{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LWYLFP2PBF33RK277K3E5DFPQZ","short_pith_number":"pith:LWYLFP2P","canonical_record":{"source":{"id":"1503.08936","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-31T07:22:11Z","cross_cats_sorted":["cs.FL","cs.LO"],"title_canon_sha256":"fdb13f1eeeb85d2439838abdad8b7b2f7068175e28da82136225773135c94424","abstract_canon_sha256":"d96bb32e26054f7e862e5b6f7adf9255f884f20103618b9693c407329d177b13"},"schema_version":"1.0"},"canonical_sha256":"5db0b2bf4f0977b8ab5ffab64e8caf86581f44fc324e710a7c8323cbbd73caee","source":{"kind":"arxiv","id":"1503.08936","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08936","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08936v2","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08936","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"LWYLFP2PBF33","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LWYLFP2PBF33RK27","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LWYLFP2P","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LWYLFP2PBF33RK277K3E5DFPQZ","target":"record","payload":{"canonical_record":{"source":{"id":"1503.08936","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-31T07:22:11Z","cross_cats_sorted":["cs.FL","cs.LO"],"title_canon_sha256":"fdb13f1eeeb85d2439838abdad8b7b2f7068175e28da82136225773135c94424","abstract_canon_sha256":"d96bb32e26054f7e862e5b6f7adf9255f884f20103618b9693c407329d177b13"},"schema_version":"1.0"},"canonical_sha256":"5db0b2bf4f0977b8ab5ffab64e8caf86581f44fc324e710a7c8323cbbd73caee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:02.860655Z","signature_b64":"ObtjL2lGLZFukzxP4P4mVR5ya8LCjHhwEryBE2NZAOm+B9IrRSVUjq8qPyD3VoVC6Pt9jKOQUinp0+tSSkkfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5db0b2bf4f0977b8ab5ffab64e8caf86581f44fc324e710a7c8323cbbd73caee","last_reissued_at":"2026-05-18T01:16:02.859961Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:02.859961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.08936","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":"2026-05-18T01:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z7OZK770rOeIlAi4MeHX9AQ7XQcBQs5lIGqEois9P2S63WSQh93w3WL7AnHdEBccUGwiNezgtGneb29P/TwiAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:28:04.504737Z"},"content_sha256":"21b6c294c77e6bed464bc3a6436ed6c213a0692d6f906d16b22ac07c96e50bc2","schema_version":"1.0","event_id":"sha256:21b6c294c77e6bed464bc3a6436ed6c213a0692d6f906d16b22ac07c96e50bc2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LWYLFP2PBF33RK277K3E5DFPQZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A model-theoretic characterization of monadic second order logic on infinite words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.FL","cs.LO"],"primary_cat":"math.LO","authors_text":"Samuel J. van Gool, Silvio Ghilardi","submitted_at":"2015-03-31T07:22:11Z","abstract_excerpt":"Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary predicate symbols.\n  Monadic second order logic over infinite words (S1S) can alternatively be described as a first-order logic interpreted in $\\mathcal{P}(\\omega)$, the power set Boolean algebra of the natural numbers, equipped with modal operators for 'initial', 'next' and 'future' states. We prove that the first-order theory of this structure is the model co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08936","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":"2026-05-18T01:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RxC5FlZKo8q1d+ALC36XS8Ahbkw7K+99sVMotCH9ZWs/zdyZxshaJxrP58KfUehI59qIKRWwcVpJ0OA9S0xKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:28:04.505090Z"},"content_sha256":"4638ff51582ad0245458274f7cc5002c5dc666b534fd43120266a362e8ea7a62","schema_version":"1.0","event_id":"sha256:4638ff51582ad0245458274f7cc5002c5dc666b534fd43120266a362e8ea7a62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LWYLFP2PBF33RK277K3E5DFPQZ/bundle.json","state_url":"https://pith.science/pith/LWYLFP2PBF33RK277K3E5DFPQZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LWYLFP2PBF33RK277K3E5DFPQZ/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":"2026-06-21T22:28:04Z","links":{"resolver":"https://pith.science/pith/LWYLFP2PBF33RK277K3E5DFPQZ","bundle":"https://pith.science/pith/LWYLFP2PBF33RK277K3E5DFPQZ/bundle.json","state":"https://pith.science/pith/LWYLFP2PBF33RK277K3E5DFPQZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LWYLFP2PBF33RK277K3E5DFPQZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LWYLFP2PBF33RK277K3E5DFPQZ","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":"d96bb32e26054f7e862e5b6f7adf9255f884f20103618b9693c407329d177b13","cross_cats_sorted":["cs.FL","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-31T07:22:11Z","title_canon_sha256":"fdb13f1eeeb85d2439838abdad8b7b2f7068175e28da82136225773135c94424"},"schema_version":"1.0","source":{"id":"1503.08936","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.08936","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"1503.08936v2","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.08936","created_at":"2026-05-18T01:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"LWYLFP2PBF33","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LWYLFP2PBF33RK27","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LWYLFP2P","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:4638ff51582ad0245458274f7cc5002c5dc666b534fd43120266a362e8ea7a62","target":"graph","created_at":"2026-05-18T01:16:02Z","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":"Monadic second order logic and linear temporal logic are two logical formalisms that can be used to describe classes of infinite words, i.e., first-order models based on the natural numbers with order, successor, and finitely many unary predicate symbols.\n  Monadic second order logic over infinite words (S1S) can alternatively be described as a first-order logic interpreted in $\\mathcal{P}(\\omega)$, the power set Boolean algebra of the natural numbers, equipped with modal operators for 'initial', 'next' and 'future' states. We prove that the first-order theory of this structure is the model co","authors_text":"Samuel J. van Gool, Silvio Ghilardi","cross_cats":["cs.FL","cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-31T07:22:11Z","title":"A model-theoretic characterization of monadic second order logic on infinite words"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08936","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":"sha256:21b6c294c77e6bed464bc3a6436ed6c213a0692d6f906d16b22ac07c96e50bc2","target":"record","created_at":"2026-05-18T01:16:02Z","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":"d96bb32e26054f7e862e5b6f7adf9255f884f20103618b9693c407329d177b13","cross_cats_sorted":["cs.FL","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-03-31T07:22:11Z","title_canon_sha256":"fdb13f1eeeb85d2439838abdad8b7b2f7068175e28da82136225773135c94424"},"schema_version":"1.0","source":{"id":"1503.08936","kind":"arxiv","version":2}},"canonical_sha256":"5db0b2bf4f0977b8ab5ffab64e8caf86581f44fc324e710a7c8323cbbd73caee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5db0b2bf4f0977b8ab5ffab64e8caf86581f44fc324e710a7c8323cbbd73caee","first_computed_at":"2026-05-18T01:16:02.859961Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:02.859961Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ObtjL2lGLZFukzxP4P4mVR5ya8LCjHhwEryBE2NZAOm+B9IrRSVUjq8qPyD3VoVC6Pt9jKOQUinp0+tSSkkfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:02.860655Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.08936","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21b6c294c77e6bed464bc3a6436ed6c213a0692d6f906d16b22ac07c96e50bc2","sha256:4638ff51582ad0245458274f7cc5002c5dc666b534fd43120266a362e8ea7a62"],"state_sha256":"d8e04563a70fe82763ad7ad35e4b28c286a2430b5720a1cc9c2a6a0a3fdec237"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"79f66FpweT0nTiuuXbBNkgSqrrJDLdQ+XxL/D/qsphW3FfCzumEHpP8NMEiL1hmwoDaIzKnnbPWibmU7dgHQAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:28:04.507163Z","bundle_sha256":"781ffb77225a46cabeeb36ee2807ea193de2c5675d3e98f754bd0aafa90a7647"}}