{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:BI74UE4ZFRYQQCQDCEDPMTB6LF","short_pith_number":"pith:BI74UE4Z","canonical_record":{"source":{"id":"1608.01465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-04T08:49:03Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8dcd2a16ed7a5572952cba19cded7c983be3d3518caa76b5e835dfba24e48f91","abstract_canon_sha256":"5c0399b577b5f74f5dbff59657667f91b43f9bc64ae97cd6141c0ec9a619f595"},"schema_version":"1.0"},"canonical_sha256":"0a3fca13992c71080a031106f64c3e59740c91605b718c1f2fd3c7710197d7e3","source":{"kind":"arxiv","id":"1608.01465","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01465","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01465v1","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01465","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"BI74UE4ZFRYQ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BI74UE4ZFRYQQCQD","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BI74UE4Z","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:BI74UE4ZFRYQQCQDCEDPMTB6LF","target":"record","payload":{"canonical_record":{"source":{"id":"1608.01465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-04T08:49:03Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"8dcd2a16ed7a5572952cba19cded7c983be3d3518caa76b5e835dfba24e48f91","abstract_canon_sha256":"5c0399b577b5f74f5dbff59657667f91b43f9bc64ae97cd6141c0ec9a619f595"},"schema_version":"1.0"},"canonical_sha256":"0a3fca13992c71080a031106f64c3e59740c91605b718c1f2fd3c7710197d7e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:52.368880Z","signature_b64":"xV4yqitJghs5jPDPJws8peeZGX9TjyZ0uDhTRsAg4QSzuyQinWprRL4patYhLm0Qpzfc40J2woO0Z/y1GhL2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a3fca13992c71080a031106f64c3e59740c91605b718c1f2fd3c7710197d7e3","last_reissued_at":"2026-05-18T01:09:52.368241Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:52.368241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.01465","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":"2026-05-18T01:09:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2wi1fNXWiB2wOAXC1QN9onMNUnMRUjiLdlhhD35v1WnuDDRhaoA/RGfq62OQdd5IJrGk8I9zdRQV0GhF4WQ9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:35:40.154515Z"},"content_sha256":"fcd731146ea25555d7b7039bb24ead604d9da185526d78e1c6e2ae63e2030bf6","schema_version":"1.0","event_id":"sha256:fcd731146ea25555d7b7039bb24ead604d9da185526d78e1c6e2ae63e2030bf6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:BI74UE4ZFRYQQCQDCEDPMTB6LF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"J\\'er\\'emie Lumbroso, Maryam Bahrani","submitted_at":"2016-08-04T08:49:03Z","abstract_excerpt":"Forbidden characterizations may sometimes be the most natural way to describe families of graphs, and yet these characterizations are usually very hard to exploit for enumerative purposes.\n  By building on the work of Gioan and Paul (2012) and Chauve et al. (2014), we show a methodology by which we constrain a split-decomposition tree to avoid certain patterns, thereby avoiding the corresponding induced subgraphs in the original graph.\n  We thus provide the grammars and full enumeration for a wide set of graph classes: ptolemaic, block, and variants of cactus graphs (2,3-cacti, 3-cacti and 4-c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01465","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":""},"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":"2026-05-18T01:09:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JqFdlH73/RuJFH6DF1nfWXADssg3AuT8guVhwakv20cG29M4VAB0WSZP//PfvhU+uG/EewEgx6btz9Rp+my0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T12:35:40.154865Z"},"content_sha256":"7a48378147d92a10ef7bde751783791f0b06e2849fbe60fd4637af38ffc97e9b","schema_version":"1.0","event_id":"sha256:7a48378147d92a10ef7bde751783791f0b06e2849fbe60fd4637af38ffc97e9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BI74UE4ZFRYQQCQDCEDPMTB6LF/bundle.json","state_url":"https://pith.science/pith/BI74UE4ZFRYQQCQDCEDPMTB6LF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BI74UE4ZFRYQQCQDCEDPMTB6LF/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":"2026-06-11T12:35:40Z","links":{"resolver":"https://pith.science/pith/BI74UE4ZFRYQQCQDCEDPMTB6LF","bundle":"https://pith.science/pith/BI74UE4ZFRYQQCQDCEDPMTB6LF/bundle.json","state":"https://pith.science/pith/BI74UE4ZFRYQQCQDCEDPMTB6LF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BI74UE4ZFRYQQCQDCEDPMTB6LF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BI74UE4ZFRYQQCQDCEDPMTB6LF","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":"5c0399b577b5f74f5dbff59657667f91b43f9bc64ae97cd6141c0ec9a619f595","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-04T08:49:03Z","title_canon_sha256":"8dcd2a16ed7a5572952cba19cded7c983be3d3518caa76b5e835dfba24e48f91"},"schema_version":"1.0","source":{"id":"1608.01465","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.01465","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"arxiv_version","alias_value":"1608.01465v1","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.01465","created_at":"2026-05-18T01:09:52Z"},{"alias_kind":"pith_short_12","alias_value":"BI74UE4ZFRYQ","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"BI74UE4ZFRYQQCQD","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"BI74UE4Z","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:7a48378147d92a10ef7bde751783791f0b06e2849fbe60fd4637af38ffc97e9b","target":"graph","created_at":"2026-05-18T01:09:52Z","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":"Forbidden characterizations may sometimes be the most natural way to describe families of graphs, and yet these characterizations are usually very hard to exploit for enumerative purposes.\n  By building on the work of Gioan and Paul (2012) and Chauve et al. (2014), we show a methodology by which we constrain a split-decomposition tree to avoid certain patterns, thereby avoiding the corresponding induced subgraphs in the original graph.\n  We thus provide the grammars and full enumeration for a wide set of graph classes: ptolemaic, block, and variants of cactus graphs (2,3-cacti, 3-cacti and 4-c","authors_text":"J\\'er\\'emie Lumbroso, Maryam Bahrani","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-04T08:49:03Z","title":"Enumerations, Forbidden Subgraph Characterizations, and the Split-Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01465","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:fcd731146ea25555d7b7039bb24ead604d9da185526d78e1c6e2ae63e2030bf6","target":"record","created_at":"2026-05-18T01:09:52Z","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":"5c0399b577b5f74f5dbff59657667f91b43f9bc64ae97cd6141c0ec9a619f595","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-08-04T08:49:03Z","title_canon_sha256":"8dcd2a16ed7a5572952cba19cded7c983be3d3518caa76b5e835dfba24e48f91"},"schema_version":"1.0","source":{"id":"1608.01465","kind":"arxiv","version":1}},"canonical_sha256":"0a3fca13992c71080a031106f64c3e59740c91605b718c1f2fd3c7710197d7e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a3fca13992c71080a031106f64c3e59740c91605b718c1f2fd3c7710197d7e3","first_computed_at":"2026-05-18T01:09:52.368241Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:52.368241Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xV4yqitJghs5jPDPJws8peeZGX9TjyZ0uDhTRsAg4QSzuyQinWprRL4patYhLm0Qpzfc40J2woO0Z/y1GhL2Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:52.368880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.01465","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcd731146ea25555d7b7039bb24ead604d9da185526d78e1c6e2ae63e2030bf6","sha256:7a48378147d92a10ef7bde751783791f0b06e2849fbe60fd4637af38ffc97e9b"],"state_sha256":"48d83871ca34f04a4c4b30a82dd8a53ccf7fc5016c5886084691e96cbf541108"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N/kbQbrPtPYq8HWNmUfSBzOJi9UXYK6wR3G9SJKxt30GNjG+pkBfOQW4jicJJVdcYG/HOCLe5fURsuntAlMyAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T12:35:40.156775Z","bundle_sha256":"1ca0c97a5b29632885c27606633e447cd05648ddc6c733ff94c8a361860e7b28"}}