Research note: price a width-9 spectral split with dirty restoration

research/clean-residual-dilation/CERTIFICATE.json

@@ -0,0 +1,83 @@
+{
+  "assignment_seed": 51,
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "collapsed_host_moment_ratio": "2",
+  "collapsed_host_sandwich_profile": {
+    "9": 2
+  },
+  "coverage": {
+    "Walsh_child_reduction_columns_both_directions": 1024,
+    "binomial_dp_widths": [
+      0,
+      288
+    ],
+    "clean_basis_columns": 512,
+    "collapsed_program_basis_columns": 1024,
+    "dilation_counts_sha256": "eb2a043145ad2440ac4248b31833b6ed865c438d91fc6aa62271441c531fd45a",
+    "dilation_f": [
+      1,
+      32
+    ],
+    "dirty_basis_columns": 512,
+    "dirty_repaired_basis_columns": 512,
+    "independent_tensor_columns": 512
+  },
+  "dirty_complement_multiplicities": [
+    24,
+    88,
+    232,
+    168
+  ],
+  "free_host_moment_ratio_lower_bound": "4",
+  "free_host_width_profile": {
+    "4": 2,
+    "5": 2,
+    "9": 2
+  },
+  "host_multiplicities": [
+    160,
+    224,
+    352,
+    288
+  ],
+  "moment_ratio_lower_bound_for_0_lt_sigma_le_1": "5",
+  "negative_controls": {
+    "omit_host_calls": "REJECTED on source basis column 0",
+    "omit_host_entry": "REJECTED on source basis column 0",
+    "omit_normalization": "REJECTED on source basis column 0",
+    "omit_source_boundaries": "REJECTED on source basis column 0",
+    "rank_two_into_two_rank_one_owners": "REJECTED: missing -1 eigenspace",
+    "unrestored_dirty_workspace": {
+      "scratch_basis_column": 63,
+      "status": "REJECTED",
+      "unrepaired_phase_exponent": 3
+    },
+    "wrong_dirty_repair_sign": {
+      "scratch_basis_column": 63,
+      "status": "REJECTED",
+      "unrepaired_phase_exponent": 3
+    },
+    "wrong_eigenvalue_route": "REJECTED"
+  },
+  "object": {
+    "a": 4,
+    "b": 5,
+    "coefficients_per_stream": 512,
+    "r": 9
+  },
+  "recursive_width_profile": {
+    "4": 3,
+    "5": 3,
+    "9": 2
+  },
+  "route_sha256": "a73a93797b26756588687ca65516c17d45ee59079f8c901d3911d6b2a879454b",
+  "scope": "Exact finite operator replay and written all-f algebraic argument; this literal encoder loses even with free routing and owner calls. No all-size tape compiler, global lower bound, or new kappa.",
+  "source_multiplicities": [
+    136,
+    136,
+    120,
+    120
+  ],
+  "status": "PASS_EXACT_DILATION_AND_UNFAVORABLE_BOUNDARY_BUDGET",
+  "uniform_capacity_slack_lower_bound": "3/64"
+}

research/clean-residual-dilation/CLAIM.json

@@ -0,0 +1,55 @@
+{
+  "track": "Recursive interfaces",
+  "assignment_seed": 51,
+  "randomness": "python3 secrets.randbelow(100), operating-system randomness; drawn once",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "started_utc": "2026-10-13T02:56:12Z",
+  "selection_deadline_utc": "2026-10-13T03:04:12Z",
+  "verification_starts_by_utc": "2026-10-13T03:26:12Z",
+  "expected_finish_utc": "2026-10-13T03:36:12Z",
+  "coordination": "No pinned issues; only open issue #650 concerns Discussions. Claim recorded locally as requested.",
+  "candidates": [
+    {
+      "task": "Defer dirty-helper cleanup across successive calls",
+      "decision": "Not selected: extensive cold-end, gauge and deferred-readout work in existing suppliers and open PRs."
+    },
+    {
+      "task": "Clean-workspace spectral embedding of a width-9 complex residual into two separate owners",
+      "decision": "Selected: changes the arbitrary-dirty similarity hypothesis in #451; explicit encoder and full boundary cost, not another split-routing replay."
+    },
+    {
+      "task": "Fuse consecutive native bit queries",
+      "decision": "Not selected: #521 already supplies an exact dirty-input primitive; avoid duplicating it."
+    }
+  ],
+  "object": "C_(9f) into C_(4f) direct-sum C_(5f), one equally sized zero workspace, f>=1. Seed selects a=1+(51 mod 8)=4, b=9-a=5.",
+  "method": "Exact fourth-root eigenspace multiplicities and an explicit Walsh/permutation encoder; exact finite all-basis replay and negative controls; bill both encoder boundaries, owners, workspace and restoration.",
+  "deliverable": "Scoped research note, exact reproducible standard-library certificate/checker and full conditional cost recurrence; no kappa claim.",
+  "overlap_checked": {
+    "open_pr_count": 480,
+    "relevant_prs": [
+      448,
+      451,
+      480,
+      481,
+      494,
+      521,
+      627,
+      633
+    ]
+  },
+  "scope_exclusions": [
+    "No selected-certificate edits",
+    "No supplier or upstream modifications",
+    "No claim that a finite replay proves an all-size tape compiler"
+  ],
+  "result": {
+    "status": "Completed research note and scoped negative cost result; no new kappa",
+    "finding": "For every f>=1, C_(9f) embeds in C_(4f) direct-sum C_(5f) with a complementary workspace phase. One phase pass restores arbitrary dirty workspace. The literal recursive moment costs at least five times a single residual (four with free hosts); host collapse leaves two width-9f transforms, and full collapse recovers the original call.",
+    "evidence": "512 clean columns, 512 dirty columns, 512 repaired columns; independent tensor entries; 1024 Walsh reduction checks; 1024 collapsed-circuit columns; 8 mathematical negative controls.",
+    "refinement": "The clean embedding also supplies a dirty interface after an explicit complementary phase repair; this is the same encoded residual, not a second investigation.",
+    "link": "https://github.com/CrocSwap/integer-mult-bounds/tree/research/seed51-clean-residual-dilation/research/clean-residual-dilation",
+    "verification_started_utc": "2026-10-13T03:12:40Z",
+    "reproduce": "python3 -B research/clean-residual-dilation/verify.py"
+  }
+}