{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:NMGNNUMBPZIKOFM5QTYCPYHFHD","short_pith_number":"pith:NMGNNUMB","schema_version":"1.0","canonical_sha256":"6b0cd6d1817e50a7159d84f027e0e538edfdc99ebca47ffc69a0ec7131fef105","source":{"kind":"arxiv","id":"1210.4809","version":1},"attestation_state":"computed","paper":{"title":"On provability logics with linearly ordered modalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Fern\\'andez-Duque, Joost J. Joosten, Lev D. Beklemishev","submitted_at":"2012-10-17T18:14:23Z","abstract_excerpt":"We introduce the logics GLP(\\Lambda), a generalization of Japaridze's polymodal provability logic GLP(\\omega) where \\Lambda is any linearly ordered set representing a hierarchy of provability operators of increasing strength.\n  We shall provide a reduction of these logics to GLP(\\omega) yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP(\\Lambda) and the decidability of GLP(\\Lambda) for recursive orderings \\Lambda. Further, we give a restricted axiomatization of the variable-free fragment of GLP(\\Lambda)."},"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":"1210.4809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-10-17T18:14:23Z","cross_cats_sorted":[],"title_canon_sha256":"afc16d45c62f1b78fa93e40a6ec74fb7334f7862deac5f7484267c837ad4e69a","abstract_canon_sha256":"03fbac2a012dd4dc2533ee73787576132e16d7a9f653ab3f0f776828b4a4d334"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:42:56.176910Z","signature_b64":"rNWsXNPElW66YirfuEGNHope9XwU/bnz503K9be+PNXw0HykFq8p31PYR0jO0XxlZV+1NHqZy1UhpLQDoW5KCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b0cd6d1817e50a7159d84f027e0e538edfdc99ebca47ffc69a0ec7131fef105","last_reissued_at":"2026-05-18T03:42:56.176472Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:42:56.176472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On provability logics with linearly ordered modalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"David Fern\\'andez-Duque, Joost J. Joosten, Lev D. Beklemishev","submitted_at":"2012-10-17T18:14:23Z","abstract_excerpt":"We introduce the logics GLP(\\Lambda), a generalization of Japaridze's polymodal provability logic GLP(\\omega) where \\Lambda is any linearly ordered set representing a hierarchy of provability operators of increasing strength.\n  We shall provide a reduction of these logics to GLP(\\omega) yielding among other things a finitary proof of the normal form theorem for the variable-free fragment of GLP(\\Lambda) and the decidability of GLP(\\Lambda) for recursive orderings \\Lambda. Further, we give a restricted axiomatization of the variable-free fragment of GLP(\\Lambda)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.4809","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":"1210.4809","created_at":"2026-05-18T03:42:56.176537+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.4809v1","created_at":"2026-05-18T03:42:56.176537+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.4809","created_at":"2026-05-18T03:42:56.176537+00:00"},{"alias_kind":"pith_short_12","alias_value":"NMGNNUMBPZIK","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"NMGNNUMBPZIKOFM5","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"NMGNNUMB","created_at":"2026-05-18T12:27:16.716162+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NMGNNUMBPZIKOFM5QTYCPYHFHD","json":"https://pith.science/pith/NMGNNUMBPZIKOFM5QTYCPYHFHD.json","graph_json":"https://pith.science/api/pith-number/NMGNNUMBPZIKOFM5QTYCPYHFHD/graph.json","events_json":"https://pith.science/api/pith-number/NMGNNUMBPZIKOFM5QTYCPYHFHD/events.json","paper":"https://pith.science/paper/NMGNNUMB"},"agent_actions":{"view_html":"https://pith.science/pith/NMGNNUMBPZIKOFM5QTYCPYHFHD","download_json":"https://pith.science/pith/NMGNNUMBPZIKOFM5QTYCPYHFHD.json","view_paper":"https://pith.science/paper/NMGNNUMB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.4809&json=true","fetch_graph":"https://pith.science/api/pith-number/NMGNNUMBPZIKOFM5QTYCPYHFHD/graph.json","fetch_events":"https://pith.science/api/pith-number/NMGNNUMBPZIKOFM5QTYCPYHFHD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NMGNNUMBPZIKOFM5QTYCPYHFHD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NMGNNUMBPZIKOFM5QTYCPYHFHD/action/storage_attestation","attest_author":"https://pith.science/pith/NMGNNUMBPZIKOFM5QTYCPYHFHD/action/author_attestation","sign_citation":"https://pith.science/pith/NMGNNUMBPZIKOFM5QTYCPYHFHD/action/citation_signature","submit_replication":"https://pith.science/pith/NMGNNUMBPZIKOFM5QTYCPYHFHD/action/replication_record"}},"created_at":"2026-05-18T03:42:56.176537+00:00","updated_at":"2026-05-18T03:42:56.176537+00:00"}