{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:KF3Y27FAD4ZVOK5BRIYGXPO7GE","short_pith_number":"pith:KF3Y27FA","canonical_record":{"source":{"id":"2411.03274","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2024-11-05T17:17:30Z","cross_cats_sorted":[],"title_canon_sha256":"a529cc058fe2a1b901166ba818cb9d9a18ec5dc1a9dcc23dad50254ace9e0984","abstract_canon_sha256":"e9b6057f6f506a5e6536cfc92ecacad44ca77d87da322905c3b03b7cbad7aafb"},"schema_version":"1.0"},"canonical_sha256":"51778d7ca01f33572ba18a306bbddf31044637785cfb0f1bb7714d2ef417a819","source":{"kind":"arxiv","id":"2411.03274","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.03274","created_at":"2026-07-05T09:31:27Z"},{"alias_kind":"arxiv_version","alias_value":"2411.03274v1","created_at":"2026-07-05T09:31:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.03274","created_at":"2026-07-05T09:31:27Z"},{"alias_kind":"pith_short_12","alias_value":"KF3Y27FAD4ZV","created_at":"2026-07-05T09:31:27Z"},{"alias_kind":"pith_short_16","alias_value":"KF3Y27FAD4ZVOK5B","created_at":"2026-07-05T09:31:27Z"},{"alias_kind":"pith_short_8","alias_value":"KF3Y27FA","created_at":"2026-07-05T09:31:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:KF3Y27FAD4ZVOK5BRIYGXPO7GE","target":"record","payload":{"canonical_record":{"source":{"id":"2411.03274","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2024-11-05T17:17:30Z","cross_cats_sorted":[],"title_canon_sha256":"a529cc058fe2a1b901166ba818cb9d9a18ec5dc1a9dcc23dad50254ace9e0984","abstract_canon_sha256":"e9b6057f6f506a5e6536cfc92ecacad44ca77d87da322905c3b03b7cbad7aafb"},"schema_version":"1.0"},"canonical_sha256":"51778d7ca01f33572ba18a306bbddf31044637785cfb0f1bb7714d2ef417a819","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:31:27.800897Z","signature_b64":"p5U6vtz89sAUK0t7LD1GKM1mSpYlZDTYt8I7t2pw2M3U4gK30B3oWl7j0QtGqkuCVq/RJ9LQx7f4qYGV20a3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"51778d7ca01f33572ba18a306bbddf31044637785cfb0f1bb7714d2ef417a819","last_reissued_at":"2026-07-05T09:31:27.800449Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:31:27.800449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.03274","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":"2026-07-05T09:31:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G2BSfSK0rNSXYvoToiKfUosImoL5NzntFXvFLgYmY03sjHFuK7PwbKFUEJML8vw9oS/NLPQsJp4XOs41sMi7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T14:16:46.870107Z"},"content_sha256":"5ac399ef55aae922b3ee57e1d8d271d43ad49c1ce654c3df644bd758a84c3df5","schema_version":"1.0","event_id":"sha256:5ac399ef55aae922b3ee57e1d8d271d43ad49c1ce654c3df644bd758a84c3df5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:KF3Y27FAD4ZVOK5BRIYGXPO7GE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized Word-Representable Graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Henning Fernau, Kevin Mann, Pamela Fleischmann, Silas Cato Sacher, Zhidan Feng","submitted_at":"2024-11-05T17:17:30Z","abstract_excerpt":"The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our framework, we can associate a graph class to each language over the binary alphabet \\{0,1\\}. All graph classes that are language-representable in this sense are hereditary and enjoy further common properties. Besides word-representable graphs and, more generally, 1^k- or k-11-representable graphs, we can identify many more graph classes in our framework, like "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.03274","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.03274/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":"2026-07-05T09:31:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qVrlO2twH0nWGZay4h1hLQ0QSRXIeaiPbpxYgVYUdnjSXxREsphmDI7HcAKbWZSThoORaoN4+bX8PwrzNWJ7Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T14:16:46.870599Z"},"content_sha256":"32ff978791dad2a110f2bddc533122e0760afc257001e9ffc446638a64c797cf","schema_version":"1.0","event_id":"sha256:32ff978791dad2a110f2bddc533122e0760afc257001e9ffc446638a64c797cf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KF3Y27FAD4ZVOK5BRIYGXPO7GE/bundle.json","state_url":"https://pith.science/pith/KF3Y27FAD4ZVOK5BRIYGXPO7GE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KF3Y27FAD4ZVOK5BRIYGXPO7GE/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":"2026-08-21T14:16:46Z","links":{"resolver":"https://pith.science/pith/KF3Y27FAD4ZVOK5BRIYGXPO7GE","bundle":"https://pith.science/pith/KF3Y27FAD4ZVOK5BRIYGXPO7GE/bundle.json","state":"https://pith.science/pith/KF3Y27FAD4ZVOK5BRIYGXPO7GE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KF3Y27FAD4ZVOK5BRIYGXPO7GE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:KF3Y27FAD4ZVOK5BRIYGXPO7GE","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":"e9b6057f6f506a5e6536cfc92ecacad44ca77d87da322905c3b03b7cbad7aafb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2024-11-05T17:17:30Z","title_canon_sha256":"a529cc058fe2a1b901166ba818cb9d9a18ec5dc1a9dcc23dad50254ace9e0984"},"schema_version":"1.0","source":{"id":"2411.03274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.03274","created_at":"2026-07-05T09:31:27Z"},{"alias_kind":"arxiv_version","alias_value":"2411.03274v1","created_at":"2026-07-05T09:31:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.03274","created_at":"2026-07-05T09:31:27Z"},{"alias_kind":"pith_short_12","alias_value":"KF3Y27FAD4ZV","created_at":"2026-07-05T09:31:27Z"},{"alias_kind":"pith_short_16","alias_value":"KF3Y27FAD4ZVOK5B","created_at":"2026-07-05T09:31:27Z"},{"alias_kind":"pith_short_8","alias_value":"KF3Y27FA","created_at":"2026-07-05T09:31:27Z"}],"graph_snapshots":[{"event_id":"sha256:32ff978791dad2a110f2bddc533122e0760afc257001e9ffc446638a64c797cf","target":"graph","created_at":"2026-07-05T09:31:27Z","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/2411.03274/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The literature on word-representable graphs is quite rich, and a number of variations of the original definition have been proposed over the years. We are initiating a systematic study of such variations based on formal languages. In our framework, we can associate a graph class to each language over the binary alphabet \\{0,1\\}. All graph classes that are language-representable in this sense are hereditary and enjoy further common properties. Besides word-representable graphs and, more generally, 1^k- or k-11-representable graphs, we can identify many more graph classes in our framework, like ","authors_text":"Henning Fernau, Kevin Mann, Pamela Fleischmann, Silas Cato Sacher, Zhidan Feng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2024-11-05T17:17:30Z","title":"Generalized Word-Representable Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.03274","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":"sha256:5ac399ef55aae922b3ee57e1d8d271d43ad49c1ce654c3df644bd758a84c3df5","target":"record","created_at":"2026-07-05T09:31:27Z","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":"e9b6057f6f506a5e6536cfc92ecacad44ca77d87da322905c3b03b7cbad7aafb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DM","submitted_at":"2024-11-05T17:17:30Z","title_canon_sha256":"a529cc058fe2a1b901166ba818cb9d9a18ec5dc1a9dcc23dad50254ace9e0984"},"schema_version":"1.0","source":{"id":"2411.03274","kind":"arxiv","version":1}},"canonical_sha256":"51778d7ca01f33572ba18a306bbddf31044637785cfb0f1bb7714d2ef417a819","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51778d7ca01f33572ba18a306bbddf31044637785cfb0f1bb7714d2ef417a819","first_computed_at":"2026-07-05T09:31:27.800449Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:31:27.800449Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p5U6vtz89sAUK0t7LD1GKM1mSpYlZDTYt8I7t2pw2M3U4gK30B3oWl7j0QtGqkuCVq/RJ9LQx7f4qYGV20a3Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T09:31:27.800897Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.03274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ac399ef55aae922b3ee57e1d8d271d43ad49c1ce654c3df644bd758a84c3df5","sha256:32ff978791dad2a110f2bddc533122e0760afc257001e9ffc446638a64c797cf"],"state_sha256":"4b87cee3134b24774d27937bfd46b2ef5034d65c68800ea60e29557493311f39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YuMLlIbOGuz5tmii5QGrgt9aJ1KGc+dWlCUFSKI0ptJ/yRKtJNaCAxmkLIE9W9yKM0+bShf6SuUgjJXXHxe/Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T14:16:46.874348Z","bundle_sha256":"3e64c5ba8b1ff18fc55af690b09785282c08d305d9fc2ab86efe5abc55528573"}}