{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PA4BUYYULJUVC6HDVSYSFQTILO","short_pith_number":"pith:PA4BUYYU","canonical_record":{"source":{"id":"1905.07829","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-19T23:36:49Z","cross_cats_sorted":[],"title_canon_sha256":"b79938a7592f07317ce8df58bbb7c05789ce31c2239abfe22ca383403c2c09bc","abstract_canon_sha256":"8c38686ac10f2d9b87d07f32e6b08d16c665fcf4e96a34001d3b18aa366b0d67"},"schema_version":"1.0"},"canonical_sha256":"78381a63145a695178e3acb122c2685b9a66a11746691318d3a0aac1918e652a","source":{"kind":"arxiv","id":"1905.07829","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07829","created_at":"2026-05-17T23:45:14Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07829v3","created_at":"2026-05-17T23:45:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07829","created_at":"2026-05-17T23:45:14Z"},{"alias_kind":"pith_short_12","alias_value":"PA4BUYYULJUV","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PA4BUYYULJUVC6HD","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PA4BUYYU","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PA4BUYYULJUVC6HDVSYSFQTILO","target":"record","payload":{"canonical_record":{"source":{"id":"1905.07829","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-19T23:36:49Z","cross_cats_sorted":[],"title_canon_sha256":"b79938a7592f07317ce8df58bbb7c05789ce31c2239abfe22ca383403c2c09bc","abstract_canon_sha256":"8c38686ac10f2d9b87d07f32e6b08d16c665fcf4e96a34001d3b18aa366b0d67"},"schema_version":"1.0"},"canonical_sha256":"78381a63145a695178e3acb122c2685b9a66a11746691318d3a0aac1918e652a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:14.482416Z","signature_b64":"UG4Xo4OcfJ/aeIj9ImRK0hYpg/6sk7wK/WJ1lkbDF4UvvQ+Hrd/47lGKp3QWNW3D7U4Ii40NzTD1IyiDwddqBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78381a63145a695178e3acb122c2685b9a66a11746691318d3a0aac1918e652a","last_reissued_at":"2026-05-17T23:45:14.481771Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:14.481771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.07829","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:45:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m1IJE7xtw3sACDbaB5RWQCyM5wzAq5gsxD8tca5fu8J/xAM+cFi98nS3rs0huNDxnfmOcy/J+x6970VUQaFUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T07:06:35.178451Z"},"content_sha256":"88d55dea2a6b2d086c92f126f7ba53374bdc933639132035db78c3ff04d8a270","schema_version":"1.0","event_id":"sha256:88d55dea2a6b2d086c92f126f7ba53374bdc933639132035db78c3ff04d8a270"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PA4BUYYULJUVC6HDVSYSFQTILO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small unit-distance graphs in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Aidan Globus, Hans Parshall","submitted_at":"2019-05-19T23:36:49Z","abstract_excerpt":"We prove that a graph on up to 9 vertices is a unit-distance graph if and only if it does not contain one of 74 so-called minimal forbidden graphs. This extends the work of Chilakamarri and Mahoney (1995), who provide a similar classification for unit-distance graphs on up to 7 vertices."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07829","kind":"arxiv","version":3},"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":"2026-05-17T23:45:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aIQ/5ixUK85doIb7IHu/0Ms/moqn0ZpsTKq44qS0YhAYoxuIH0t8UuOl5ZrhCHQnsqdrT/r7Yv40nboD6pnsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T07:06:35.178845Z"},"content_sha256":"7495cc0fdef97dc6972a032b33a41793a32074b8d76f3136a5103b453e516aca","schema_version":"1.0","event_id":"sha256:7495cc0fdef97dc6972a032b33a41793a32074b8d76f3136a5103b453e516aca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PA4BUYYULJUVC6HDVSYSFQTILO/bundle.json","state_url":"https://pith.science/pith/PA4BUYYULJUVC6HDVSYSFQTILO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PA4BUYYULJUVC6HDVSYSFQTILO/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":"2026-06-04T07:06:35Z","links":{"resolver":"https://pith.science/pith/PA4BUYYULJUVC6HDVSYSFQTILO","bundle":"https://pith.science/pith/PA4BUYYULJUVC6HDVSYSFQTILO/bundle.json","state":"https://pith.science/pith/PA4BUYYULJUVC6HDVSYSFQTILO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PA4BUYYULJUVC6HDVSYSFQTILO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PA4BUYYULJUVC6HDVSYSFQTILO","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":"8c38686ac10f2d9b87d07f32e6b08d16c665fcf4e96a34001d3b18aa366b0d67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-19T23:36:49Z","title_canon_sha256":"b79938a7592f07317ce8df58bbb7c05789ce31c2239abfe22ca383403c2c09bc"},"schema_version":"1.0","source":{"id":"1905.07829","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.07829","created_at":"2026-05-17T23:45:14Z"},{"alias_kind":"arxiv_version","alias_value":"1905.07829v3","created_at":"2026-05-17T23:45:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.07829","created_at":"2026-05-17T23:45:14Z"},{"alias_kind":"pith_short_12","alias_value":"PA4BUYYULJUV","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PA4BUYYULJUVC6HD","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PA4BUYYU","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:7495cc0fdef97dc6972a032b33a41793a32074b8d76f3136a5103b453e516aca","target":"graph","created_at":"2026-05-17T23:45:14Z","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":"We prove that a graph on up to 9 vertices is a unit-distance graph if and only if it does not contain one of 74 so-called minimal forbidden graphs. This extends the work of Chilakamarri and Mahoney (1995), who provide a similar classification for unit-distance graphs on up to 7 vertices.","authors_text":"Aidan Globus, Hans Parshall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-19T23:36:49Z","title":"Small unit-distance graphs in the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07829","kind":"arxiv","version":3},"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":"sha256:88d55dea2a6b2d086c92f126f7ba53374bdc933639132035db78c3ff04d8a270","target":"record","created_at":"2026-05-17T23:45:14Z","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":"8c38686ac10f2d9b87d07f32e6b08d16c665fcf4e96a34001d3b18aa366b0d67","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-19T23:36:49Z","title_canon_sha256":"b79938a7592f07317ce8df58bbb7c05789ce31c2239abfe22ca383403c2c09bc"},"schema_version":"1.0","source":{"id":"1905.07829","kind":"arxiv","version":3}},"canonical_sha256":"78381a63145a695178e3acb122c2685b9a66a11746691318d3a0aac1918e652a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78381a63145a695178e3acb122c2685b9a66a11746691318d3a0aac1918e652a","first_computed_at":"2026-05-17T23:45:14.481771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:14.481771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UG4Xo4OcfJ/aeIj9ImRK0hYpg/6sk7wK/WJ1lkbDF4UvvQ+Hrd/47lGKp3QWNW3D7U4Ii40NzTD1IyiDwddqBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:14.482416Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.07829","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88d55dea2a6b2d086c92f126f7ba53374bdc933639132035db78c3ff04d8a270","sha256:7495cc0fdef97dc6972a032b33a41793a32074b8d76f3136a5103b453e516aca"],"state_sha256":"35c712f60b01b017a0e1d0556eb4f55ce45f01bfd67f5494098389df04b490df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1iCM9CzlmGwuLkD/nHV1GZu98aqdL+bIJofVeLtwRaW2QVCbn+CbC7SVAtqTHwetkNupSBGgZuVoUSC5JcAaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T07:06:35.182048Z","bundle_sha256":"8746f9237ddc73d5363d45b21b4d2eb89726e35bb08e5c9bdc2ae0873dfd8316"}}