{"paper":{"title":"Foundational Analysis Of The Solvability Complexity Index: The Weihrauch-SCI Intermediate Hierarchy","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"The unrestricted SCI model fails to be a Type-2 computability model, but restricting its base post-processing to continuous, Borel or Baire classes produces well-posed and representation-invariant intermediate hierarchies.","cross_cats":["cs.LO","math.SP"],"primary_cat":"math.LO","authors_text":"Christopher Sorg","submitted_at":"2026-03-19T14:24:40Z","abstract_excerpt":"The Solvability Complexity Index (SCI) provides an extensional limit-height formalism for recovering a target map $\\Xi$ from finite samples of an evaluation interface $\\Lambda\\subseteq\\mathbb C^\\Omega$ by finite-height towers of pointwise limits. We first give a foundational analysis of what this extensional framework does and does not determine. We show that the SCI separation axiom is equivalent to a factorization of $\\Xi$ through the full evaluation table, and we isolate the minimal logical role of $\\Lambda$ as an information interface.\n  To connect the SCI to Type-2 computability and Weihr"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The unrestricted raw type-G SCI model is generally not a computability model in the Type-2/Weihrauch sense; restricting admissible base-level post-processing to regularity classes yields hierarchies that are well-posed and representation-invariant.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the chosen regularity restrictions (continuous/Borel/Baire) together with fixed versus adaptive query policies are sufficient to recover a robust computability model while preserving the essential separation properties of the original SCI framework.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Defines the Weihrauch-SCI rank as the minimal number of iterated limit-oracles needed in the Weihrauch sense and proves that restricting SCI post-processing to continuous/Borel/Baire classes yields well-posed hierarchies with comparison theorems.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The unrestricted SCI model fails to be a Type-2 computability model, but restricting its base post-processing to continuous, Borel or Baire classes produces well-posed and representation-invariant intermediate hierarchies.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"9eb2d41382e9db98764eae0774798ef48f971679de804ba3fa65327ce6ef46b7"},"source":{"id":"2603.18955","kind":"arxiv","version":2},"verdict":{"id":"7c9860e5-c5df-437d-8731-8efb9762abf5","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T08:32:59.834370Z","strongest_claim":"The unrestricted raw type-G SCI model is generally not a computability model in the Type-2/Weihrauch sense; restricting admissible base-level post-processing to regularity classes yields hierarchies that are well-posed and representation-invariant.","one_line_summary":"Defines the Weihrauch-SCI rank as the minimal number of iterated limit-oracles needed in the Weihrauch sense and proves that restricting SCI post-processing to continuous/Borel/Baire classes yields well-posed hierarchies with comparison theorems.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the chosen regularity restrictions (continuous/Borel/Baire) together with fixed versus adaptive query policies are sufficient to recover a robust computability model while preserving the essential separation properties of the original SCI framework.","pith_extraction_headline":"The unrestricted SCI model fails to be a Type-2 computability model, but restricting its base post-processing to continuous, Borel or Baire classes produces well-posed and representation-invariant intermediate hierarchies."},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5959bd2224c02310f16d9402bb148e4a03b2c3e0a8a564c6b3811e94eafb106d"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}