{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:KL3BIDTZ72QR4ELYWIS5COE7UL","short_pith_number":"pith:KL3BIDTZ","schema_version":"1.0","canonical_sha256":"52f6140e79fea11e1178b225d1389fa2c557346bb4a04360a3afd8410a4e58b5","source":{"kind":"arxiv","id":"1709.09036","version":1},"attestation_state":"computed","paper":{"title":"The strength of SCT soundness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Emanuele Frittaion, Florian Pelupessy, Keita Yokoyama, Silvia Steila","submitted_at":"2017-09-26T14:24:29Z","abstract_excerpt":"In this paper we continue the study, from Frittaion, Steila and Yokoyama (2017), on size-change termination in the context of Reverse Mathematics. We analyze the soundness of the SCT method. In particular, we prove that the statement \"any program which satisfies the combinatorial condition provided by the SCT criterion is terminating\" is equivalent to $\\mathrm{WO}(\\omega_3)$ over $\\mathsf{RCA_0}$"},"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":false},"canonical_record":{"source":{"id":"1709.09036","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2017-09-26T14:24:29Z","cross_cats_sorted":[],"title_canon_sha256":"c32a41e9b1e3c76dd7230056c1b4200ed1d58ce257d1cdf12b77d286b312a7c3","abstract_canon_sha256":"f4430daa58db93f99dffb6c461af1d17b4b936678a4968b4c5203fc771e9b14e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:21.309469Z","signature_b64":"Qq9Tmq/eMeZPJ/AttLTAKtTtcYDzsmbf5BIoDziaWhnT9QgfbKC3AFXG2+bxu5NB+qm1eonBRAHaFZxk/u3mCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"52f6140e79fea11e1178b225d1389fa2c557346bb4a04360a3afd8410a4e58b5","last_reissued_at":"2026-05-18T00:34:21.308956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:21.308956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The strength of SCT soundness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Emanuele Frittaion, Florian Pelupessy, Keita Yokoyama, Silvia Steila","submitted_at":"2017-09-26T14:24:29Z","abstract_excerpt":"In this paper we continue the study, from Frittaion, Steila and Yokoyama (2017), on size-change termination in the context of Reverse Mathematics. We analyze the soundness of the SCT method. In particular, we prove that the statement \"any program which satisfies the combinatorial condition provided by the SCT criterion is terminating\" is equivalent to $\\mathrm{WO}(\\omega_3)$ over $\\mathsf{RCA_0}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09036","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.09036","created_at":"2026-05-18T00:34:21.309035+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.09036v1","created_at":"2026-05-18T00:34:21.309035+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09036","created_at":"2026-05-18T00:34:21.309035+00:00"},{"alias_kind":"pith_short_12","alias_value":"KL3BIDTZ72QR","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_16","alias_value":"KL3BIDTZ72QR4ELY","created_at":"2026-05-18T12:31:24.725408+00:00"},{"alias_kind":"pith_short_8","alias_value":"KL3BIDTZ","created_at":"2026-05-18T12:31:24.725408+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2604.22844","citing_title":"Operational Inexpressibility at the Step-Duplicating Primitive Recursor Orientation Boundary","ref_index":13,"is_internal_anchor":true},{"citing_arxiv_id":"2604.22844","citing_title":"Operational Inexpressibility at the Step-Duplicating Primitive Recursor Orientation Boundary","ref_index":13,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KL3BIDTZ72QR4ELYWIS5COE7UL","json":"https://pith.science/pith/KL3BIDTZ72QR4ELYWIS5COE7UL.json","graph_json":"https://pith.science/api/pith-number/KL3BIDTZ72QR4ELYWIS5COE7UL/graph.json","events_json":"https://pith.science/api/pith-number/KL3BIDTZ72QR4ELYWIS5COE7UL/events.json","paper":"https://pith.science/paper/KL3BIDTZ"},"agent_actions":{"view_html":"https://pith.science/pith/KL3BIDTZ72QR4ELYWIS5COE7UL","download_json":"https://pith.science/pith/KL3BIDTZ72QR4ELYWIS5COE7UL.json","view_paper":"https://pith.science/paper/KL3BIDTZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.09036&json=true","fetch_graph":"https://pith.science/api/pith-number/KL3BIDTZ72QR4ELYWIS5COE7UL/graph.json","fetch_events":"https://pith.science/api/pith-number/KL3BIDTZ72QR4ELYWIS5COE7UL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KL3BIDTZ72QR4ELYWIS5COE7UL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KL3BIDTZ72QR4ELYWIS5COE7UL/action/storage_attestation","attest_author":"https://pith.science/pith/KL3BIDTZ72QR4ELYWIS5COE7UL/action/author_attestation","sign_citation":"https://pith.science/pith/KL3BIDTZ72QR4ELYWIS5COE7UL/action/citation_signature","submit_replication":"https://pith.science/pith/KL3BIDTZ72QR4ELYWIS5COE7UL/action/replication_record"}},"created_at":"2026-05-18T00:34:21.309035+00:00","updated_at":"2026-05-18T00:34:21.309035+00:00"}