{"paper":{"title":"Syntactic Separation Implies Computational Indistinguishability: An Abstract Obstruction Theorem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CR"],"primary_cat":"cs.LO","authors_text":"Fabio F.G. Buono","submitted_at":"2026-06-28T03:46:33Z","abstract_excerpt":"We prove that syntactic separation implies computational indistinguishability. A local syntactic system R acts on terms within radius r0 without consulting any model; when two Skolem functions are syntactically separated in R, no derivation can prove their equivalence (Case 1), and any sound local extension requires Omega(n) steps, improving to Omega(2^n) under clause-per-configuration encoding (Case 2). Both bounds are new: the derivation-length lower bound does not appear in prior work on Skolemization or saturation proving, and the cryptographic reading, syntactic separation as ciphertext i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29177","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.29177/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":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}