Research: Rounded scalar tables

research/current-rounded-scalar-tables/ARITHMETIC.json

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+{
+  "current_SCALE_accepts": 1998,
+  "current_SCALE_cases": 3224,
+  "current_SCALE_rejects": 1226,
+  "max_current_SCALE_actions": 2428,
+  "oracle": "direct mathematical floor and final signed range; no table transitions imported",
+  "seam_all_inputs_cases": 1020,
+  "small_ADD_accepts": 1706,
+  "small_ADD_cases": 2380,
+  "small_ADD_rejects": 674
+}

research/current-rounded-scalar-tables/CONTROLS.json

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+{
+  "additional_controls": [
+    "even_positive_and_negative_ties",
+    "floor_not_truncation"
+  ],
+  "table_mutants_detected": [
+    "missing_signed_residue_correction",
+    "missing_upward_rounding_offset",
+    "wrong_final_signed_guard"
+  ]
+}

research/current-rounded-scalar-tables/DEPENDENCIES.json

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+{
+  "schema_version": 1,
+  "files": [
+    {
+      "local_path": "data/word.json.gz",
+      "repository": "DreamingOfClouds/integer-mult-bounds",
+      "commit": "03626137d0bd57f09b0bf9597376183ce6fa9683",
+      "original_path": "research/p104-main-wire-native/data/word.json.gz",
+      "bytes": 349022,
+      "git_blob": "d93e67ca7628bf5531ae6e369da4dd7b7907b88f",
+      "sha256": "273e81f176f001684b1fa3eb857992bf58b54748004fcfe806b83adb48d2cc00"
+    },
+    {
+      "local_path": "reference/ROUNDED-DIVISION-6937.md",
+      "repository": "DreamingOfClouds/integer-mult-bounds",
+      "commit": "a98df73ddae1d1ea85a62b6bdf2714b28cb7b359",
+      "original_path": "research/p104-two-chain-findings/ROUNDED-DIVISION.md",
+      "bytes": 40736,
+      "git_blob": "ed609f6a0e26dd00d6c55f876b667e15051507ca",
+      "sha256": "9ecff5835fae5fcdbf416711a5ef0e69d51afb535c55570ab3e1fef6f920f146"
+    },
+    {
+      "local_path": "vendor/exact_scalar_tables.py",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "13193a22b1070a74a8580c5d3ea27470443f815a",
+      "original_path": "research/current-scalar-flat-tables/tables.py",
+      "bytes": 12650,
+      "git_blob": "1cc22f75fbe53d48b84be42782e581c04820cd49",
+      "sha256": "654e9734ef80a9394807ca508543b1bc164afb5768d23d0e5a88c790d2f13bac"
+    },
+    {
+      "local_path": "vendor/machine.py",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "ab239cb6ee884e7a900dd9101c34448077fad0b0",
+      "original_path": "research/compiled-owned-bank-lifecycle/machine.py",
+      "bytes": 14932,
+      "git_blob": "acf475e4fccaff2fb64bd5b0b3f3fc0d246dc592",
+      "sha256": "ec597bce13275003ff30e4be481c936401826c1d4af642b55eec0c410774d1df"
+    },
+    {
+      "local_path": "reference/check_6937.py",
+      "repository": "DreamingOfClouds/integer-mult-bounds",
+      "commit": "a98df73ddae1d1ea85a62b6bdf2714b28cb7b359",
+      "original_path": "research/p104-two-chain-findings/check.py",
+      "bytes": 4796,
+      "git_blob": "cebc2062a3939e5b2e415fe5aa6d3d8ce1d6cdac",
+      "sha256": "f25a9960396561e166264f8b695a3012b2d062b46744e39d073d57ecbc43f163"
+    },
+    {
+      "local_path": "reference/PRECISION-PROOF.md",
+      "repository": "CubeJerry/integer-mult-bounds",
+      "commit": "56bc9383594a3efc303148e00bb746851abd1ed5",
+      "original_path": "research/query-only-precision-envelope/PROOF.md",
+      "bytes": 26757,
+      "git_blob": "465a5dddd83bdea5db09f1030f99dffe698fe600",
+      "sha256": "8ddafd9a4c5b51d4c0e3f9b4a9eba27712335a16de1868ba156557344af86e63"
+    }
+  ]
+}

research/current-rounded-scalar-tables/ENVIRONMENT.json

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+{
+  "python": "3.12.14 (main, Aug 25 2026, 14:00:49) [Clang 22.1.3 ]",
+  "implementation": "CPython",
+  "platform": "Linux-6.18.57-x86_64-with-glibc2.39",
+  "dependencies": "Standard library only; no Git, network, subprocess or solver in package replay",
+  "canonical_base": "7c49fe32c55de02c2c873655c804b16e4c3fef0a"
+}

research/current-rounded-scalar-tables/HISTORY.json

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+{
+  "borrowed_binary_contexts": 3,
+  "combined_cost_samples": [
+    {
+      "coefficient": "-2/3",
+      "op": "SCALE",
+      "physical_actions": 1644,
+      "table_rows": 255,
+      "width": 3
+    },
+    {
+      "coefficient": "-5/48",
+      "op": "SCALE",
+      "physical_actions": 1252,
+      "table_rows": 199,
+      "width": 2
+    },
+    {
+      "coefficient": "-5/6",
+      "op": "ADD",
+      "physical_actions": 1920,
+      "table_rows": 285,
+      "width": 3
+    }
+  ],
+  "dirty_failure_then_success": true,
+  "failure_scope": "public unchanged; failed heads and scratch may remain unrestored",
+  "history": [
+    {
+      "actions": 75916,
+      "bound": 152792,
+      "components": 12,
+      "historical_backing": [
+        1800,
+        2400
+      ],
+      "old_backing": 4200,
+      "width": 19
+    },
+    {
+      "actions": 1202,
+      "bound": 3584,
+      "components": 2,
+      "historical_backing": [
+        1800,
+        2400
+      ],
+      "old_backing": 0,
+      "width": 2
+    },
+    {
+      "actions": 6228,
+      "bound": 16896,
+      "components": 4,
+      "historical_backing": [
+        1800,
+        2400
+      ],
+      "old_backing": 0,
+      "width": 7
+    },
+    {
+      "actions": 1594,
+      "bound": 4608,
+      "components": 2,
+      "historical_backing": [
+        1800,
+        2400
+      ],
+      "old_backing": 0,
+      "width": 3
+    }
+  ],
+  "late_overflow_public_unchanged": true,
+  "malformed_rejected": [
+    "empty",
+    "odd_component",
+    "empty_component",
+    "foreign_numeric_symbol",
+    "unterminated",
+    "ADD_component_shape"
+  ],
+  "residue_marker_failure_reused": true
+}

research/current-rounded-scalar-tables/PR-DESCRIPTION.md

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+## What changed and why
+
+The current odd word's exact scalar service rejects off-grid rational
+results, including a permitted one-grid child defect immediately before
+SCALE37480 by -2/3. A total rounded-child contract therefore requires a
+different numerical service.
+
+This package builds literal fixed-rational nearest-up SCALE/ADD tables
+through the unchanged lifecycle Controller.primitive/execute_table ABI.
+An LSF signed-residue prepass is followed by an exact odd quotient and
+low-bit discard. Runtime instructions are only branch, write, unit move,
+goto, halt and reject; there are no numerical payload callbacks.
+
+All 52 current SCALE coefficients are instantiated and registered under
+their 3,660 exact local source tokens. The actual -2/3 seam maps numerator1
+to -1 and, universally, accepts every signed input for W>=2. The theorem
+handles negative floor, even-denominator upward ties, widths smaller than
+the discarded-bit count, signed endpoints and complete-field staging.
+
+## Exact dependencies and novelty
+
+Canonical base: `7c49fe32c55de02c2c873655c804b16e4c3fef0a`.
+Source: DreamingOfClouds' CrocSwap/integer-mult-bounds#6936 at
+`03626137d0bd57f09b0bf9597376183ce6fa9683`.
+Credit the total RDiv proposal and abstract division automaton in
+CrocSwap/integer-mult-bounds#6937. That note explicitly leaves physical
+recounting/services open; this package provides a literal two-bank join,
+not a claim to have invented rounding.
+
+The fixed builder and exact arithmetic predecessor are published at
+`13193a22b1070a74a8580c5d3ea27470443f815a`; the unchanged lifecycle at
+`ab239cb6ee884e7a900dd9101c34448077fad0b0`. The source precision seam is
+published in [the precision package at 56bc938](https://github.com/CubeJerry/integer-mult-bounds/tree/56bc9383594a3efc303148e00bb746851abd1ed5/research/query-only-precision-envelope).
+Six unchanged dependencies have exact commit/path/blob/SHA-256 pins.
+
+## Proof, physical checks and reproduction
+
+```bash
+python3 -I -B research/current-rounded-scalar-tables/verify.py --suite all
+python3 -I -O -B research/current-rounded-scalar-tables/verify.py --suite all
+```
+
+The proof supplies signed residue correction, a bounded carry invariant,
+final range iff, mathematical floor after low-bit discard, and whole-field
+staging. Independent direct integer oracles cover 3,224 current SCALE
+cases, 2,380 small ADD pairs and 1,020 exhaustive -2/3 inputs. Tests include
+late rejection, dirty long-to-short reuse, failure-work retirement, context
+preservation, detected malformed shapes and three compiled mutants.
+Standard library only; no Git/network is required for package replay.
+
+The positive physical/control bound is
+512(S+1)+64dR+7(A_0+A_1)+16Q_c, with S the complete numeric extent,
+R the component count, d the denominator's two-adic exponent, A_i old dirty
+scratch lengths and Q_c borrowed contexts. It includes entry/exit erasure,
+all passes, copying and head return. No extra bank is introduced; historical
+backing and positive fixed source/table setup remain in the ledger.
+
+## Scope, limits and kappa
+
+**No new kappa. No full caller admission or unconditional theorem.**
+The 4,079 current odd ADD occurrences are uninstantiated; the generic ADD
+theorem and small fixtures are not their complete catalogue. Full recursive
+source/row binding, other native/Lambda/error/ownership contracts, a common
+physical tariff and rounded outer recovery remain open. The numerical
+semantics are explicitly RDiv mode, not an unannounced replacement of the
+exact-child or selected rule.
+
+Input encoding, matching shape/grid, distinct tapes, origin public/context
+heads and contiguous dirty work with blank historical tails are premises.
+Detected failure leaves the public target unchanged but need not restore
+heads/work. The source guard does not validate hidden dirt after a blank or
+noncanonical encoded frontiers. The physical bound is not imported into
+the old 10^9 tariff as an assumed exchange rate.
+
+Prepared for **@CubeJerry**, with substantial **OpenAI assistance** in
+research, proof, code and verification. Separate AI reviews are identified
+in REVIEW.md and do not imply independent human or proof-kernel review.
+No selected certificate or unrelated source is modified.