{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CEULOM53H4RKDFFGNCRXLG72MB","short_pith_number":"pith:CEULOM53","canonical_record":{"source":{"id":"1809.03896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-09-10T12:05:05Z","cross_cats_sorted":[],"title_canon_sha256":"3de700cea46895a135a33bdea049897534fed6229c01c5fbff3ccea916b87d75","abstract_canon_sha256":"a8dddce08e504a9a2cfbe16b42bf3fc68ad4c7d5c03612b082b3898474c9a854"},"schema_version":"1.0"},"canonical_sha256":"1128b733bb3f22a194a668a3759bfa60528d933cd9468d5d8c6553c8354dfc9b","source":{"kind":"arxiv","id":"1809.03896","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03896","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03896v1","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03896","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"CEULOM53H4RK","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CEULOM53H4RKDFFG","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CEULOM53","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CEULOM53H4RKDFFGNCRXLG72MB","target":"record","payload":{"canonical_record":{"source":{"id":"1809.03896","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-09-10T12:05:05Z","cross_cats_sorted":[],"title_canon_sha256":"3de700cea46895a135a33bdea049897534fed6229c01c5fbff3ccea916b87d75","abstract_canon_sha256":"a8dddce08e504a9a2cfbe16b42bf3fc68ad4c7d5c03612b082b3898474c9a854"},"schema_version":"1.0"},"canonical_sha256":"1128b733bb3f22a194a668a3759bfa60528d933cd9468d5d8c6553c8354dfc9b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:57.787087Z","signature_b64":"Be4K5uNukoBcg8s+6gdh+PbRTCLT/LRkz/tztgUe9jXJeE4j5onHNmTSspqMbxxU6NtOQ+xbryc/NRr4QEFVAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1128b733bb3f22a194a668a3759bfa60528d933cd9468d5d8c6553c8354dfc9b","last_reissued_at":"2026-05-18T00:05:57.786673Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:57.786673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.03896","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sP9uF2n6DE7qXVPgiDDpX87ID5Fr3sKQLmrVnFIRDmo6LP3YI7G69Sa9lsfEa8ECqG3n4L6KK6SeeVIRZ08MBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:04:55.495363Z"},"content_sha256":"fb28f65c02a1cebaa1943ed33ceee614be24f17ffbb93b03cfd2fe9966273ec8","schema_version":"1.0","event_id":"sha256:fb28f65c02a1cebaa1943ed33ceee614be24f17ffbb93b03cfd2fe9966273ec8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CEULOM53H4RKDFFGNCRXLG72MB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Power of the Weak","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Alessandro Facchini, Fabio Zanasi, Facundo Carreiro, Yde Venema","submitted_at":"2018-09-10T12:05:05Z","abstract_excerpt":"A landmark result in the study of logics for formal verification is Janin & Walukiewicz's theorem, stating that the modal $\\mu$-calculus ($\\mu\\mathrm{ML}$) is equivalent modulo bisimilarity to standard monadic second-order logic (here abbreviated as $\\mathrm{smso}$), over the class of labelled transition systems (LTSs for short). Our work proves two results of the same kind, one for the alternation-free fragment of $\\mu\\mathrm{ML}$ ($\\mu_D\\mathrm{ML}$) and one for weak $\\mathrm{mso}$ ($\\mathrm{wmso}$). Whereas it was known that $\\mu_D\\mathrm{ML}$ and $\\mathrm{wmso}$ are equivalent modulo bisim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03896","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:05:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TGV9ig3GrAxTWzX4StFmJ+GIZVu5NmSACPSiB77YhTC1isKkUDhQQXQ7OrT1Q6h9MeORu+k/IjNwtxK0on8fCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:04:55.495714Z"},"content_sha256":"90fc4614765288f2adf7d3b719d7ce9d404670890aefe4e2700a966035a761d0","schema_version":"1.0","event_id":"sha256:90fc4614765288f2adf7d3b719d7ce9d404670890aefe4e2700a966035a761d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CEULOM53H4RKDFFGNCRXLG72MB/bundle.json","state_url":"https://pith.science/pith/CEULOM53H4RKDFFGNCRXLG72MB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CEULOM53H4RKDFFGNCRXLG72MB/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":"2026-06-30T07:04:55Z","links":{"resolver":"https://pith.science/pith/CEULOM53H4RKDFFGNCRXLG72MB","bundle":"https://pith.science/pith/CEULOM53H4RKDFFGNCRXLG72MB/bundle.json","state":"https://pith.science/pith/CEULOM53H4RKDFFGNCRXLG72MB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CEULOM53H4RKDFFGNCRXLG72MB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CEULOM53H4RKDFFGNCRXLG72MB","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":"a8dddce08e504a9a2cfbe16b42bf3fc68ad4c7d5c03612b082b3898474c9a854","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-09-10T12:05:05Z","title_canon_sha256":"3de700cea46895a135a33bdea049897534fed6229c01c5fbff3ccea916b87d75"},"schema_version":"1.0","source":{"id":"1809.03896","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03896","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03896v1","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03896","created_at":"2026-05-18T00:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"CEULOM53H4RK","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"CEULOM53H4RKDFFG","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"CEULOM53","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:90fc4614765288f2adf7d3b719d7ce9d404670890aefe4e2700a966035a761d0","target":"graph","created_at":"2026-05-18T00:05:57Z","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":"A landmark result in the study of logics for formal verification is Janin & Walukiewicz's theorem, stating that the modal $\\mu$-calculus ($\\mu\\mathrm{ML}$) is equivalent modulo bisimilarity to standard monadic second-order logic (here abbreviated as $\\mathrm{smso}$), over the class of labelled transition systems (LTSs for short). Our work proves two results of the same kind, one for the alternation-free fragment of $\\mu\\mathrm{ML}$ ($\\mu_D\\mathrm{ML}$) and one for weak $\\mathrm{mso}$ ($\\mathrm{wmso}$). Whereas it was known that $\\mu_D\\mathrm{ML}$ and $\\mathrm{wmso}$ are equivalent modulo bisim","authors_text":"Alessandro Facchini, Fabio Zanasi, Facundo Carreiro, Yde Venema","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-09-10T12:05:05Z","title":"The Power of the Weak"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03896","kind":"arxiv","version":1},"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:fb28f65c02a1cebaa1943ed33ceee614be24f17ffbb93b03cfd2fe9966273ec8","target":"record","created_at":"2026-05-18T00:05:57Z","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":"a8dddce08e504a9a2cfbe16b42bf3fc68ad4c7d5c03612b082b3898474c9a854","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-09-10T12:05:05Z","title_canon_sha256":"3de700cea46895a135a33bdea049897534fed6229c01c5fbff3ccea916b87d75"},"schema_version":"1.0","source":{"id":"1809.03896","kind":"arxiv","version":1}},"canonical_sha256":"1128b733bb3f22a194a668a3759bfa60528d933cd9468d5d8c6553c8354dfc9b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1128b733bb3f22a194a668a3759bfa60528d933cd9468d5d8c6553c8354dfc9b","first_computed_at":"2026-05-18T00:05:57.786673Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:57.786673Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Be4K5uNukoBcg8s+6gdh+PbRTCLT/LRkz/tztgUe9jXJeE4j5onHNmTSspqMbxxU6NtOQ+xbryc/NRr4QEFVAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:57.787087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03896","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb28f65c02a1cebaa1943ed33ceee614be24f17ffbb93b03cfd2fe9966273ec8","sha256:90fc4614765288f2adf7d3b719d7ce9d404670890aefe4e2700a966035a761d0"],"state_sha256":"92be956b91df60a72bd9f1cac19b59de2cb0680d52b93205f8c664fc76293ac6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HTF+jAXL+ek8GW124H/BgVAgm6jJhJnidZP9F306AVWpfa4sBZaig4DCo9qstoZXOL04znRWvY0Gi44/ekkPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T07:04:55.497706Z","bundle_sha256":"cfc591ada20fe656a8a7299bab015b4f3acf707d916e57d61f0b77f003eafdae"}}