{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:G4HYH5EG3KWZD3736YK2NATMPL","short_pith_number":"pith:G4HYH5EG","canonical_record":{"source":{"id":"1807.01794","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-04T21:38:12Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"0a54481d3e2f73a04ca59eed512364b0c74b6c60c63b7d217963d3e52784f9d5","abstract_canon_sha256":"77b22e8cad17a3b30431e3573d9806af86fbefcaf7fdea8aa356e660ca5f3e4c"},"schema_version":"1.0"},"canonical_sha256":"370f83f486daad91effbf615a6826c7ade1e0bdde090ce96bc6e67fc4042c772","source":{"kind":"arxiv","id":"1807.01794","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01794","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01794v2","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01794","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"G4HYH5EG3KWZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G4HYH5EG3KWZD373","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G4HYH5EG","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:G4HYH5EG3KWZD3736YK2NATMPL","target":"record","payload":{"canonical_record":{"source":{"id":"1807.01794","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-04T21:38:12Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"0a54481d3e2f73a04ca59eed512364b0c74b6c60c63b7d217963d3e52784f9d5","abstract_canon_sha256":"77b22e8cad17a3b30431e3573d9806af86fbefcaf7fdea8aa356e660ca5f3e4c"},"schema_version":"1.0"},"canonical_sha256":"370f83f486daad91effbf615a6826c7ade1e0bdde090ce96bc6e67fc4042c772","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:32.445462Z","signature_b64":"lXjDnYES2qq0qQ3eGyuKxkwAqItoS6HxjtP74POpC8XomCt3g6oEw2Bpxg9TlkP3KYGeGrdEosqo3p2BYhlKDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"370f83f486daad91effbf615a6826c7ade1e0bdde090ce96bc6e67fc4042c772","last_reissued_at":"2026-05-17T23:59:32.444902Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:32.444902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.01794","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":"2026-05-17T23:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J+6kdGZyIbgn8VFeV9RvT4+7uoBH5Ry92kKkgZJhVc79+16gD6btfsvMl6T6ZewHdprRJrxW1nhjPGezFijSAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:47:54.002824Z"},"content_sha256":"8f075050974fd4f093ac7f4316ebdca4c262ce327c7bec0cca3fd743c770ec43","schema_version":"1.0","event_id":"sha256:8f075050974fd4f093ac7f4316ebdca4c262ce327c7bec0cca3fd743c770ec43"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:G4HYH5EG3KWZD3736YK2NATMPL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existential monadic second order logic of undirected graphs: a disproof of the Le Bars conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CO","authors_text":"Maksim Zhukovskii, Svetlana Popova","submitted_at":"2018-07-04T21:38:12Z","abstract_excerpt":"In 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) about undirected graphs. He proved that there exists an EMSO sentence $\\phi$ such that ${\\sf P}(G_n \\models\\phi)$ does not converge as $n\\to\\infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\\{1, \\dots, n\\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01794","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":"2026-05-17T23:59:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I0CD0OzEDGya9FDxX/mL9fTCRC7juVKaRjn29npCqWZZPzdFH3M85g823fVCixIZ7e82TsHLIrN6xXAk3Yt8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:47:54.003165Z"},"content_sha256":"3395cc0a5e9d93f01967794db7f226d3eb563b28755812fb1c627b857e818b93","schema_version":"1.0","event_id":"sha256:3395cc0a5e9d93f01967794db7f226d3eb563b28755812fb1c627b857e818b93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G4HYH5EG3KWZD3736YK2NATMPL/bundle.json","state_url":"https://pith.science/pith/G4HYH5EG3KWZD3736YK2NATMPL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G4HYH5EG3KWZD3736YK2NATMPL/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":"2026-06-02T19:47:54Z","links":{"resolver":"https://pith.science/pith/G4HYH5EG3KWZD3736YK2NATMPL","bundle":"https://pith.science/pith/G4HYH5EG3KWZD3736YK2NATMPL/bundle.json","state":"https://pith.science/pith/G4HYH5EG3KWZD3736YK2NATMPL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G4HYH5EG3KWZD3736YK2NATMPL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:G4HYH5EG3KWZD3736YK2NATMPL","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":"77b22e8cad17a3b30431e3573d9806af86fbefcaf7fdea8aa356e660ca5f3e4c","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-04T21:38:12Z","title_canon_sha256":"0a54481d3e2f73a04ca59eed512364b0c74b6c60c63b7d217963d3e52784f9d5"},"schema_version":"1.0","source":{"id":"1807.01794","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01794","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01794v2","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01794","created_at":"2026-05-17T23:59:32Z"},{"alias_kind":"pith_short_12","alias_value":"G4HYH5EG3KWZ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"G4HYH5EG3KWZD373","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"G4HYH5EG","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:3395cc0a5e9d93f01967794db7f226d3eb563b28755812fb1c627b857e818b93","target":"graph","created_at":"2026-05-17T23:59:32Z","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 2001, J.-M. Le Bars disproved the zero-one law (that says that every sentence from a certain logic is either true asymptotically almost surely (a.a.s.), or false a.a.s.) for existential monadic second order sentences (EMSO) about undirected graphs. He proved that there exists an EMSO sentence $\\phi$ such that ${\\sf P}(G_n \\models\\phi)$ does not converge as $n\\to\\infty$ (here, the probability distribution is uniform over the set of all graphs on the labeled set of vertices $\\{1, \\dots, n\\}$). In the same paper, he conjectured that, for EMSO sentences with 2 first order variables, the zero-on","authors_text":"Maksim Zhukovskii, Svetlana Popova","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-04T21:38:12Z","title":"Existential monadic second order logic of undirected graphs: a disproof of the Le Bars conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01794","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":"sha256:8f075050974fd4f093ac7f4316ebdca4c262ce327c7bec0cca3fd743c770ec43","target":"record","created_at":"2026-05-17T23:59:32Z","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":"77b22e8cad17a3b30431e3573d9806af86fbefcaf7fdea8aa356e660ca5f3e4c","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-07-04T21:38:12Z","title_canon_sha256":"0a54481d3e2f73a04ca59eed512364b0c74b6c60c63b7d217963d3e52784f9d5"},"schema_version":"1.0","source":{"id":"1807.01794","kind":"arxiv","version":2}},"canonical_sha256":"370f83f486daad91effbf615a6826c7ade1e0bdde090ce96bc6e67fc4042c772","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"370f83f486daad91effbf615a6826c7ade1e0bdde090ce96bc6e67fc4042c772","first_computed_at":"2026-05-17T23:59:32.444902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:32.444902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lXjDnYES2qq0qQ3eGyuKxkwAqItoS6HxjtP74POpC8XomCt3g6oEw2Bpxg9TlkP3KYGeGrdEosqo3p2BYhlKDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:32.445462Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01794","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f075050974fd4f093ac7f4316ebdca4c262ce327c7bec0cca3fd743c770ec43","sha256:3395cc0a5e9d93f01967794db7f226d3eb563b28755812fb1c627b857e818b93"],"state_sha256":"7541e20dd57029538cdfa0fd7bb854e88871669bf02a2ba2e5c827a080a30d41"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qzjTo4lnqn4Zi0bIl+egMbe/1jaVa/kdrfViqy/FTgCmeUK4x9IzpDZgfM62fRXgoqDO70CUeF713jPQKR70AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:47:54.005093Z","bundle_sha256":"c76102ed8913c9030f02bc235775bd352dd8bfd4126e3d8021a6c18fc657f1c6"}}