{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:Q4JNWBJFZXNOXD3YGKZNR3LVJB","short_pith_number":"pith:Q4JNWBJF","schema_version":"1.0","canonical_sha256":"8712db0525cddaeb8f7832b2d8ed7548756109d5d9996374e470bd1ba86cba93","source":{"kind":"arxiv","id":"2606.01165","version":1},"attestation_state":"computed","paper":{"title":"G\\\"odel coding on fibrations and geminal categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.CT"],"primary_cat":"math.LO","authors_text":"Yuto Ikeda","submitted_at":"2026-05-31T11:14:17Z","abstract_excerpt":"Ramesh's 2023 dissertation introduces the categorical notions of introspective theories and geminal categories, which formalize \"self-internalizing\" structures sharing the form of L\\\"ob's theorem ($\\Box A \\vdash A$ implies $\\vdash A$). We reorganize the theory of geminal categories in a self-contained manner by introducing \"code structures on fibrations,\" which serve as a categorical abstraction of G\\\"odel coding. This framework leads to a significant simplification of the proof of L\\\"ob's theorem for geminal categories, as well as to a new categorical counterpart of the G\\\"odel-L\\\"ob axiom ($"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.01165","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2026-05-31T11:14:17Z","cross_cats_sorted":["cs.LO","math.CT"],"title_canon_sha256":"56c4c7ad4ecdb40963a586dfeb0e94f178cd3a7f41811c8818d9d23e280fada1","abstract_canon_sha256":"fbb97a26ec315805ac399a01893d98ee713571ca221e4f5f5b427a36d2192644"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:25.519051Z","signature_b64":"KR6UruPkKR8ywZm+MZJSawH4VEcwWHxZ0SfXgH7sWvJCPYz/1w41AP6RFQz8Xahl2X6ChHqZN0XJV70ZGZC0CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8712db0525cddaeb8f7832b2d8ed7548756109d5d9996374e470bd1ba86cba93","last_reissued_at":"2026-06-02T02:04:25.518693Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:25.518693Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"G\\\"odel coding on fibrations and geminal categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LO","math.CT"],"primary_cat":"math.LO","authors_text":"Yuto Ikeda","submitted_at":"2026-05-31T11:14:17Z","abstract_excerpt":"Ramesh's 2023 dissertation introduces the categorical notions of introspective theories and geminal categories, which formalize \"self-internalizing\" structures sharing the form of L\\\"ob's theorem ($\\Box A \\vdash A$ implies $\\vdash A$). We reorganize the theory of geminal categories in a self-contained manner by introducing \"code structures on fibrations,\" which serve as a categorical abstraction of G\\\"odel coding. This framework leads to a significant simplification of the proof of L\\\"ob's theorem for geminal categories, as well as to a new categorical counterpart of the G\\\"odel-L\\\"ob axiom ($"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01165","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/2606.01165/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.01165","created_at":"2026-06-02T02:04:25.518754+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.01165v1","created_at":"2026-06-02T02:04:25.518754+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01165","created_at":"2026-06-02T02:04:25.518754+00:00"},{"alias_kind":"pith_short_12","alias_value":"Q4JNWBJFZXNO","created_at":"2026-06-02T02:04:25.518754+00:00"},{"alias_kind":"pith_short_16","alias_value":"Q4JNWBJFZXNOXD3Y","created_at":"2026-06-02T02:04:25.518754+00:00"},{"alias_kind":"pith_short_8","alias_value":"Q4JNWBJF","created_at":"2026-06-02T02:04:25.518754+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/Q4JNWBJFZXNOXD3YGKZNR3LVJB","json":"https://pith.science/pith/Q4JNWBJFZXNOXD3YGKZNR3LVJB.json","graph_json":"https://pith.science/api/pith-number/Q4JNWBJFZXNOXD3YGKZNR3LVJB/graph.json","events_json":"https://pith.science/api/pith-number/Q4JNWBJFZXNOXD3YGKZNR3LVJB/events.json","paper":"https://pith.science/paper/Q4JNWBJF"},"agent_actions":{"view_html":"https://pith.science/pith/Q4JNWBJFZXNOXD3YGKZNR3LVJB","download_json":"https://pith.science/pith/Q4JNWBJFZXNOXD3YGKZNR3LVJB.json","view_paper":"https://pith.science/paper/Q4JNWBJF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.01165&json=true","fetch_graph":"https://pith.science/api/pith-number/Q4JNWBJFZXNOXD3YGKZNR3LVJB/graph.json","fetch_events":"https://pith.science/api/pith-number/Q4JNWBJFZXNOXD3YGKZNR3LVJB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Q4JNWBJFZXNOXD3YGKZNR3LVJB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Q4JNWBJFZXNOXD3YGKZNR3LVJB/action/storage_attestation","attest_author":"https://pith.science/pith/Q4JNWBJFZXNOXD3YGKZNR3LVJB/action/author_attestation","sign_citation":"https://pith.science/pith/Q4JNWBJFZXNOXD3YGKZNR3LVJB/action/citation_signature","submit_replication":"https://pith.science/pith/Q4JNWBJFZXNOXD3YGKZNR3LVJB/action/replication_record"}},"created_at":"2026-06-02T02:04:25.518754+00:00","updated_at":"2026-06-02T02:04:25.518754+00:00"}