Where rounded native codes keep their history: a sharp precision–state frontier

research/precision-state-frontier/MUTATIONS.json

@@ -0,0 +1,110 @@
+{
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+    {
+      "file": "frontier.py",
+      "modes": [
+        {
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+          "optimized": false,
+          "rejection": "ValueError: scalar fiber ceiling"
+        },
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+          "optimized": true,
+          "rejection": "ValueError: scalar fiber ceiling"
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+        "before": "(abs(value)+26)//52"
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+          "optimized": false,
+          "rejection": "ValueError: source precision/state ceiling"
+        },
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+          "optimized": true,
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+        }
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+      "replacement": {
+        "after": "patterns = list(range(256))",
+        "before": "patterns = self.signatures.get(signature, [])"
+      }
+    },
+    {
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+          "rejection": "ValueError: exact source reconstruction"
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+          "optimized": true,
+          "rejection": "ValueError: exact source reconstruction"
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+        "after": "q = [round52(t) for t in self.transpose(x)]",
+        "before": "q = [round52(scale*t) for t in self.transpose(x)]"
+      }
+    },
+    {
+      "file": "frontier.py",
+      "modes": [
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+          "exit_code": 1,
+          "optimized": false,
+          "rejection": "ValueError: source precision/state ceiling"
+        },
+        {
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+          "optimized": true,
+          "rejection": "ValueError: source precision/state ceiling"
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+        "after": "for z in self.dual if z.bit_count() != 4)",
+        "before": "for z in self.dual)"
+      }
+    },
+    {
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+      "modes": [
+        {
+          "exit_code": 1,
+          "optimized": false,
+          "rejection": "ValueError: sharp history alphabet"
+        },
+        {
+          "exit_code": 1,
+          "optimized": true,
+          "rejection": "ValueError: sharp history alphabet"
+        }
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+      "name": "reuse-history-after-every-round",
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+      "replacement": {
+        "after": "exponent = 8*components",
+        "before": "exponent = 8*rounds*components"
+      }
+    }
+  ],
+  "status": "PASS_SEMANTIC_MUTATION_CONTROLS"
+}

research/precision-state-frontier/OVERLAP.json

@@ -0,0 +1,160 @@
+{
+  "additional_local_overlap": {
+    "path": "research/rounded-borrowing-contract/README.md",
+    "relationship": "Classifies rounded safe-translation lattices and saved residues at a different borrowed-child contract. Read as overlap; no claim that generic lattice or recovery counting is new."
+  },
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+    "head": "32890bc5de034ab8fc93ac88ead7279a6a416d04",
+    "matches": 0,
+    "scope": "All committed matching README/PROOF paths, including omitted sparse-checkout files; exact terms only."
+  },
+  "limits": [
+    "Remote query searches PR bodies and Discussions, not all code or proofs.",
+    "Cached local note corpus was at a8e0467c60fc851f7a94b1ad5524fd562f5922bd; canonical exact-term Git search supplements it.",
+    "No match is not evidence of global priority; closed and outside work are not exhaustively surveyed.",
+    "No new Discussion post, shared-ledger update or selected-frontier update. The scoped contribution is prepared for authorized PR publication."
+  ],
+  "nearest_work": [
+    {
+      "role": "Direct predecessor, sharp same-grid recovery; not claimed new.",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5323"
+    },
+    {
+      "role": "Actual finite kernel, half-away rounding, destructive owned cleanup.",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5035"
+    },
+    {
+      "role": "Actual physical matrix and access contract.",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4933"
+    },
+    {
+      "role": "Native code geometry.",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/4929"
+    },
+    {
+      "role": "Cheaper unchanged kernel arithmetic; does not price the new codec.",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5321"
+    },
+    {
+      "role": "Physical residual precision; absolute guards are not relative refinement.",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5333"
+    },
+    {
+      "role": "Proposed selected-caller exact grids; mathematical comparison, not source dependency.",
+      "url": "https://github.com/CrocSwap/integer-mult-bounds/pull/5438"
+    }
+  ],
+  "novelty_scope": "Exact relative-precision frontier and constructive coset codec for this source; sharp arbitrary fixed unimodular changing-frame history law. Classical coding duality and volume counting are explicitly credited.",
+  "refresh_utc": "2026-10-24T15:28:52.588764+00:00",
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+      "searched_at": "2026-10-24T14:46:22.687355+00:00",
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+        "recovery tags",
+        "guard bits",
+        "Construction A",
+        "weight enumerator",
+        "fiber size"
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+      "matches_total": 3,
+      "searched_at": "2026-10-24T14:55:18.874163+00:00",
+      "terms": [
+        "relative precision",
+        "five guard",
+        "51008161",
+        "362401",
+        "history growth",
+        "recovery tags"
+      ],
+      "warnings": []
+    }
+  ],
+  "specific_matches": [
+    {
+      "excerpt": "# Exact recovery tags with a sharp state bound for the rounded inverse code\n\nFINDING \u2014 the rounded inverse-code kernel has a sharp recovery-state bound: 13^8 states, or 30 packed bits, per real scalar coordinate of its 112 owners. Eight separate four-bit quotient tags give a simple 32-bit implementation of the injective output interface. This answers part of the ownership question left by [PR #5035](https://github.com/CrocSwap/integer-mult-bounds/pull/5035); it is not a reversible circuit, a fre",
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+      "matched_terms": [
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+      "title": "research/inverse-code-recovery-tags/README.md"
+    },
+    {
+      "excerpt": " T^2 < 2^200014 < 2^210000` (precision), and\n   `2T + 18 < 2^100003 < 2^210000` (tape).\n\nThus those five guards cannot fail alone while the stated hypotheses hold. `verify.py`\nchecks each maximal integer bound exactly. The inequalities are monotone over the stated\nnonnegative domain, which supplies the quantified implication rather than merely sampling it.\nFor the honest geometry, `M < 73S` follows from\n`rank_mass = 73 * live - 5120`, `physical = live + helpers + 10`, and positive helpers.\n**Non",
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+      "title": "research/t16-invoice-boundary-audit/README.md"
+    },
+    {
+      "excerpt": "589231b23e12ceef3e4bad129\"\n      }\n    ]\n  },\n  \"scope_status\": \"refined\",\n  \"actual_scope\": \"Exact recovery tags with a sharp state bound for the rounded inverse code\",\n  \"scope_change_reason\": \"Publish the completed, scoped Discussion result as a source-bound proof and replay package. The local interface or error obligation is separate from the complete physical caller.\",\n  \"bottleneck_link\": \"The physical construction needs funded precision and owned state. This result supplies one exact loca",
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+        "recovery tags"
+      ],
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+    }
+  ],
+  "status": "LOCAL_DRAFT_OVERLAP_REVIEW_NOT_A_NOVELTY_CERTIFICATE",
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+  }
+}

research/precision-state-frontier/PORTABLE.json

@@ -0,0 +1,18 @@
+{
+  "cli_rejections": 3,
+  "cli_roundtrips": [
+    {
+      "relative_bits": 4,
+      "states": 16
+    },
+    {
+      "relative_bits": 5,
+      "states": 1
+    }
+  ],
+  "empty_path": true,
+  "history_cli_bits": 533,
+  "normal_and_optimized_receipt_sha256": "77e707e013c8656146436ade8f561ebff0f553d5b66dc9c43f692f1fca18ae38",
+  "read_only_package": true,
+  "status": "PASS_PORTABLE_PRECISION_STATE_PACKAGE"
+}