{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CI4U4GW7DMZ4UHFHQL4CNZ5WZZ","short_pith_number":"pith:CI4U4GW7","canonical_record":{"source":{"id":"1408.2879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-12T23:27:12Z","cross_cats_sorted":[],"title_canon_sha256":"d5d65399bf78b12f1ada39b78c7c11e1190da5cf0466782f6caf6d189bd25c35","abstract_canon_sha256":"85e2ef1c46f424dfc4259ad7475179017086d56d6b3adfca304472dd1c047864"},"schema_version":"1.0"},"canonical_sha256":"12394e1adf1b33ca1ca782f826e7b6ce53f6e263c13ce7013b65459751ef74ad","source":{"kind":"arxiv","id":"1408.2879","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2879","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2879v2","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2879","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"CI4U4GW7DMZ4","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CI4U4GW7DMZ4UHFH","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CI4U4GW7","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CI4U4GW7DMZ4UHFHQL4CNZ5WZZ","target":"record","payload":{"canonical_record":{"source":{"id":"1408.2879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-12T23:27:12Z","cross_cats_sorted":[],"title_canon_sha256":"d5d65399bf78b12f1ada39b78c7c11e1190da5cf0466782f6caf6d189bd25c35","abstract_canon_sha256":"85e2ef1c46f424dfc4259ad7475179017086d56d6b3adfca304472dd1c047864"},"schema_version":"1.0"},"canonical_sha256":"12394e1adf1b33ca1ca782f826e7b6ce53f6e263c13ce7013b65459751ef74ad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:21.896034Z","signature_b64":"dsyvUlhznoRrtI4tAVR3zU6GvxPUsMnJP5i1pfwQnTNKXFSRtFa8fxRiB2Tqkle62b+d0RrZ34ZMLM+twP1VCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12394e1adf1b33ca1ca782f826e7b6ce53f6e263c13ce7013b65459751ef74ad","last_reissued_at":"2026-05-18T01:22:21.895280Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:21.895280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.2879","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":"2026-05-18T01:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"euQTZeupj8+tk38vy2zdWZvP/F36qnBw+RxgvQMYLtnUMhxl58IdksCO96HLrNige7lJ6WPJscN5echtPztiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:46:42.987048Z"},"content_sha256":"a6d7e37f85d06c13ec5bd7615faf7decfaab93f4f682e3d53aadce9700f18cad","schema_version":"1.0","event_id":"sha256:a6d7e37f85d06c13ec5bd7615faf7decfaab93f4f682e3d53aadce9700f18cad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CI4U4GW7DMZ4UHFHQL4CNZ5WZZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Levi Graph of Point-Line Configurations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jazmin Ortiz, Jessica Hauschild, Oscar Vega","submitted_at":"2014-08-12T23:27:12Z","abstract_excerpt":"We prove that the well-covered dimension of the Levi graph of a point-line configuration (v_r, b_k) is equal to 0, whenever r > 2."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2879","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":"2026-05-18T01:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2sa4Ga+7/o6MCi0CE95ZuGQxV3Bc90iihLnAju7iSxcQzp92SV1wT0vOj/elhXfi+mv4yxhlCkam/t3EqkoXBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:46:42.987406Z"},"content_sha256":"c8416ec63f5f5d3924dceacd73eedd1bab4ec2e4e714542cd98337ec0f0f9b7f","schema_version":"1.0","event_id":"sha256:c8416ec63f5f5d3924dceacd73eedd1bab4ec2e4e714542cd98337ec0f0f9b7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CI4U4GW7DMZ4UHFHQL4CNZ5WZZ/bundle.json","state_url":"https://pith.science/pith/CI4U4GW7DMZ4UHFHQL4CNZ5WZZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CI4U4GW7DMZ4UHFHQL4CNZ5WZZ/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":"2026-06-11T09:46:42Z","links":{"resolver":"https://pith.science/pith/CI4U4GW7DMZ4UHFHQL4CNZ5WZZ","bundle":"https://pith.science/pith/CI4U4GW7DMZ4UHFHQL4CNZ5WZZ/bundle.json","state":"https://pith.science/pith/CI4U4GW7DMZ4UHFHQL4CNZ5WZZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CI4U4GW7DMZ4UHFHQL4CNZ5WZZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CI4U4GW7DMZ4UHFHQL4CNZ5WZZ","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":"85e2ef1c46f424dfc4259ad7475179017086d56d6b3adfca304472dd1c047864","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-12T23:27:12Z","title_canon_sha256":"d5d65399bf78b12f1ada39b78c7c11e1190da5cf0466782f6caf6d189bd25c35"},"schema_version":"1.0","source":{"id":"1408.2879","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2879","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2879v2","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2879","created_at":"2026-05-18T01:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"CI4U4GW7DMZ4","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CI4U4GW7DMZ4UHFH","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CI4U4GW7","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:c8416ec63f5f5d3924dceacd73eedd1bab4ec2e4e714542cd98337ec0f0f9b7f","target":"graph","created_at":"2026-05-18T01:22:21Z","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 the well-covered dimension of the Levi graph of a point-line configuration (v_r, b_k) is equal to 0, whenever r > 2.","authors_text":"Jazmin Ortiz, Jessica Hauschild, Oscar Vega","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-12T23:27:12Z","title":"On the Levi Graph of Point-Line Configurations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2879","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:a6d7e37f85d06c13ec5bd7615faf7decfaab93f4f682e3d53aadce9700f18cad","target":"record","created_at":"2026-05-18T01:22:21Z","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":"85e2ef1c46f424dfc4259ad7475179017086d56d6b3adfca304472dd1c047864","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-08-12T23:27:12Z","title_canon_sha256":"d5d65399bf78b12f1ada39b78c7c11e1190da5cf0466782f6caf6d189bd25c35"},"schema_version":"1.0","source":{"id":"1408.2879","kind":"arxiv","version":2}},"canonical_sha256":"12394e1adf1b33ca1ca782f826e7b6ce53f6e263c13ce7013b65459751ef74ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12394e1adf1b33ca1ca782f826e7b6ce53f6e263c13ce7013b65459751ef74ad","first_computed_at":"2026-05-18T01:22:21.895280Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:21.895280Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dsyvUlhznoRrtI4tAVR3zU6GvxPUsMnJP5i1pfwQnTNKXFSRtFa8fxRiB2Tqkle62b+d0RrZ34ZMLM+twP1VCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:21.896034Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2879","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a6d7e37f85d06c13ec5bd7615faf7decfaab93f4f682e3d53aadce9700f18cad","sha256:c8416ec63f5f5d3924dceacd73eedd1bab4ec2e4e714542cd98337ec0f0f9b7f"],"state_sha256":"0d16fb748bb02bf476eb4c214f794a550baf4e7c3d5e8d0694fb00d41380c7ee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p65POk7198UChBsCrT7AdCYE9ZkTAZnKRbY/PD+RWjzy9i5ZdQggBDhAn7Z1CQoT5YH5+wz45HOyRRr9r5A2DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:46:42.989300Z","bundle_sha256":"5fd86d34a0e0e2549e1a77cbf2d9d6df1b4b9b6205ab7f8a5a1d4884b4a85172"}}