{"paper":{"title":"The Orientation Boundary for Step-Duplicating Recursors: Mechanized Impossibility, Escape, and Certification","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"A mechanized theorem proves that a fixed step-duplicating recursor lies outside all named direct termination measure classes.","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Moses Rahnama","submitted_at":"2025-11-26T00:50:17Z","abstract_excerpt":"We formalize the orientation boundary for first-order step-duplicating recursors, centered on the Right-Duplicating Recursor Schema (RDRS), $\\mathrm{recur}(b,s,\\mathrm{succ}(n))\\to\\mathrm{wrap}(s,\\mathrm{recur}(b,s,n))$. In Lean 4, the no-go side excludes twelve base direct-measure classes (two unconditional, six scalar growth, four tracked vector / pair), with arctic / tropical matrix continuations, a WPO-facing polynomial-branch corollary, and a KBO obstruction. Four meta-theorems organize the stack: projected-primary dominance, scalar-projection lift, mixed-matrix scalarization, and the sym"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We formalize the orientation boundary for first-order step-duplicating recursors: a mechanized object-level barrier theorem, proved without reductions or undecidability, showing that a fixed terminating recursor lies outside named direct termination-measure classes.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The twelve base measure classes (additive, transparency-constrained compositional, scalar growth families, tracked vector and pair families) together with the arctic/tropical extensions and scalar-dominance data exhaust the relevant direct termination measures for the recursor in question.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Lean 4 formalization establishes an object-level orientation boundary showing fixed step-duplicating recursors lie outside explicit direct termination-measure classes, with three escape routes and tool connections.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A mechanized theorem proves that a fixed step-duplicating recursor lies outside all named direct termination measure classes.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"dc9ee7d7b51f6660546600dad145468df4c11014211785d5d2f577083bb5758f"},"source":{"id":"2512.00081","kind":"arxiv","version":10},"verdict":{"id":"a77d3de9-2cb7-484f-bd56-c467d560e9e2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-17T05:35:09.055278Z","strongest_claim":"We formalize the orientation boundary for first-order step-duplicating recursors: a mechanized object-level barrier theorem, proved without reductions or undecidability, showing that a fixed terminating recursor lies outside named direct termination-measure classes.","one_line_summary":"Lean 4 formalization establishes an object-level orientation boundary showing fixed step-duplicating recursors lie outside explicit direct termination-measure classes, with three escape routes and tool connections.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The twelve base measure classes (additive, transparency-constrained compositional, scalar growth families, tracked vector and pair families) together with the arctic/tropical extensions and scalar-dominance data exhaust the relevant direct termination measures for the recursor in question.","pith_extraction_headline":"A mechanized theorem proves that a fixed step-duplicating recursor lies outside all named direct termination measure classes."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.00081/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"28b6037826a3a83cfc8505416140fe7083bd1164e146eb8a843dfafed4e1ecdd"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}