Independently validate κ = 0.00302728823 for the direct backward caller

research/direct-backward-independent-validation/.gitattributes

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+* -text

research/direct-backward-independent-validation/CLAIMS.json

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+{
+  "assumptions": [
+    {
+      "id": "native_all_columns",
+      "statement": "Retained native operators, phase conventions, spectators and whole-job adapters work at every positive column multiplicity."
+    },
+    {
+      "id": "owned_erasure",
+      "statement": "Owned streams and suspended centers obey the retained allocation, erasure and ownership contracts."
+    },
+    {
+      "id": "compiler",
+      "statement": "The finite mixed-target compiler and chronological product, completion and splitting satisfy the retained uniform closure contract."
+    },
+    {
+      "id": "precision_tape",
+      "statement": "Retained fixed-tape movement and precision/storage prescriptions apply to the new fixed finite template."
+    },
+    {
+      "id": "analytic_recovery",
+      "statement": "Analytic decomposition, fine-prime avoidance and exact integer recovery follow the retained upstream/outer framework."
+    }
+  ],
+  "candidates": [
+    {
+      "author": "Ali Romman",
+      "decimal": ".00302728823",
+      "head": "174fb211493b43a42210434083e9702b4fb7a2ce",
+      "kappa": "302728823/100000000000",
+      "package": "research/kappa-backward-controller-20261023",
+      "pr": 5398
+    }
+  ],
+  "canonical_main": "1ec1119972c9aefe42525172d07b332fcff81cb4",
+  "construction_claim": "No new native construction is claimed by this independent review.",
+  "fresh_commands": [
+    "caller",
+    "numeric",
+    "precision"
+  ],
+  "gains": {
+    "PR5387": "122693/200000000000",
+    "PR5392": "3823/100000000000",
+    "selected": "551243/100000000000"
+  },
+  "new_unconditional_or_Lean_theorem": false,
+  "reused_review": {
+    "head": "787efce72a908f92b8a8b4ebb677a6fdb7729e33",
+    "pr": 5396
+  },
+  "review_kind": "Independent direct-backward caller, complete invoice, directed arithmetic and fresh precision; authenticated reuse of unchanged PR5383 supplier reviewed by PR5396",
+  "review_status": "READY_FOR_COLD_REPLAY",
+  "same_selected_assumptions_required": true,
+  "schema_version": 1,
+  "selected_baseline": ".0030217758",
+  "selected_kappa": "15108879/5000000000",
+  "selected_metadata_role": "Frozen historical provenance; future selected-result updates do not invalidate this review.",
+  "selected_record_changed": false,
+  "selection_authorized": false,
+  "uniform_word_materialized": false
+}

research/direct-backward-independent-validation/COMMANDS.json

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+{
+  "commands": [
+    {
+      "argv": [
+        "agents/caller/check.py",
+        "--repository",
+        "repository"
+      ],
+      "name": "literal-caller-physical-phase-helper-normalization",
+      "timeout_seconds": 120
+    },
+    {
+      "argv": [
+        "agents/numeric/review5398.py",
+        "--repo",
+        "repository",
+        "--prior",
+        "reuse/5383",
+        "--output-dir",
+        "agents/numeric",
+        "--source-manifest",
+        "agents/numeric/SOURCE-BINDINGS-v2.json"
+      ],
+      "name": "complete-invoice-and-directed-funding",
+      "timeout_seconds": 120
+    },
+    {
+      "argv": [
+        "agents/precision/check_precision.py",
+        "--root",
+        "repository",
+        "--prior-word",
+        "reuse/5383/WORD.json.gz",
+        "--prior-native",
+        "reuse/5383/native.py",
+        "--prior-witness",
+        "reuse/5383/WITNESS.json",
+        "--finite-precompilation",
+        "reuse/framework/FINITE-PRECOMPILATION.md",
+        "--finite-template-closure",
+        "reuse/framework/FINITE-TEMPLATE-CLOSURE.md",
+        "--specialization",
+        "reuse/framework/SPECIALIZATION.md",
+        "--framework-proof",
+        "reuse/framework/PROOF.md",
+        "--reuse-manifest",
+        "reuse/5396-REUSE-MANIFEST.json",
+        "--sources",
+        "agents/precision/SOURCES.json",
+        "--out",
+        "agents/precision/CHECK.json"
+      ],
+      "name": "fresh-all-size-precision-stock-compiler",
+      "timeout_seconds": 30
+    }
+  ],
+  "schema_version": 1,
+  "status": "FROZEN"
+}

research/direct-backward-independent-validation/PROOF.md

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+# Direct backward review: proof dependencies and reuse boundary
+
+The target is Ali Romman's PR5398 head
+`174fb211493b43a42210434083e9702b4fb7a2ce`, conditional κ `.00302728823`.
+The three independent component reports and their root-run receipts are
+frozen inputs. The registered wrapper requires fresh complete caller, numerical
+and precision outputs in each normal and optimized replay.
+
+## Exact source and unchanged supplier
+
+The canonical framework is `1ec1119972c9aefe42525172d07b332fcff81cb4`.
+The native implementation and eight-relation WITNESS in the target are byte
+identical to PR5383's `4bd6efa51a495a7c7b7754915cf0244e7e60969e` files.
+The source-bound literal supplier payload SHA256 is
+`2aee5e997df99726fc763e510d9cb69fbe4f86114dc8d2cd33ad26c6c462a21d`.
+The published PR5396 review at
+`787efce72a908f92b8a8b4ebb677a6fdb7729e33` supplies its proof and exact
+prior coverage under the same physical ABI. Published documents are vendored
+with raw Git membership witnesses. Local raw old checker outputs are explicitly
+identified as external execution evidence.
+
+Reuse is limited to the unchanged supplier: sixteen unrestricted relations,
+rank-eight simultaneous preparation, 624 retained arbitrary inputs, seventeen
+arbitrary owned inputs, retained endpoints and owned zero returns. It includes
+source-identical native factors and inherited absolute phases only in their
+proved domains. It does not establish the changed caller, helper conversion,
+ordinary bill, new compiler endpoint or new precision specialization.
+
+## Fresh caller and normalization obligations
+
+The caller engine must prove the literal 32-row Laurent endpoint, both actual
+changed wrapper stages, exact phase-bearing contacts and all signed scalar
+programs. Productive backward helper outputs require their actual ordered
+positive-child factorization and both ordinary monomial normalizers, with no
+rank-only shortcut. Scalar signs remain outside tensor substitution. Every
+owned bank and productive helper occurrence must be separately named and
+charged; borrowed main inputs cannot become destructive scratch.
+
+## Complete invoice and exact arithmetic
+
+The numeric engine independently parses the complete caller and unchanged
+supplier to derive the paid/productive histograms and ordinary bill. It imports
+no submitted evaluator. Its directed rational bounds must establish alpha,
+higher paid and target completion tails, reserve and rounding, split/capacity,
+strict finite compiler grid, ordinary BIT conversion/stock and all 54 strict
+plus four functional outer predicates. The necessary fixed-profile moment root
+is distinct from a funded endpoint and from compiler optimality. Fresh outputs
+must identify the exact invoice and engine bytes.
+
+## Fresh all-size specialization
+
+The precision report instantiates the generic induction with the actual
+expanded direct-backward template, including 306 local owned-bank positions,
+7200 distinct productive helper owners and simultaneously suspended ancestors.
+It must bound full completed/replicated/compiler/matcher/restoration templates,
+not merely count raw slots. Its effective integer recurrence defines new
+W,P,U,O,R,G,N and E,B,C0,C1, stopping and layout thresholds, Gaussian
+chunk/rounding reserve and simultaneous complex/BIT stock. The compiled word is
+algorithmically specified rather than materialized. The written induction,
+exact integer inequalities and negative controls remain separate from physical
+tape execution and a proof-kernel theorem.
+
+## Invalidation
+
+Any changed source, native phase, witness, supplier chronology, caller word,
+productive profile, helper adapter, owned domain, compiler tuple, reserve,
+endpoint or retained assumption invalidates the affected application. Binding
+and source guards run before execution; fresh outputs are validated for full
+coverage after execution. Historical status strings alone never establish a
+changed object.

research/direct-backward-independent-validation/README.md

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+# Independent validation of the direct backward caller
+
+This package reviews Ali Romman's PR5398 at exact head
+`174fb211493b43a42210434083e9702b4fb7a2ce`, conditional κ
+`.00302728823`. The independent scientific acceptance review accepts this fixed object
+under the retained five premises. Three independent engines and their written
+proofs supply the changed caller, funding and precision coverage; registered
+cold replay validates their complete fresh outputs against the frozen review. Final committed/exported
+transport, independent acceptance and any maintainer selection are separate
+gates.
+
+The new review concerns the literal direct backward caller, its phase-bearing
+wrapper and positive helper normalization, the complete recursive and ordinary
+bill, directed funding and outer arithmetic, and a fresh all-size precision and
+stock specialization. The unchanged eight-relation PR5383 supplier is reused
+through its exact native source, witness and literal payload, together with the
+published PR5396 proof. Those old scientific engines are not rerun by this
+package. PR5392's different caller is outside this review target.
+
+The canonical selected baseline remains `.0030217758` at
+`1ec1119972c9aefe42525172d07b332fcff81cb4`. The five retained premises are
+literal statements in `CLAIMS.json`: native all-column realization and phase;
+owned allocation/erasure; finite compiler closure; precision and tape; analytic
+and exact-recovery transfer. This package changes no selected record and makes
+no unconditional multiplication theorem, formal-kernel acceptance or practical
+speedup claim.
+
+## Reproduction
+
+From the repository root, with standard-library Python 3.12:
+
+```sh
+python3 -B scripts/research_package.py --package research/direct-backward-independent-validation
+```
+
+The registered manifest runs both normal and optimized modes. For explicit
+receipt destinations:
+
+```sh
+python3 -I -B research/direct-backward-independent-validation/verify.py --output /tmp/direct-backward-normal.json
+python3 -I -O -B research/direct-backward-independent-validation/verify.py --output /tmp/direct-backward-optimized.json
+```
+
+The verifier begins with a builtin-only isolated-Python bootstrap so local
+standard-library shadows cannot execute. It authenticates both helpers before
+executing either, and the complete input
+manifest before any engine executes. It rejects changed bytes, undeclared files,
+symlink or hardlink input aliases, stale bytecode caches, wrong source heads and
+Git membership proofs. Raw Git commit/tree data establishes file membership
+offline; replay needs neither Git nor a private object store nor a network.
+The independent scientific engines are preserved byte for byte at their final
+review freezes.
+
+Replay copies the capsule to a new private scratch tree, sets only its newly
+created directories to `0700`, and gives every subprocess a fresh bytecode-cache
+prefix. Frozen `0444` files and `0555` directories remain untouched. The three
+engines run serially, with explicit `-O` propagation; fresh JSON is checked for
+complete semantic coverage and source/claim identity. Exit status alone cannot
+satisfy the review. Outputs and raw logs stay outside the frozen package.
+
+`SOURCE-BINDINGS.json` lists every package-local input; its exact bytes and the
+command schedule are pinned by the committed verifier. `SOURCES.json` records
+canonical provenance. Published PR5396 proof documents have offline Git
+membership proofs. The separately labelled old raw algebra/ownership receipts
+were frozen external execution evidence; they were **not** files in PR5396's
+published tree. Their reuse does not assert a fresh historical replay.
+
+## Open next questions
+
+The retained five premises require independent closure beyond this scoped
+conditional review. A successor must supply a complete changed caller, every
+productive-output loss, ordinary helper/phase normalization charges, fresh
+expanded precision/stock constants and a funded strict endpoint. `TASK.json`
+gives feasible first steps and invalidation rules.
+
+## Credit and license
+
+Ali Romman retains PR5383 and PR5398 construction credit. Cao Yifan supplied the
+selected PR4610 framework/source word. Chris R / Clear1nsight supplied the
+independent PR5241 and PR5396 reviews and this review, with substantial OpenAI
+Codex assistance. Retained source credits include Cinna Davis, zxv, Jacob Alan
+Sussman, Dugongue, ToikY and native, Clifford, BIT, compiler, precision and
+analytic contributors. Exact source notices remain in vendored inputs. New
+review work is under the repository Apache-2.0 license.