Prove the scoped 112-call standalone fanout optimum (no new κ)

certificates/research/fanout-optimality-package-validation-v1.json

@@ -0,0 +1,154 @@
+{
+  "schema": "root-fanout-package-three-guards-four-replays/v1",
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+          "scripts/research_package.py",
+          "--package",
+          "research/fanout-optimality-support"
+        ],
+        "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/fanout-optimality-support-package-20261024",
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+        "scope": "Fresh command execution only; scientific claim determined by reviewed output."
+      }
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+      "name": "fanout-optimality-readonly-normal-v1",
+      "guard": {
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+        "command": [
+          "/usr/bin/env",
+          "-u",
+          "GIT_DIR",
+          "-u",
+          "GIT_WORK_TREE",
+          "-u",
+          "GIT_COMMON_DIR",
+          "PATH=",
+          "GIT_CEILING_DIRECTORIES=/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1",
+          "/usr/bin/python3",
+          "-I",
+          "-Werror",
+          "-B",
+          "verify.py"
+        ],
+        "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1",
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+        "scope": "Fresh command execution only; scientific claim determined by reviewed output."
+      }
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+    {
+      "name": "fanout-optimality-readonly-optimized-v1",
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+        "command": [
+          "/usr/bin/env",
+          "-u",
+          "GIT_DIR",
+          "-u",
+          "GIT_WORK_TREE",
+          "-u",
+          "GIT_COMMON_DIR",
+          "PATH=",
+          "GIT_CEILING_DIRECTORIES=/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1",
+          "/usr/bin/python3",
+          "-I",
+          "-O",
+          "-Werror",
+          "-B",
+          "verify.py"
+        ],
+        "cwd": "/home/d3lerium/.codex/.chatgpt-projects/g-p-6ad5817fd84881918865926b6fd51453/outputs/fanout-optimality-publication-20261024/readonly-package-v1",
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+        "rss_samples": 46,
+        "memory_limit_mib": 256,
+        "timeout_seconds": 30.0,
+        "python": "3.12.3 (main, Aug 31 2026, 10:18:26) [GCC 13.3.0]",
+        "log_sha256": "63fa9f527e479d852c8b48e95c7962809947ff0d1f380d4f2c55a876a63a2854",
+        "scope": "Fresh command execution only; scientific claim determined by reviewed output."
+      }
+    }
+  ],
+  "fresh_artifacts": [
+    {
+      "run": "fanout-optimality-registered-normal-optimized-v1",
+      "optimized": false,
+      "program_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+      "result_sha256": "bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7",
+      "raw_and_typed_equal": true,
+      "actual_artifacts": [
+        "race-kappa0033-sol-high-20261024/coordination/fanout-package-fresh-v1/run0-0-PROGRAM.json",
+        "race-kappa0033-sol-high-20261024/coordination/fanout-package-fresh-v1/run0-0-RESULT.json"
+      ],
+      "comparison_exclusions": []
+    },
+    {
+      "run": "fanout-optimality-registered-normal-optimized-v1",
+      "optimized": true,
+      "program_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+      "result_sha256": "bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7",
+      "raw_and_typed_equal": true,
+      "actual_artifacts": [
+        "race-kappa0033-sol-high-20261024/coordination/fanout-package-fresh-v1/run0-1-PROGRAM.json",
+        "race-kappa0033-sol-high-20261024/coordination/fanout-package-fresh-v1/run0-1-RESULT.json"
+      ],
+      "comparison_exclusions": []
+    },
+    {
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+      "optimized": false,
+      "program_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+      "result_sha256": "bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7",
+      "raw_and_typed_equal": true,
+      "actual_artifacts": [
+        "race-kappa0033-sol-high-20261024/coordination/fanout-package-fresh-v1/run1-0-PROGRAM.json",
+        "race-kappa0033-sol-high-20261024/coordination/fanout-package-fresh-v1/run1-0-RESULT.json"
+      ],
+      "comparison_exclusions": []
+    },
+    {
+      "run": "fanout-optimality-readonly-optimized-v1",
+      "optimized": true,
+      "program_sha256": "5575fc71eb94f1b75b3421d787d3313716ece5e72d3498ce348500f3628291f7",
+      "result_sha256": "bf29a13f9e7ef9feb87befcc71b6919ed75726e6fef87b139e0c9c6ad244cdb7",
+      "raw_and_typed_equal": true,
+      "actual_artifacts": [
+        "race-kappa0033-sol-high-20261024/coordination/fanout-package-fresh-v1/run2-0-PROGRAM.json",
+        "race-kappa0033-sol-high-20261024/coordination/fanout-package-fresh-v1/run2-0-RESULT.json"
+      ],
+      "comparison_exclusions": []
+    }
+  ],
+  "all67_frozen_files_bytes_sizes_modes_unchanged": true,
+  "all23_readonly_directory_modes_unchanged": true,
+  "decompression_bounded_to_expected_bytes_plus_one": true,
+  "new_kappa": null,
+  "scope": "Packaging of unchanged standalone112 upper checker; written lower proof authenticated only, no new numerical lower computation, global or incremental bound."
+}

docs/ci-verification.md

@@ -1,8 +1,40 @@
 # CI verification
 
-## Current selected-family replay: #4610 with #5241
+## Current selected-family replay: #5413 with #5407 and #5414
 
 The [selected record](../certificates/selected-result.json) binds conditional
+κ = 0.003027288235, the [promotion and scope](research/pr-intake-evidence/pr5413-promotion/PROMOTION.md),
+[explicit source closure](../certificates/frontier5413-source.json),
+[review validation](research/pr-intake-evidence/pr5413-promotion/VALIDATION.json), and
+[integration receipt](research/pr-intake-evidence/pr5413-promotion/INTEGRATION.json).
+
+`make frontier5413-verify` authenticates the selected source manifest, derives
+the certificate from frozen numerical evidence, and exports the complete
+three-package execution closure. It replays #5407's five-stage provider audit,
+#5413's eight-stage admission, and #5414's independent companion screen serially.
+The exported inputs are checked again afterward. Source-bound #4610/#5241 and
+earlier BIT/native/compiler/tape/analytic foundation coverage is explicitly
+reused; its historical suites are not rerun.
+
+Each package runs under an external sampled 1 GiB aggregate descendant-memory
+guard, with timeouts of 660 seconds for the provider and primary packages and
+120 seconds for the companion. On macOS the replay uses the reviewed RLIMIT_AS
+adapter; on Linux it invokes the unmodified package wrappers. The recorded
+successful local macOS replay does not establish a hosted Linux pass.
+
+The [frontier5413 workflow](../.github/workflows/frontier5413.yml) is manual-only,
+uses Python 3.12 on Ubuntu, materializes the declared source closure, and uploads
+receipts and logs. Its status is separate from local validation and recorded in
+the integration receipt. Routine donor PRs do not launch this selected replay.
+
+`make selected-record-check` verifies metadata and source/proof hashes. It does
+not execute the operators or prove the five inherited framework assumptions.
+The finite checks do not establish the full integer multiplication theorem,
+and the uniform word remains unmaterialized.
+
+## Historical selected-family replay: #4610 with #5241
+
+The historical [selected record](../certificates/checkpoints/frontier4610.json) binds conditional
 κ = 0.0030217758, the [review](research/pr-intake-evidence/pr4610/PROOF-REVIEW.md),
 [explicit source closure](../certificates/frontier4610-source.json),
 [review validation](research/pr-intake-evidence/pr4610/VALIDATION.json), and

research/fanout-optimality-support/.gitattributes

@@ -0,0 +1 @@
+* -text

research/fanout-optimality-support/CLAIMS.json

@@ -0,0 +1,58 @@
+{
+  "schema": "fanout-scoped-optimality-claims/v1",
+  "status": "MATCHING_STANDALONE_UPPER_AND_STATICALLY_REVIEWED_SCOPED_LOWER",
+  "interface": "y112 += q^-1 W_s h8; h strictly read-only;17arbitrary-owned returned zero",
+  "upper": {
+    "paid_H1": 112,
+    "query_savings": 0,
+    "ordinary_counts": {
+      "CLEAR": 249,
+      "ZERO_RETAG": 249,
+      "COPY": 8,
+      "MONOMIAL": 344,
+      "ADD": 672,
+      "GAUSSIAN": 112
+    },
+    "source_rows": 112,
+    "singleton_classes": 112,
+    "class_rank_sum": 112,
+    "alias_column_comparisons": 57344,
+    "alias_coverage": "112 singleton SELF-alias identities,512columns each",
+    "full_137_field_physical_endpoint_replay": false,
+    "endpoint_basis": "COMPOSITIONAL_SOURCE_FACTORIZATION_LITERAL_COEFFICIENTS_AND_LIFETIMES",
+    "runtime_odd_divisions": 0,
+    "owned_arbitrary_entry_zero_exit": 17
+  },
+  "lower": {
+    "minimum_total_gaussian_field_calls": 112,
+    "bound_interpretation": "TOTAL_STANDALONE_NOT_INCREMENTAL",
+    "fixed_finite_program": true,
+    "fixed_exterior_coefficients": true,
+    "finite_columnwise_ordinary_group": true,
+    "width_quantifier": "ALL_POSITIVE_WIDTHS_OR_ONE_CONSECUTIVE_TAIL",
+    "ordinary_initial_span_only": true,
+    "fixed_common_field_capacity": true,
+    "paid_output_rows_per_call": 1,
+    "central_scalar_M_shared_right_Km": true,
+    "arbitrary_independent_originals": true,
+    "exact_per_column_phases": true,
+    "finite_feedback_allowed": true,
+    "ordinary_zero_divisors_allowed": true,
+    "weighted_recursive_invoice_claimed": false,
+    "proof_kind": "WRITTEN_PROOF_WITH_INDEPENDENT_STATIC_REVIEW_NOT_FORMAL_KERNEL"
+  },
+  "exclusions": [
+    "nonordinary Gaussian/native/cached initial observations",
+    "incremental112per global cut or additive sharing bound",
+    "width-dependent or width-growing programs/coefficients",
+    "restricted subsequences of widths",
+    "inter-column ordinary operations",
+    "packing/splitting/changed field capacity or multiple outputs per chargedcall",
+    "dependent originals or changed source/right-factor structure",
+    "approximate/nonlinear/antilinear or projective-phase computations"
+  ],
+  "full_physical_raw_dual": false,
+  "complete_caller": false,
+  "compiler_precision_stock_admitted": false,
+  "new_kappa": null
+}