistance; no independent human review is claimed.
diff --git a/research/seed48-p120-orthogonal-shared-total/RESULT.json b/research/seed48-p120-orthogonal-shared-total/RESULT.json
new file mode 100644
index 0000000000..abf69e4c0f
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/RESULT.json
@@ -0,0 +1,41 @@
+{
+  "status": "scoped negative result",
+  "seed": 48,
+  "track": "structural decoder research",
+  "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "predecessor_commit": "21046cb8fa0d4f0e9b2f826ba71e01baaf9be02c",
+  "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/1386",
+  "object": {
+    "ports": 120,
+    "e_index": 48,
+    "d0_index": 91,
+    "inner_product": 0,
+    "orthogonal_candidates": 63,
+    "selection_rule": "sorted orthogonal root indices, index seed mod 63"
+  },
+  "domain": {
+    "targets": 120,
+    "nonzero_sink_words_per_target": 511,
+    "target_word_pairs_tested": 61320,
+    "distinct_target_pairs_after_row_filter": 2048,
+    "shared_total_available_pairs": 1056
+  },
+  "finding": {
+    "calibrated_nonzero_diagonal_rows": 65,
+    "pairs_with_both_target_diagonals_cancelled": 1024,
+    "pairs_with_one_target_diagonal_cancelled": 32,
+    "pairs_with_no_target_diagonal_cancelled": 0,
+    "exact_pairs": 0
+  },
+  "positive_control": "P112 C.6 full 112x112 unit: targets 75,76; sink words 329,438; shared total size 24.",
+  "negative_controls": [
+    "PR1366 odd-pair P120 regression reproduces 27 rows, 351 available pairs and 351 both-diagonal obstructions.",
+    "Removing one required source from the P112 shared total breaks exactness.",
+    "A mutated label fails the Gram-pairing identity."
+  ],
+  "limitations": [
+    "Only e=L48,d0=L91 and the calibrated one-total family are covered.",
+    "No exact decoder, complete supplier, recursive profile, or new kappa is claimed.",
+    "Other orthogonal pairs, uncalibrated rows, alternate totals and rank-nine factorizations remain open."
+  ]
+}
diff --git a/research/seed48-p120-orthogonal-shared-total/SOURCES.json b/research/seed48-p120-orthogonal-shared-total/SOURCES.json
new file mode 100644
index 0000000000..5baf72f736
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/SOURCES.json
@@ -0,0 +1,86 @@
+{
+  "schema_version": 1,
+  "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "files": [
+    {
+      "path": "CONTRIBUTING.md",
+      "usage": "provenance",
+      "git_blob": "e51435543687f1bd88ab22248082dc689ce8b853",
+      "sha256": "df5b5646602f42cb5da5844f04ac925182ddcd0f627b9de1c96a5095bb7a277a"
+    },
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
+      "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
+    },
+    {
+      "path": "docs/research/current-status.md",
+      "usage": "provenance",
+      "git_blob": "aa3cf49715cd367ad8c4e63ab28856fc0d19794f",
+      "sha256": "1f59d648763c77d574d18dc59ea8bf62d2ee74aaed3c202c9c8cfa4f901badbd"
+    },
+    {
+      "path": "docs/research/pr-ledger.md",
+      "usage": "provenance",
+      "git_blob": "4331ba3175b3418f70fb5cf7ee9689b3505c0678",
+      "sha256": "8030b58f708e40aee4e40f950a20a0b0ccef3f92b08e6e089fe35db82ec027e6"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "c05fafaa25ba95b2d5af86b1800427198e3d20eb",
+      "sha256": "89b5928bc92c81e2647b6d702a7ad85a6795b8f44e2eb267b2ff3145d8f2b2ce"
+    },
+    {
+      "path": "docs/research/community-batch1099-review.md",
+      "usage": "provenance",
+      "git_blob": "6cb6ec061a071a06a2d18cd4dc3e9a2b05d28099",
+      "sha256": "7e76d2c38e5fce30587835b7251df1430488ae4dd372611ef69a3f03f476b6cb"
+    },
+    {
+      "path": "research/community-frontier1094-audit/SELECTED-SOURCE.json",
+      "usage": "provenance",
+      "git_blob": "6a75493790b4eff9c4a98051ef8b01d6aad0d5a8",
+      "sha256": "79b3de5db3dbcb9829789ba58e9e45758926031e2a7d80667a08429d369be53b"
+    },
+    {
+      "path": "research/community-frontier1094-audit/ASSEMBLY.json",
+      "usage": "provenance",
+      "git_blob": "5fd676df060f3b450782fdf5ff5f6beb63a5eeb0",
+      "sha256": "1122cb3a575f8c788345fc1bf4c108ac7c3250fb81a5988671f5eb04b3ab3045"
+    },
+    {
+      "path": "research/format-limits/README.md",
+      "usage": "provenance",
+      "git_blob": "2f7aaf5b8225717394fe6adda6b313026eaf8090",
+      "sha256": "0fa0d6b2df96ddc06b876c41c5fa8d2335b97f36bc8f17d1371296d23199c263"
+    },
+    {
+      "path": "research/complex-frame-pair-decoders/README.md",
+      "usage": "provenance",
+      "git_blob": "be5bbbee8e30a4ee39fa513896e8fc7e0bb3721e",
+      "sha256": "edd848b0177dc73a6e2646d4fd82f0b2ceae37e642bf19d6af602579a041a57e"
+    },
+    {
+      "path": "research/complex-frame-pair-decoders/PROOF.md",
+      "usage": "provenance",
+      "git_blob": "889f3a653ed1bdbb7df61ebe3af4f2103602a1f4",
+      "sha256": "ba53c1d8a9bc2d935d546bde46ca7341bd65f8515013e07b073296b4db2a9a74"
+    }
+  ],
+  "external_sources": [
+    {
+      "repository": "CrocSwap/integer-mult-bounds",
+      "commit": "21046cb8fa0d4f0e9b2f826ba71e01baaf9be02c",
+      "files": [
+        {
+          "source_path": "research/p120-calibrated-two-target-seed51/certificate.tsv",
+          "vendored_path": "research/seed48-p120-orthogonal-shared-total/vendor/seed51/certificate.tsv",
+          "git_blob": "38629ccf4b6e9bfa45e09488d66cc89aab577ad7",
+          "sha256": "61f903f72551d3aa8f70bc5774ee28d163fd72ca09a430e7403008ba269f2494"
+        }
+      ]
+    }
+  ]
+}
diff --git a/research/seed48-p120-orthogonal-shared-total/TASK.json b/research/seed48-p120-orthogonal-shared-total/TASK.json
new file mode 100644
index 0000000000..f425881203
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/TASK.json
@@ -0,0 +1,67 @@
+{
+  "schema_version": 1,
+  "task_id": "complex-masked-decoder",
+  "priority_revision": 2,
+  "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "original_card": {
+    "id": "complex-masked-decoder",
+    "question": "Can one specified masked or overcomplete decoder improve the complete moment budget?",
+    "starting_points": [
+      "research/complex-decoder-field-extension-seed44/README.md",
+      "research/complex-frame-pair-decoders/README.md"
+    ],
+    "methods": [
+      "Synthesize a decoder with exact coefficients and fully priced helper endpoints.",
+      "Bound the best possible budget for a fixed support alphabet before synthesis."
+    ],
+    "acceptance_gate": "Change an assumption of the eight-term all-pairs bound and count all copied information, frames and restoration.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "research/complex-decoder-field-extension-seed44/verify.py"
+      ],
+      "expected": "PASS_COMPLEX_DECODER_FIELD_EXTENSION_S44",
+      "inspect": "Locate the excluded classes: masked identities, at least nine terms, and deeper punctures.",
+      "scope": "Positive control / source-bound orientation only; this is not a new construction or full cold replay."
+    },
+    "first_experiment": "Choose one finite support alphabet and test exact decoding constraints before building a whole network.",
+    "bottleneck_link": "A cheaper fully realized decoder could increase deficit or lower recursive cost on the binding complex side.",
+    "allowed_variations": [
+      "Select a specific masked or overcomplete family with exact labels and supports."
+    ],
+    "scope_change_triggers": [
+      "Repeating the exact eight-term all-pairs search inside its proved scope."
+    ],
+    "overlap_terms": [
+      "masked decoder",
+      "overcomplete",
+      "eight-term"
+    ]
+  },
+  "scope_status": "refined",
+  "actual_scope": "For the full P120 root/label certificate, enumerate the calibrated one-row family and all distinct-target pairs for one shared d0-direction total at the seed-selected orthogonal pencil e=L48, d0=L91.",
+  "scope_change_reason": "The original complex-masked-decoder card asks for a specified masked family; this refinement changes the relative root geometry from PR1366\u2019s odd pair to one seed-selected orthogonal pair and fully exhausts that finite subfamily.",
+  "bottleneck_link": "An exact unit would have local COPY cost 65, seven below the P120 all-pairs floor 72. The exact negative result rules out that potential saving for this orthogonal pencil and total rule only.",
+  "budget_minutes": 60,
+  "stop_rule": "Exhaust all 120 targets and 511 nonzero sink words, then all distinct-target pairs in the calibrated one-total family; verify the PR1366 regression, P112 C.6 positive control and controls. Do not search other pencils or total rules.",
+  "outcome": "negative-result",
+  "evidence": "Independent exact enumeration finds 65 nonzero-diagonal calibrated rows and 2,048 distinct-target pairs. Of 1,056 pairs where the union total is available at both sinks, all have at least one cross-target diagonal cancellation (1,024 both, 32 one); exact pair count is zero. The P112 C.6 full-unit positive control and mutation controls pass.",
+  "author": "1337isnot1337",
+  "ai_assistance": "Substantial OpenAI Codex assistance in task scoping, exact enumeration, proof analysis and package preparation; no independent human review claimed.",
+  "open_questions": [
+    {
+      "question": "Does any other orthogonal P120 root-pair orbit admit an exact shared-total pair?",
+      "why_it_matters": "A surviving orbit could realize the 65-versus-72 local COPY opportunity not available in this seed-selected case.",
+      "first_step": "Classify ordered orthogonal root pairs under the E8 stabilizer and replay one representative per orbit.",
+      "blocked_by": "A checked orbit reduction and complete cost model for any surviving pair."
+    },
+    {
+      "question": "Can distinct correction totals preserve both target diagonals when one shared d0 total cannot?",
+      "why_it_matters": "Changing the number or direction of totals changes the current pairwise cross-target obstruction.",
+      "first_step": "Specify the totals, coefficients and sink source sets, then derive their exact copy-rank cost before enumerating.",
+      "blocked_by": "A favorable cost budget for the extra totals."
+    }
+  ],
+  "no_open_questions_reason": ""
+}
diff --git a/research/seed48-p120-orthogonal-shared-total/VALIDATION.json b/research/seed48-p120-orthogonal-shared-total/VALIDATION.json
new file mode 100644
index 0000000000..53f90052aa
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/VALIDATION.json
@@ -0,0 +1,31 @@
+{
+  "status": "passed locally; PR #1386 open; CI pending after the final claim update",
+  "base_commit": "bce54fb3f895cbe5cd4c0eb477c3afeed100190f",
+  "predecessor_commit": "21046cb8fa0d4f0e9b2f826ba71e01baaf9be02c",
+  "local_python": "3.14.7",
+  "manifest_python": "3.12",
+  "local_python_note": "Python 3.12 is not installed here. The standard-library verifier passed on Python 3.14.7; VERIFY.json registers the repository's Python 3.12 replay.",
+  "commands": [
+    "python3 -I -B research/seed48-p120-orthogonal-shared-total/verify.py",
+    "python3 scripts/research_package.py --package research/seed48-p120-orthogonal-shared-total --check-only"
+  ],
+  "expected_final_marker": "PASS_P120_ORTHOGONAL_SHARED_TOTAL: no exact pair in the complete calibrated one-total family; no new kappa",
+  "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/1386",
+  "results": [
+    "PASS_SOURCE_AND_E8_CERTIFICATE: roots=120 labels=F2^9 pairings=14400",
+    "PASS_P120_ORTHOGONAL_SHARED_TOTAL: 65 calibrated rows; 1,056 available pairs; 1,024 both-target and 32 one-target diagonal obstructions; zero exact pairs",
+    "PASS_PR1366_REGRESSION: odd-pair 27 rows, 351 available pairs, 351 both-diagonal obstructions",
+    "PASS_P112_C6_CONTROL: exact full 112x112 unit, targets 75/76, sink words 329/438, total size 24",
+    "PASS_NEGATIVE_CONTROLS: required-total-source removal and label mutation detected",
+    "PASS_PACKAGE_METADATA_AND_PINS (not a mathematical acceptance check)",
+    "PASS_ALL_PACKAGE_JSON"
+  ],
+  "overlap_refresh": {
+    "checked_at_utc": "2026-10-13T23:53:35Z",
+    "open_prs": 853,
+    "discussions": 100,
+    "pagination_complete": true,
+    "warnings": [],
+    "direct_overlap": "PR #1366 is the only direct shared-total result match; it covers the odd-pair predecessor e=L51,d0=L1. The other remote match was a routine start-here coordination comment. No orthogonal e=L48,d0=L91 claim was found. The active P112 rank-nine single-entry claim #1360 and PR #1320/#1323 remain adjacent but distinct scopes."
+  }
+}
diff --git a/research/seed48-p120-orthogonal-shared-total/VERIFY.json b/research/seed48-p120-orthogonal-shared-total/VERIFY.json
new file mode 100644
index 0000000000..47a77ed316
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/VERIFY.json
@@ -0,0 +1,21 @@
+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/seed48-p120-orthogonal-shared-total/vendor/seed51/certificate.tsv"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 300,
+      "checks": "Base and predecessor source hashes; all root/Gram/label data; the seed-selected orthogonal P120 census over 120x511 rows and all distinct-target pairs; PR1366 regression; P112 C.6 full-unit positive control; total-source and label-mutation negative controls."
+    }
+  ]
+}
diff --git a/research/seed48-p120-orthogonal-shared-total/vendor/seed51/certificate.tsv b/research/seed48-p120-orthogonal-shared-total/vendor/seed51/certificate.tsv
new file mode 100644
index 0000000000..38629ccf4b
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/vendor/seed51/certificate.tsv
@@ -0,0 +1,123 @@
+# schema=1
+#! seed=51 track=structural-decoder ports=P120 e_index=51 d0_index=1
+#! columns=index root8_csv label9_bits
+0	2,0,0,0,0,0,0,0	100000000
+1	0,2,0,0,0,0,0,0	111000000
+2	0,0,2,0,0,0,0,0	111110000
+3	0,0,0,2,0,0,0,0	100110000
+4	0,0,0,0,2,0,0,0	111111100
+5	0,0,0,0,0,2,0,0	100111100
+6	0,0,0,0,0,0,2,0	100001100
+7	0,0,0,0,0,0,0,2	111001100
+8	0,0,0,0,1,1,1,1	100110110
+9	0,0,0,0,1,1,1,-1	100000101
+10	0,0,0,0,1,1,-1,1	111000101
+11	0,0,0,0,1,1,-1,-1	111110110
+12	0,0,0,0,1,-1,1,1	111110101
+13	0,0,0,0,1,-1,1,-1	111000110
+14	0,0,0,0,1,-1,-1,1	100000110
+15	0,0,0,0,1,-1,-1,-1	100110101
+16	0,0,1,1,0,0,1,1	100101000
+17	0,0,1,1,0,0,1,-1	100011011
+18	0,0,1,1,0,0,-1,1	111011011
+19	0,0,1,1,0,0,-1,-1	111101000
+20	0,0,1,-1,0,0,1,1	111100111
+21	0,0,1,-1,0,0,1,-1	111010100
+22	0,0,1,-1,0,0,-1,1	100010100
+23	0,0,1,-1,0,0,-1,-1	100100111
+24	0,0,1,1,1,1,0,0	100100001
+25	0,0,1,1,1,-1,0,0	111100010
+26	0,0,1,1,-1,1,0,0	100100010
+27	0,0,1,1,-1,-1,0,0	111100001
+28	0,0,1,-1,1,1,0,0	111101110
+29	0,0,1,-1,1,-1,0,0	100101101
+30	0,0,1,-1,-1,1,0,0	111101101
+31	0,0,1,-1,-1,-1,0,0	100101110
+32	0,1,0,1,0,1,0,1	101100000
+33	0,1,0,1,0,1,0,-1	101010011
+34	0,1,0,1,0,-1,0,1	110100011
+35	0,1,0,1,0,-1,0,-1	110010000
+36	0,1,0,-1,0,1,0,1	110101111
+37	0,1,0,-1,0,1,0,-1	110011100
+38	0,1,0,-1,0,-1,0,1	101101100
+39	0,1,0,-1,0,-1,0,-1	101011111
+40	0,1,0,1,1,0,1,0	101011001
+41	0,1,0,1,1,0,-1,0	110101010
+42	0,1,0,1,-1,0,1,0	101011010
+43	0,1,0,1,-1,0,-1,0	110101001
+44	0,1,0,-1,1,0,1,0	110010110
+45	0,1,0,-1,1,0,-1,0	101100101
+46	0,1,0,-1,-1,0,1,0	110010101
+47	0,1,0,-1,-1,0,-1,0	101100110
+48	0,1,1,0,0,1,1,0	101001011
+49	0,1,1,0,0,1,-1,0	110111000
+50	0,1,1,0,0,-1,1,0	110001000
+51	0,1,1,0,0,-1,-1,0	101111011
+52	0,1,-1,0,0,1,1,0	101000100
+53	0,1,-1,0,0,1,-1,0	110110111
+54	0,1,-1,0,0,-1,1,0	110000111
+55	0,1,-1,0,0,-1,-1,0	101110100
+56	0,1,1,0,1,0,0,1	110110010
+57	0,1,1,0,1,0,0,-1	110000001
+58	0,1,1,0,-1,0,0,1	110110001
+59	0,1,1,0,-1,0,0,-1	110000010
+60	0,1,-1,0,1,0,0,1	110111101
+61	0,1,-1,0,1,0,0,-1	110001110
+62	0,1,-1,0,-1,0,0,1	110111110
+63	0,1,-1,0,-1,0,0,-1	110001101
+64	1,0,0,1,0,1,1,0	010000000
+65	1,0,0,1,0,1,-1,0	001110011
+66	1,0,0,1,0,-1,1,0	001000011
+67	1,0,0,1,0,-1,-1,0	010110000
+68	1,0,0,-1,0,1,1,0	001001111
+69	1,0,0,-1,0,1,-1,0	010111100
+70	1,0,0,-1,0,-1,1,0	010001100
+71	1,0,0,-1,0,-1,-1,0	001111111
+72	1,0,0,1,1,0,0,1	001111001
+73	1,0,0,1,1,0,0,-1	001001010
+74	1,0,0,1,-1,0,0,1	001111010
+75	1,0,0,1,-1,0,0,-1	001001001
+76	1,0,0,-1,1,0,0,1	010110110
+77	1,0,0,-1,1,0,0,-1	010000101
+78	1,0,0,-1,-1,0,0,1	010110101
+79	1,0,0,-1,-1,0,0,-1	010000110
+80	1,0,1,0,0,1,0,1	001101011
+81	1,0,1,0,0,1,0,-1	001011000
+82	1,0,1,0,0,-1,0,1	010101000
+83	1,0,1,0,0,-1,0,-1	010011011
+84	1,0,-1,0,0,1,0,1	001100100
+85	1,0,-1,0,0,1,0,-1	001010111
+86	1,0,-1,0,0,-1,0,1	010100111
+87	1,0,-1,0,0,-1,0,-1	010010100
+88	1,0,1,0,1,0,1,0	001010010
+89	1,0,1,0,1,0,-1,0	010100001
+90	1,0,1,0,-1,0,1,0	001010001
+91	1,0,1,0,-1,0,-1,0	010100010
+92	1,0,-1,0,1,0,1,0	001011101
+93	1,0,-1,0,1,0,-1,0	010101110
+94	1,0,-1,0,-1,0,1,0	001011110
+95	1,0,-1,0,-1,0,-1,0	010101101
+96	1,1,0,0,0,0,1,1	000010011
+97	1,1,0,0,0,0,1,-1	000100000
+98	1,1,0,0,0,0,-1,1	011100000
+99	1,1,0,0,0,0,-1,-1	011010011
+100	1,-1,0,0,0,0,1,1	000101100
+101	1,-1,0,0,0,0,1,-1	000011111
+102	1,-1,0,0,0,0,-1,1	011011111
+103	1,-1,0,0,0,0,-1,-1	011101100
+104	1,1,0,0,1,1,0,0	000011010
+105	1,1,0,0,1,-1,0,0	011011001
+106	1,1,0,0,-1,1,0,0	000011001
+107	1,1,0,0,-1,-1,0,0	011011010
+108	1,-1,0,0,1,1,0,0	000100101
+109	1,-1,0,0,1,-1,0,0	011100110
+110	1,-1,0,0,-1,1,0,0	000100110
+111	1,-1,0,0,-1,-1,0,0	011100101
+112	1,1,1,1,0,0,0,0	000000100
+113	1,1,1,-1,0,0,0,0	011001011
+114	1,1,-1,1,0,0,0,0	000001011
+115	1,1,-1,-1,0,0,0,0	011000100
+116	1,-1,1,1,0,0,0,0	000111011
+117	1,-1,1,-1,0,0,0,0	011110100
+118	1,-1,-1,1,0,0,0,0	000110100
+119	1,-1,-1,-1,0,0,0,0	011111011
diff --git a/research/seed48-p120-orthogonal-shared-total/verify.py b/research/seed48-p120-orthogonal-shared-total/verify.py
new file mode 100644
index 0000000000..38cbfde51a
--- /dev/null
+++ b/research/seed48-p120-orthogonal-shared-total/verify.py
@@ -0,0 +1,272 @@
+#!/usr/bin/env python3
+"""Exact P120 census for one orthogonal root-pencil shared-total decoder family."""
+from fractions import Fraction
+from hashlib import sha1, sha256
+import json
+from pathlib import Path
+import subprocess
+
+
+ROOT = Path(__file__).resolve().parents[2]
+PACKAGE = "research/seed48-p120-orthogonal-shared-total"
+MANIFEST = ROOT / PACKAGE / "SOURCES.json"
+CERT = ROOT / PACKAGE / "vendor/seed51/certificate.tsv"
+SEED = 48
+PORTS = tuple(range(120))
+
+
+def require(ok, message):
+    if not ok:
+        raise SystemExit("FAIL " + message)
+
+
+def blob_id(data):
+    return sha1(b"blob " + str(len(data)).encode("ascii") + b"\0" + data).hexdigest()
+
+
+def verify_source_pins(manifest):
+    for row in manifest["files"]:
+        proc = subprocess.run(["git", "show", manifest["base_commit"] + ":" + row["path"]],
+                              cwd=ROOT, check=True, capture_output=True)
+        data = proc.stdout
+        require(sha256(data).hexdigest() == row["sha256"], "base SHA-256 mismatch: " + row["path"])
+        require(blob_id(data) == row["git_blob"], "base Git blob mismatch: " + row["path"])
+    source = manifest["external_sources"][0]["files"][0]
+    data = CERT.read_bytes()
+    require(sha256(data).hexdigest() == source["sha256"], "vendored certificate SHA-256 mismatch")
+    require(blob_id(data) == source["git_blob"], "vendored certificate Git blob mismatch")
+
+
+def read_certificate(path):
+    lines = path.read_text().splitlines()
+    require(lines[:3] == [
+        "# schema=1",
+        "#! seed=51 track=structural-decoder ports=P120 e_index=51 d0_index=1",
+        "#! columns=index root8_csv label9_bits",
+    ], "predecessor certificate header changed")
+    roots, labels = [], []
+    for expected, line in enumerate(lines[3:]):
+        index, root, label = line.split("\t")
+        require(int(index) == expected and len(label) == 9 and set(label) <= {"0", "1"},
+                "malformed root or label certificate row")
+        roots.append(tuple(int(x) for x in root.split(",")))
+        labels.append(int(label, 2))
+    require(len(roots) == len(labels) == 120 and all(len(row) == 8 for row in roots),
+            "wrong root/label dimensions")
+    return roots, labels
+
+
+def dot(a, b):
+    return sum(x * y for x, y in zip(a, b))
+
+
+def parity_dot(a, b):
+    return (a & b).bit_count() & 1
+
+
+def validate_certificate(roots, labels):
+    gram = [[dot(a, b) // 2 for b in roots] for a in roots]
+    require(len(set(roots)) == 120, "duplicate root representatives")
+    require(all(dot(a, a) == 4 for a in roots), "root norm is not four")
+    require(all(dot(a, b) % 2 == 0 for a in roots for b in roots), "half-Gram is nonintegral")
+    require(all(gram[i][i] == 2 for i in PORTS), "wrong Gram diagonal")
+    require(all(gram[i][j] in (-1, 0, 1) for i in PORTS for j in PORTS if i != j),
+            "unexpected off-diagonal Gram value")
+    require(all(parity_dot(labels[i], labels[j]) == ((1 + gram[i][j]) & 1)
+                for i in PORTS for j in PORTS), "root labels fail a Gram parity")
+    require(all(0 <= x < 512 for x in labels), "label outside F2^9")
+    return gram
+
+
+def supports_by_word(labels):
+    out = [0] * 512
+    for word in range(1, 512):
+        mask = 0
+        for source, label in enumerate(labels):
+            if parity_dot(word, label):
+                mask |= 1 << source
+        out[word] = mask
+    return out
+
+
+def enumerate_rows(ports, roots, labels, support, e_index, d_index):
+    e, d0 = roots[e_index], roots[d_index]
+    pe = {s: dot(roots[s], e) for s in ports}
+    pd = {s: dot(roots[s], d0) for s in ports}
+    nodes = []
+    counts = {"label_eligible": 0, "unique_calibrator": 0, "calibrated": 0,
+              "nonzero_diagonal": 0}
+    port_mask = sum(1 << s for s in ports)
+    for target in ports:
+        for word in range(1, 512):
+            z = support[word] & port_mask
+            if not (z >> target & 1) or word == labels[target]:
+                continue
+            counts["label_eligible"] += 1
+            ratios = {
+                Fraction(-pd[s], pe[s])
+                for s in ports if s != target and (z >> s & 1) and pe[s] != 0
+            }
+            if len(ratios) > 1:
+                continue
+            counts["unique_calibrator"] += 1
+            if not ratios:
+                continue
+            counts["calibrated"] += 1
+            mu = next(iter(ratios))
+            if pd[target] + mu * pe[target] == 0:
+                continue
+            counts["nonzero_diagonal"] += 1
+            correction = 0
+            for s in ports:
+                if s != target and (z >> s & 1) and pe[s] == 0 and pd[s] != 0:
+                    correction |= 1 << s
+            nodes.append({"target": target, "word": word, "mu": mu, "Z": z, "E": correction})
+    return nodes, counts, pe, pd
+
+
+def row_exact(target, mu, total, z, ports, pe, pd):
+    for s in ports:
+        coefficient = Fraction(pd[s]) + mu * pe[s] - (pd[s] if total >> s & 1 else 0)
+        if s == target:
+            if not (z >> s & 1) or coefficient == 0:
+                return False
+        elif (z >> s & 1) and coefficient != 0:
+            return False
+    return True
+
+
+def pair_census(nodes, ports, pe, pd):
+    raw = available = cross_a = cross_b = both = exact_pairs = 0
+    no_cross = 0
+    for i, a in enumerate(nodes):
+        for b in nodes[i + 1:]:
+            if a["target"] == b["target"]:
+                continue
+            raw += 1
+            if a["E"] & ~b["Z"] or b["E"] & ~a["Z"]:
+                continue
+            available += 1
+            a_hit = bool(b["E"] >> a["target"] & 1)
+            b_hit = bool(a["E"] >> b["target"] & 1)
+            cross_a += a_hit
+            cross_b += b_hit
+            both += a_hit and b_hit
+            no_cross += not a_hit and not b_hit
+            if a_hit:
+                require(pe[a["target"]] == 0 and pd[a["target"]] != 0,
+                        "first target is not a forced total cancellation")
+                require(Fraction(pd[a["target"]]) + a["mu"] * pe[a["target"]]
+                        - pd[a["target"]] == 0, "first contaminated diagonal did not vanish")
+            if b_hit:
+                require(pe[b["target"]] == 0 and pd[b["target"]] != 0,
+                        "second target is not a forced total cancellation")
+                require(Fraction(pd[b["target"]]) + b["mu"] * pe[b["target"]]
+                        - pd[b["target"]] == 0, "second contaminated diagonal did not vanish")
+            total = a["E"] | b["E"]
+            exact_a = row_exact(a["target"], a["mu"], total, a["Z"], ports, pe, pd)
+            exact_b = row_exact(b["target"], b["mu"], total, b["Z"], ports, pe, pd)
+            exact_pairs += exact_a and exact_b
+    return {"distinct_target_pairs": raw, "available_pairs": available,
+            "first_target_contaminated": cross_a, "second_target_contaminated": cross_b,
+            "both_targets_contaminated": both, "no_target_contaminated": no_cross,
+            "exact_pairs": exact_pairs}
+
+
+def full_unit_exact(ports, roots, labels, gram, a, b, total, pe, pd):
+    for target in ports:
+        word = a["word"] if target == a["target"] else b["word"] if target == b["target"] else labels[target]
+        for source in ports:
+            if target == a["target"]:
+                coefficient = Fraction(pd[source]) + a["mu"] * pe[source] \
+                    - (pd[source] if total >> source & 1 else 0)
+            elif target == b["target"]:
+                coefficient = Fraction(pd[source]) + b["mu"] * pe[source] \
+                    - (pd[source] if total >> source & 1 else 0)
+            else:
+                coefficient = Fraction(gram[target][source], 2)
+            paired = parity_dot(word, labels[source])
+            if target == source:
+                if not paired or coefficient == 0:
+                    return False
+            elif paired and coefficient != 0:
+                return False
+    return True
+
+
+def first_exact_pair(ports, roots, labels, support, e_index, d_index):
+    nodes, _, pe, pd = enumerate_rows(ports, roots, labels, support, e_index, d_index)
+    for i, a in enumerate(nodes):
+        for b in nodes[i + 1:]:
+            if a["target"] == b["target"] or a["E"] & ~b["Z"] or b["E"] & ~a["Z"]:
+                continue
+            total = a["E"] | b["E"]
+            if row_exact(a["target"], a["mu"], total, a["Z"], ports, pe, pd) \
+                    and row_exact(b["target"], b["mu"], total, b["Z"], ports, pe, pd):
+                return a, b, total, pe, pd
+    return None, None, None, pe, pd
+
+
+def main():
+    manifest = json.loads(MANIFEST.read_text())
+    verify_source_pins(manifest)
+    roots, labels = read_certificate(CERT)
+    gram = validate_certificate(roots, labels)
+    support = supports_by_word(labels)
+    print("PASS_SOURCE_AND_E8_CERTIFICATE: roots=120 labels=F2^9 pairings=14400")
+
+    e_index = SEED
+    orthogonal = [j for j in PORTS if j != e_index and dot(roots[e_index], roots[j]) == 0]
+    d_index = orthogonal[SEED % len(orthogonal)]
+    require(len(orthogonal) == 63 and d_index == 91 and dot(roots[e_index], roots[d_index]) == 0,
+            "seed-selected orthogonal pencil changed")
+    nodes, row_counts, pe, pd = enumerate_rows(PORTS, roots, labels, support, e_index, d_index)
+    require(row_counts == {"label_eligible": 30600, "unique_calibrator": 190,
+                           "calibrated": 190, "nonzero_diagonal": 65} and len(nodes) == 65,
+            "orthogonal P120 row census changed: " + repr(row_counts))
+    census = pair_census(nodes, PORTS, pe, pd)
+    require(census == {"distinct_target_pairs": 2048, "available_pairs": 1056,
+                       "first_target_contaminated": 1049, "second_target_contaminated": 1031,
+                       "both_targets_contaminated": 1024, "no_target_contaminated": 0,
+                       "exact_pairs": 0},
+            "orthogonal P120 pair census changed: " + repr(census))
+    print("P120_ORTHOGONAL: e=L48 d0=L91 <e,d0>=0 rows=" + repr(row_counts))
+    print("P120_ORTHOGONAL_PAIRS: " + repr(census))
+
+    # Regression control: independently reproduce the fixed odd-pair case from PR #1366.
+    odd_nodes, odd_counts, odd_pe, odd_pd = enumerate_rows(PORTS, roots, labels, support, 51, 1)
+    odd_census = pair_census(odd_nodes, PORTS, odd_pe, odd_pd)
+    require(odd_counts == {"label_eligible": 30600, "unique_calibrator": 63,
+                           "calibrated": 63, "nonzero_diagonal": 27} and len(odd_nodes) == 27,
+            "PR #1366 regression row census changed")
+    require(odd_census["distinct_target_pairs"] == 351 and odd_census["available_pairs"] == 351
+            and odd_census["both_targets_contaminated"] == 351
+            and odd_census["exact_pairs"] == 0,
+            "PR #1366 regression pair result changed")
+
+    # Positive control: published P112 C.6 exact two-target unit.
+    p112 = tuple(range(8, 120))
+    a, b, total, pe112, pd112 = first_exact_pair(p112, roots, labels, support, 0, 76)
+    require(a is not None and b is not None, "P112 C.6 positive control not found")
+    require((a["target"], a["word"], b["target"], b["word"], total.bit_count())
+            == (75, 329, 76, 438, 24), "P112 C.6 witness changed")
+    require(full_unit_exact(p112, roots, labels, gram, a, b, total, pe112, pd112),
+            "P112 C.6 full 112-by-112 positive control failed")
+    altered_total = total & ~(total & -total)
+    require(not full_unit_exact(p112, roots, labels, gram, a, b, altered_total, pe112, pd112),
+            "removing one required shared-total source escaped the negative control")
+
+    # Certificate mutation control.
+    bad_labels = labels[:]
+    bad_labels[0] ^= 1
+    require(any(parity_dot(bad_labels[0], labels[j]) != ((1 + gram[0][j]) & 1)
+                for j in PORTS), "label mutation control failed")
+
+    print("PASS_PR1366_REGRESSION: odd-pair nodes=27 available=351 both-diagonal obstruction=351")
+    print("PASS_P112_C6_CONTROL: targets=75,76 sinks=329,438 total_sources=24 full_unit=112x112")
+    print("PASS_NEGATIVE_CONTROLS: required-total-source removal and label mutation detected")
+    print("PASS_P120_ORTHOGONAL_SHARED_TOTAL: no exact pair in the complete calibrated one-total family; no new kappa")
+
+
+if __name__ == "__main__":
+    main()