{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:UKENMDJKJIC7MTLEKFILOPFEPP","short_pith_number":"pith:UKENMDJK","canonical_record":{"source":{"id":"1804.09451","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-25T09:42:52Z","cross_cats_sorted":[],"title_canon_sha256":"cffed18f3448eb62f14ac25b088301bf856758594e8908fe0d4e54a15c104e9d","abstract_canon_sha256":"2681932778d7f01d3f603f99a261af1cf15c31b29b76fd7b459ec3f86cf2dd57"},"schema_version":"1.0"},"canonical_sha256":"a288d60d2a4a05f64d645150b73ca47be18f0908860dd0b2a8fc6435dd524b99","source":{"kind":"arxiv","id":"1804.09451","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09451","created_at":"2026-05-18T00:14:13Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09451v2","created_at":"2026-05-18T00:14:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09451","created_at":"2026-05-18T00:14:13Z"},{"alias_kind":"pith_short_12","alias_value":"UKENMDJKJIC7","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UKENMDJKJIC7MTLE","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UKENMDJK","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:UKENMDJKJIC7MTLEKFILOPFEPP","target":"record","payload":{"canonical_record":{"source":{"id":"1804.09451","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-25T09:42:52Z","cross_cats_sorted":[],"title_canon_sha256":"cffed18f3448eb62f14ac25b088301bf856758594e8908fe0d4e54a15c104e9d","abstract_canon_sha256":"2681932778d7f01d3f603f99a261af1cf15c31b29b76fd7b459ec3f86cf2dd57"},"schema_version":"1.0"},"canonical_sha256":"a288d60d2a4a05f64d645150b73ca47be18f0908860dd0b2a8fc6435dd524b99","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:13.708709Z","signature_b64":"4PY0TZbYxYF589DpH6q+AkDFrPvePcDEK2klMRfCZo7bWevYOKnnXqhDfEEjviP2Np9HUY2jEZZnQ9ikycdnDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a288d60d2a4a05f64d645150b73ca47be18f0908860dd0b2a8fc6435dd524b99","last_reissued_at":"2026-05-18T00:14:13.707878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:13.707878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.09451","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GGJDn0wlldCe9B8PphoiJMb82MvA84TqjbFC7FTdjxdRJewsvHSg8VAVLN7fhSD6zCM5uUbLYt7B0WSq/zPoAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:36:34.612366Z"},"content_sha256":"2788f8f901bced891fd4fb9ba0b83082cbae8763e10da3922e703550dd8540be","schema_version":"1.0","event_id":"sha256:2788f8f901bced891fd4fb9ba0b83082cbae8763e10da3922e703550dd8540be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:UKENMDJKJIC7MTLEKFILOPFEPP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Provability Logic and the Completeness Principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Albert Visser, Jetze Zoethout","submitted_at":"2018-04-25T09:42:52Z","abstract_excerpt":"In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\\Box$ and $\\triangle$ that prove the schemes $A\\to\\triangle A$ and $\\Box\\triangle S\\to\\Box S$ for $S\\in\\Sigma_1$. Using this theorem, we determine the logic of fast provability for a number of intuitionistic theories. Furthermore, we reprove a theorem previously obtained by M. Ardeshir and S. Mojtaba Mojtahedi determining the $\\Sigma_1$-provability logic of Heyting Arithmetic."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09451","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:14:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Qa0LPuxU4VtHGPXmfl/Ze3RDxdRNEYSvIB4MgcYB8xspt8FMj2FYfrXJeERfd7ou4GJ06htHZaYPu5QVSWQDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:36:34.613132Z"},"content_sha256":"0d3634b2163039d99c0fa68f697b9593c12d5f084538411714ad05c7109f6d1b","schema_version":"1.0","event_id":"sha256:0d3634b2163039d99c0fa68f697b9593c12d5f084538411714ad05c7109f6d1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UKENMDJKJIC7MTLEKFILOPFEPP/bundle.json","state_url":"https://pith.science/pith/UKENMDJKJIC7MTLEKFILOPFEPP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UKENMDJKJIC7MTLEKFILOPFEPP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T12:36:34Z","links":{"resolver":"https://pith.science/pith/UKENMDJKJIC7MTLEKFILOPFEPP","bundle":"https://pith.science/pith/UKENMDJKJIC7MTLEKFILOPFEPP/bundle.json","state":"https://pith.science/pith/UKENMDJKJIC7MTLEKFILOPFEPP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UKENMDJKJIC7MTLEKFILOPFEPP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:UKENMDJKJIC7MTLEKFILOPFEPP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"2681932778d7f01d3f603f99a261af1cf15c31b29b76fd7b459ec3f86cf2dd57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-25T09:42:52Z","title_canon_sha256":"cffed18f3448eb62f14ac25b088301bf856758594e8908fe0d4e54a15c104e9d"},"schema_version":"1.0","source":{"id":"1804.09451","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.09451","created_at":"2026-05-18T00:14:13Z"},{"alias_kind":"arxiv_version","alias_value":"1804.09451v2","created_at":"2026-05-18T00:14:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.09451","created_at":"2026-05-18T00:14:13Z"},{"alias_kind":"pith_short_12","alias_value":"UKENMDJKJIC7","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"UKENMDJKJIC7MTLE","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"UKENMDJK","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:0d3634b2163039d99c0fa68f697b9593c12d5f084538411714ad05c7109f6d1b","target":"graph","created_at":"2026-05-18T00:14:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we study the provability logic of intuitionistic theories of arithmetic that prove their own completeness. We prove a completeness theorem for theories equipped with two provability predicates $\\Box$ and $\\triangle$ that prove the schemes $A\\to\\triangle A$ and $\\Box\\triangle S\\to\\Box S$ for $S\\in\\Sigma_1$. Using this theorem, we determine the logic of fast provability for a number of intuitionistic theories. Furthermore, we reprove a theorem previously obtained by M. Ardeshir and S. Mojtaba Mojtahedi determining the $\\Sigma_1$-provability logic of Heyting Arithmetic.","authors_text":"Albert Visser, Jetze Zoethout","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-25T09:42:52Z","title":"Provability Logic and the Completeness Principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.09451","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2788f8f901bced891fd4fb9ba0b83082cbae8763e10da3922e703550dd8540be","target":"record","created_at":"2026-05-18T00:14:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2681932778d7f01d3f603f99a261af1cf15c31b29b76fd7b459ec3f86cf2dd57","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-04-25T09:42:52Z","title_canon_sha256":"cffed18f3448eb62f14ac25b088301bf856758594e8908fe0d4e54a15c104e9d"},"schema_version":"1.0","source":{"id":"1804.09451","kind":"arxiv","version":2}},"canonical_sha256":"a288d60d2a4a05f64d645150b73ca47be18f0908860dd0b2a8fc6435dd524b99","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a288d60d2a4a05f64d645150b73ca47be18f0908860dd0b2a8fc6435dd524b99","first_computed_at":"2026-05-18T00:14:13.707878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:14:13.707878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4PY0TZbYxYF589DpH6q+AkDFrPvePcDEK2klMRfCZo7bWevYOKnnXqhDfEEjviP2Np9HUY2jEZZnQ9ikycdnDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:14:13.708709Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.09451","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2788f8f901bced891fd4fb9ba0b83082cbae8763e10da3922e703550dd8540be","sha256:0d3634b2163039d99c0fa68f697b9593c12d5f084538411714ad05c7109f6d1b"],"state_sha256":"fc2e1a97f0dedca1ec0d3a2ff1b0eb6b98f32a8eb6725aca0fe4f54dc369b06e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wk5OcbmBz1mLqwfu+4kiGRvkc2RF02h/+mLdPdKRuRKKsfkT6l92WoeeAj9rFrKvM/eE6iiu1zGC8c61fc0ECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:36:34.617109Z","bundle_sha256":"d6a2d598f59d44cf96c92b505b103d37fd90568b6c43210c02a07857bbfbd8d2"}}