{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:5T7VJKKD2F4WC7AIM2C4DLQGVN","short_pith_number":"pith:5T7VJKKD","schema_version":"1.0","canonical_sha256":"ecff54a943d179617c086685c1ae06ab6d98f5aec487467749c770fc2eb339df","source":{"kind":"arxiv","id":"2603.18955","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":true},"canonical_record":{"source":{"id":"2603.18955","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2026-03-19T14:24:40Z","cross_cats_sorted":["cs.LO","math.SP"],"title_canon_sha256":"a8857e9ac229ecf2834f1ef935eb08bfdbad8db6df2e3a6cced350d700f66320","abstract_canon_sha256":"4ef008aa133767fb41aa78f49fb32d6bca69a41ad984e1787b358e7e901e6f14"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:38:59.610921Z","signature_b64":"c+VrwS/m3uJj8XpldDk16wdSwh4NI5HZHkmooiNVLv5BwiAuxnYux66njJCDPsxGqoO4D5B29nqDQdwP9zReAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecff54a943d179617c086685c1ae06ab6d98f5aec487467749c770fc2eb339df","last_reissued_at":"2026-05-17T23:38:59.610170Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:38:59.610170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2603.18955","created_at":"2026-05-17T23:38:59.610280+00:00"},{"alias_kind":"arxiv_version","alias_value":"2603.18955v2","created_at":"2026-05-17T23:38:59.610280+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.18955","created_at":"2026-05-17T23:38:59.610280+00:00"},{"alias_kind":"pith_short_12","alias_value":"5T7VJKKD2F4W","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"5T7VJKKD2F4WC7AI","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"5T7VJKKD","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2604.12750","citing_title":"From Witness-Space Sharpness To Family-Pointwise Exactness For The Solvability Complexity Index","ref_index":10,"is_internal_anchor":true},{"citing_arxiv_id":"2604.12750","citing_title":"From Witness-Space Sharpness To Family-Pointwise Exactness For The Solvability Complexity Index","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5T7VJKKD2F4WC7AIM2C4DLQGVN","json":"https://pith.science/pith/5T7VJKKD2F4WC7AIM2C4DLQGVN.json","graph_json":"https://pith.science/api/pith-number/5T7VJKKD2F4WC7AIM2C4DLQGVN/graph.json","events_json":"https://pith.science/api/pith-number/5T7VJKKD2F4WC7AIM2C4DLQGVN/events.json","paper":"https://pith.science/paper/5T7VJKKD"},"agent_actions":{"view_html":"https://pith.science/pith/5T7VJKKD2F4WC7AIM2C4DLQGVN","download_json":"https://pith.science/pith/5T7VJKKD2F4WC7AIM2C4DLQGVN.json","view_paper":"https://pith.science/paper/5T7VJKKD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2603.18955&json=true","fetch_graph":"https://pith.science/api/pith-number/5T7VJKKD2F4WC7AIM2C4DLQGVN/graph.json","fetch_events":"https://pith.science/api/pith-number/5T7VJKKD2F4WC7AIM2C4DLQGVN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5T7VJKKD2F4WC7AIM2C4DLQGVN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5T7VJKKD2F4WC7AIM2C4DLQGVN/action/storage_attestation","attest_author":"https://pith.science/pith/5T7VJKKD2F4WC7AIM2C4DLQGVN/action/author_attestation","sign_citation":"https://pith.science/pith/5T7VJKKD2F4WC7AIM2C4DLQGVN/action/citation_signature","submit_replication":"https://pith.science/pith/5T7VJKKD2F4WC7AIM2C4DLQGVN/action/replication_record"}},"created_at":"2026-05-17T23:38:59.610280+00:00","updated_at":"2026-05-17T23:38:59.610280+00:00"}