Mister-Meeseeks · Oct 14, 2026 · Oct 13, 2026
diff --git a/research/p112-two-total-rank-one-seed21/CERTIFICATE.json b/research/p112-two-total-rank-one-seed21/CERTIFICATE.json
diff --git a/research/p112-two-total-rank-one-seed21/CLAIM.md b/research/p112-two-total-rank-one-seed21/CLAIM.md
@@ -0,0 +1,82 @@
+# Local sprint claim — seed 21
+
+Track: complex supplier (OS draw `secrets.randbelow(100)` = **21**).
+Base: `1b59b624d21924f8e3537cdc1ac52d3be6eda2fe`.
+Started 2026-10-13 19:39 UTC; expected finish 20:19 UTC.
+
+## Exact scope
+
+P112 all-pairs ten-term decoders retaining the eight coordinate readers.
+Test whether two extra totals whose readers leave the coordinate column
+space can evade the #845/#998 single-lift copy floor. Use quotient-space
+rank and support-rank subadditivity, with exact Gaussian-rational examples.
+Also record the directly related k-total quotient-nullity-one corollary
+and the disjoint coefficient-support composition of single-lift bounds.
+Expected deliverable: a scoped obstruction, explicit boundary examples,
+source pins, a deterministic certificate and a separate checker; no kappa.
+
+## Three candidates and selection
+
+1. Conjugate a selected k8 helper by dyadic scales: overlaps #1161, and
+   stage consolidation #1170; rejected.
+2. Shorten CK coefficient lowering at fixed grid: overlaps #1118 and
+   #1036/#999; rejected.
+3. Two-total P112 off-column cancellation: chosen. #845 and #998 cover
+   one total, #1133 covers scalar-field descent for that single total,
+   #1098 its support lemma. None covers the two-total quotient reduction.
+   #968/#1077 cover exactly eight terms with altered readers; different class.
+
+Seed 21 selects coordinate pair index 21 in lexicographic order and port21
+for boundary examples. These are diagnostics, not claimed disjoint searches.
+The proof is uniform over complex coefficients. No search is reopened.
+
+## Source and cost gates
+
+Selected at base: PR1094, kappa 0.001672660197076918, on the seven-slot k8
+word, predecessor PR1087. Read the selected record, its source inventory,
+assembly and community-batch1099 review; selection is context only.
+
+Grant preparation, source access, frames, restoration and recursive children
+zero extra cost and test the necessary copy-rank saving first. If the floor
+64 survives, stop physical synthesis. This is not a complete moment bound:
+redistributing equal rank mass or changing other expenses remains open.
+
+## Coordination and overlap
+
+Read 786 open PR metadata entries, relevant PR bodies #1118/#1161/#1170,
+#1133/#1120/#845, the review ledger, and predecessor proofs. The GitHub
+pinnedIssues query returned no nodes; the only open issues were #650/#913.
+The live discussion board contained start-here #1163, handoffs #1166 and
+mechanisms #1167, with no comments or scoped claims at entry. Per the task's
+no-coordination-issue fallback this claim is local; no reservation issue
+is opened. Refresh PRs and discussions before submission.
+
+## Bounded work and verification
+
+Stop after the precise reduction is proved or falsified and finite boundary
+fixtures are checked. Reserve the final quarter for adversarial proof review,
+source/certificate mutation controls, optimized execution, clean relocation
+and handoff. Two delegated workers stay in this scope: proof review and a
+separately implemented finite checker. Both are AI assistance.
+
+Contributor: Philipp / @mightyOil, with substantial OpenAI Codex assistance.
+Credit Mihir Srivastava (#845), @woklerx (#998), DreamingOfClouds (#717/#446),
+and Joel Pulikkan / GamingPuzzled (#620). Apache-2.0.
+
+## DONE — one local result and handoff
+
+The [completed result](README.md), [proof](PROOF.md),
+[exact certificate](CERTIFICATE.json), and [validation](VALIDATION.json)
+exclude dependent, off-column-canceling and disjoint-support added totals
+from lowering the P112 copy-rank sum. Independent overlapping coordinate
+lifts with arbitrary source columns remain outside this result.
+
+The full package command passed, including inherited #845/#998 replay,
+1,180 independent matrix identities and eight packaging controls. Final
+refresh inspected 798 open PRs through #1186. Concurrent #1180 is credited
+and compared explicitly: its both-factors-in-code hypothesis excludes our
+outside-source fixtures. Main remains the recorded base commit. This is a
+scoped negative result, with no selected frontier change or new kappa.
+The one focused PR and its immutable local patch are supplied in the final
+user handoff. No public coordination issue existed, so this local claim is
+the only claim updated.
diff --git a/research/p112-two-total-rank-one-seed21/INDEPENDENT.json b/research/p112-two-total-rank-one-seed21/INDEPENDENT.json
@@ -0,0 +1,55 @@
+{
+  "conjugate_transpose_negative_control": "rejected",
+  "controls": {
+    "rank_one_reader": 28,
+    "rank_one_source_outside_readers": 28,
+    "rank_two_dense_overlap_control": 28,
+    "rank_two_disjoint_axes": 28,
+    "rank_two_disjoint_pairs": 210,
+    "rejected_omitted_terms": 28,
+    "rejected_source_perturbations": 28,
+    "transposed_identities": 322
+  },
+  "coordinate_pairs": 28,
+  "disjoint_support_controls": {
+    "axis_pairs": 28,
+    "combined_cost_rule": "component_1 + component_2 - 64 >= 64",
+    "component_costs": [
+      64
+    ],
+    "component_identity_count": 476,
+    "two_plus_two_partitions": 210
+  },
+  "entries_per_identity": 12544,
+  "full_matrix_identities": 1180,
+  "general_k_control": {
+    "k": 3,
+    "quotient_rank": 2,
+    "reader_rank": 3,
+    "source_rank": 1
+  },
+  "observed_total_costs": {
+    "rank_one_reader": [
+      73
+    ],
+    "rank_one_source_outside_readers": [
+      73
+    ],
+    "rank_two_dense_overlap_control": [
+      80
+    ],
+    "rank_two_disjoint_axes": [
+      64
+    ],
+    "rank_two_disjoint_pairs": [
+      64
+    ]
+  },
+  "outside_both_reductions": "rank_two_dense_overlap_control",
+  "outside_port": 78,
+  "scope": "independent exact finite fixtures; universal proof remains in PROOF.md",
+  "seed": 21,
+  "source_geometry_sha256": "4f44af368e046002553d632ee90c6470990827cea3fae41f0f54018522d7a080",
+  "status": "pass",
+  "zero_boundaries": 2
+}
diff --git a/research/p112-two-total-rank-one-seed21/NOTICE.md b/research/p112-two-total-rank-one-seed21/NOTICE.md
@@ -0,0 +1,32 @@
+# Attribution and license
+
+Prepared for Philipp / **@mightyOil** with substantial **OpenAI Codex**
+assistance in mathematics, implementation, tests and documentation.
+The separate implementations and proof review are AI-assisted; no independent
+human review or proof-assistant verification is claimed. New material is
+Apache-2.0 under the repository LICENSE.
+
+- **Mihir Srivastava / @mihir-s-05, #845**: the real fixed-reader single-lift
+  floor, geometry construction and finite-premise certificate/checkers.
+- **@woklerx, #998**: complex-to-real support transfer and the complex
+  single-lift theorem used after collapse or independently on disjoint groups.
+- **DreamingOfClouds, #717**: P112 model and open mixed-rank question;
+  **#446**: inherited separate-total physical copy-tree interpretation.
+- **Joel Pulikkan / GamingPuzzled, #620**, and predecessors: the original
+  coordinate cost 64, not a new value established by this contribution.
+- **Adam Gall / @adamgall, #1098**: separate Gram-spectrum corroboration
+  of #845's support lemma; adjacent evidence, not an executable dependency.
+- **Sagar Thakrar / @thakrarsagar, #1133**: concurrent rational single-lift support descent;
+  distinct scalar-field extension, no code or results imported.
+- **@woklerx, #1180**, head `75b408646d558147a4eb250fc407d1fbfcb8df4e`: concurrent
+  overcomplete factor-linear floor; overlap and distinct arbitrary-source
+  coverage are explained in README.md. No pending code or proof is imported.
+- The selected context retains **Rohan Arun #1094**, **Jeremy Kothe's
+  k8/slot/T16 and #1087 lineage**, **Hao Yan #858**, **Chafik Boukhalfa**,
+  **icekylinx**, **DreamingOfClouds #589**, **eumemic #555**, and the full
+  original notices. No selected-construction improvement is claimed here.
+
+No predecessor files are copied or modified. Their source-specific notices
+remain in place and are pinned along with the consumed sources. Rank-nullity
+and support/rank subadditivity are standard linear algebra; the contribution
+is their explicit cost-preserving reduction and scoped P112 consequence.