{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ZGH4ZRXMETCNOH6RISUTDXSQJF","short_pith_number":"pith:ZGH4ZRXM","canonical_record":{"source":{"id":"1902.00847","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-03T05:10:27Z","cross_cats_sorted":[],"title_canon_sha256":"903fd4fbca69694dc3caafa9ae6c50d1321a4f2e7574a053758dda8e63a59276","abstract_canon_sha256":"2693942f402f09a79698f648f3d48ef45c208a6528cc3c521e360be0b3b8c81f"},"schema_version":"1.0"},"canonical_sha256":"c98fccc6ec24c4d71fd144a931de504943ae927b0c79d9388ee8fea85a1c5b5d","source":{"kind":"arxiv","id":"1902.00847","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00847","created_at":"2026-07-05T01:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00847v2","created_at":"2026-07-05T01:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00847","created_at":"2026-07-05T01:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"ZGH4ZRXMETCN","created_at":"2026-07-05T01:10:10Z"},{"alias_kind":"pith_short_16","alias_value":"ZGH4ZRXMETCNOH6R","created_at":"2026-07-05T01:10:10Z"},{"alias_kind":"pith_short_8","alias_value":"ZGH4ZRXM","created_at":"2026-07-05T01:10:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ZGH4ZRXMETCNOH6RISUTDXSQJF","target":"record","payload":{"canonical_record":{"source":{"id":"1902.00847","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-03T05:10:27Z","cross_cats_sorted":[],"title_canon_sha256":"903fd4fbca69694dc3caafa9ae6c50d1321a4f2e7574a053758dda8e63a59276","abstract_canon_sha256":"2693942f402f09a79698f648f3d48ef45c208a6528cc3c521e360be0b3b8c81f"},"schema_version":"1.0"},"canonical_sha256":"c98fccc6ec24c4d71fd144a931de504943ae927b0c79d9388ee8fea85a1c5b5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:10:10.917212Z","signature_b64":"Nn32hW/o9YCEyOVYziumXefXdkfEWDAjggsehORCAZxWJ/5c/hfONaRr7DGKEvw+nR7m5XxczUxGWIkgk2agBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c98fccc6ec24c4d71fd144a931de504943ae927b0c79d9388ee8fea85a1c5b5d","last_reissued_at":"2026-07-05T01:10:10.916736Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:10:10.916736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.00847","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":"2026-07-05T01:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z32bCzwyDCSvlr/OMNReKtq++21pf2MPaGp3x1AsfwRipvVDKb3VogMU7Nw3LIK03HrMP7lXI7HIX9w8bDb0Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:41:50.720619Z"},"content_sha256":"38e77fa5648af33a5e1ed8540138c67264e9ece5a0e060bcb1439f1fdc51c85a","schema_version":"1.0","event_id":"sha256:38e77fa5648af33a5e1ed8540138c67264e9ece5a0e060bcb1439f1fdc51c85a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ZGH4ZRXMETCNOH6RISUTDXSQJF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Axiomatic Theory of Betweenness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Pavel Naumov, Sanaz Azimipour","submitted_at":"2019-02-03T05:10:27Z","abstract_excerpt":"Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00847","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1902.00847/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:10:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SQya0LV4Jkb4gEeojHVg2RQqqv/ZUM9TYKEjK3SyoFh1bw2Bf+1BiIJuEuuI8CXLaULf5KgL5QBAE+dJf8+pBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T13:41:50.720984Z"},"content_sha256":"0cfc21acc2d984348c101d7f833d69224d94bc0e246a29dcb74f9082f0702836","schema_version":"1.0","event_id":"sha256:0cfc21acc2d984348c101d7f833d69224d94bc0e246a29dcb74f9082f0702836"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZGH4ZRXMETCNOH6RISUTDXSQJF/bundle.json","state_url":"https://pith.science/pith/ZGH4ZRXMETCNOH6RISUTDXSQJF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZGH4ZRXMETCNOH6RISUTDXSQJF/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":"2026-07-07T13:41:50Z","links":{"resolver":"https://pith.science/pith/ZGH4ZRXMETCNOH6RISUTDXSQJF","bundle":"https://pith.science/pith/ZGH4ZRXMETCNOH6RISUTDXSQJF/bundle.json","state":"https://pith.science/pith/ZGH4ZRXMETCNOH6RISUTDXSQJF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZGH4ZRXMETCNOH6RISUTDXSQJF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ZGH4ZRXMETCNOH6RISUTDXSQJF","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":"2693942f402f09a79698f648f3d48ef45c208a6528cc3c521e360be0b3b8c81f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-03T05:10:27Z","title_canon_sha256":"903fd4fbca69694dc3caafa9ae6c50d1321a4f2e7574a053758dda8e63a59276"},"schema_version":"1.0","source":{"id":"1902.00847","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00847","created_at":"2026-07-05T01:10:10Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00847v2","created_at":"2026-07-05T01:10:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00847","created_at":"2026-07-05T01:10:10Z"},{"alias_kind":"pith_short_12","alias_value":"ZGH4ZRXMETCN","created_at":"2026-07-05T01:10:10Z"},{"alias_kind":"pith_short_16","alias_value":"ZGH4ZRXMETCNOH6R","created_at":"2026-07-05T01:10:10Z"},{"alias_kind":"pith_short_8","alias_value":"ZGH4ZRXM","created_at":"2026-07-05T01:10:10Z"}],"graph_snapshots":[{"event_id":"sha256:0cfc21acc2d984348c101d7f833d69224d94bc0e246a29dcb74f9082f0702836","target":"graph","created_at":"2026-07-05T01:10:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1902.00847/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Betweenness as a relation between three individual points has been widely studied in geometry and axiomatized by several authors in different contexts. The article proposes a more general notion of betweenness as a relation between three sets of points. The main technical result is a sound and complete logical system describing universal properties of this relation between sets of vertices of a graph.","authors_text":"Pavel Naumov, Sanaz Azimipour","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-03T05:10:27Z","title":"Axiomatic Theory of Betweenness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00847","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":"sha256:38e77fa5648af33a5e1ed8540138c67264e9ece5a0e060bcb1439f1fdc51c85a","target":"record","created_at":"2026-07-05T01:10:10Z","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":"2693942f402f09a79698f648f3d48ef45c208a6528cc3c521e360be0b3b8c81f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-02-03T05:10:27Z","title_canon_sha256":"903fd4fbca69694dc3caafa9ae6c50d1321a4f2e7574a053758dda8e63a59276"},"schema_version":"1.0","source":{"id":"1902.00847","kind":"arxiv","version":2}},"canonical_sha256":"c98fccc6ec24c4d71fd144a931de504943ae927b0c79d9388ee8fea85a1c5b5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c98fccc6ec24c4d71fd144a931de504943ae927b0c79d9388ee8fea85a1c5b5d","first_computed_at":"2026-07-05T01:10:10.916736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:10:10.916736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nn32hW/o9YCEyOVYziumXefXdkfEWDAjggsehORCAZxWJ/5c/hfONaRr7DGKEvw+nR7m5XxczUxGWIkgk2agBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:10:10.917212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00847","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38e77fa5648af33a5e1ed8540138c67264e9ece5a0e060bcb1439f1fdc51c85a","sha256:0cfc21acc2d984348c101d7f833d69224d94bc0e246a29dcb74f9082f0702836"],"state_sha256":"8bb5f29bb4299a720f6d796018fd829a98a11df4b796b1f898788740a1612b18"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n2DzdE67u9hD1qDDaIfoPz2VmfMVGNA8JqaG0ZKCcxXL4F0ZsXwBYZ7HWIUcoTmCuiGBPfm+z2Huqfa1xiHvDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T13:41:50.722905Z","bundle_sha256":"712f570ca6e7d5f88befc52915574593f2e0f7e216faf96b7bcdc183d375f0a3"}}