{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:E3WTRICJ6ABC5X26TCRMQU4K7D","short_pith_number":"pith:E3WTRICJ","canonical_record":{"source":{"id":"1204.1989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-09T20:53:18Z","cross_cats_sorted":[],"title_canon_sha256":"006799453f34587bf1f2af6ef07f53cca970dd88dfcac22a8e50af5fa3cb3f27","abstract_canon_sha256":"b567ed8bf81f8cbbfc72607da55a62ea2b614a139658e6a1dfa0c370afb8c30f"},"schema_version":"1.0"},"canonical_sha256":"26ed38a049f0022edf5e98a2c8538af8d37a818d1bfbbd13e2eaef07edb9b33e","source":{"kind":"arxiv","id":"1204.1989","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1989","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1989v1","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1989","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"E3WTRICJ6ABC","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E3WTRICJ6ABC5X26","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E3WTRICJ","created_at":"2026-05-18T12:27:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:E3WTRICJ6ABC5X26TCRMQU4K7D","target":"record","payload":{"canonical_record":{"source":{"id":"1204.1989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-09T20:53:18Z","cross_cats_sorted":[],"title_canon_sha256":"006799453f34587bf1f2af6ef07f53cca970dd88dfcac22a8e50af5fa3cb3f27","abstract_canon_sha256":"b567ed8bf81f8cbbfc72607da55a62ea2b614a139658e6a1dfa0c370afb8c30f"},"schema_version":"1.0"},"canonical_sha256":"26ed38a049f0022edf5e98a2c8538af8d37a818d1bfbbd13e2eaef07edb9b33e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:13.580772Z","signature_b64":"HXbEPY12sEG9ZtuOWle5S6Nfa2Jxm8W3VL/gRtBKwMGF/PDG/OpUIYxwSBXI0Bz4zeHrckbomiyb0L0VJUuNBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26ed38a049f0022edf5e98a2c8538af8d37a818d1bfbbd13e2eaef07edb9b33e","last_reissued_at":"2026-05-18T03:58:13.580334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:13.580334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.1989","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":"2026-05-18T03:58:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u07qfVttEQ/qvcjDnm5qKUC3KOzqL0KLJDa0E7z+/hU092wvceOtH/3Rij9G1rvHsvHiOCdJ+ljC3aWyaoPTBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:47:47.851017Z"},"content_sha256":"9b54af08a926438f182c63956cf7f253118a30fbf366d543575e2e998bcc6aa8","schema_version":"1.0","event_id":"sha256:9b54af08a926438f182c63956cf7f253118a30fbf366d543575e2e998bcc6aa8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:E3WTRICJ6ABC5X26TCRMQU4K7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multiple Petersen subdivisions in permutation graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jean-S\\'ebastien Sereni, Tom\\'a\\v{s} Kaiser, Zelealem Yilma","submitted_at":"2012-04-09T20:53:18Z","abstract_excerpt":"A permutation graph is a cubic graph admitting a 1-factor M whose complement consists of two chordless cycles. Extending results of Ellingham and of Goldwasser and Zhang, we prove that if e is an edge of M such that every 4-cycle containing an edge of M contains e, then e is contained in a subdivision of the Petersen graph of a special type. In particular, if the graph is cyclically 5-edge-connected, then every edge of M is contained in such a subdivision. Our proof is based on a characterization of cographs in terms of twin vertices. We infer a linear lower bound on the number of Petersen sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1989","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":"2026-05-18T03:58:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kE5V3ijwEb2qu2JNi8BbilUIN+nV3Vrq9w1eXpo1uCrV82EAicVmAyopAxCw9g/ryvXpnl0TQxpL8lJCO5jHAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:47:47.851416Z"},"content_sha256":"37a4f09c8ef789e3a33090f7fb8c7dfb655e7ea961eb4b2af9a2177dfe071d0d","schema_version":"1.0","event_id":"sha256:37a4f09c8ef789e3a33090f7fb8c7dfb655e7ea961eb4b2af9a2177dfe071d0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E3WTRICJ6ABC5X26TCRMQU4K7D/bundle.json","state_url":"https://pith.science/pith/E3WTRICJ6ABC5X26TCRMQU4K7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E3WTRICJ6ABC5X26TCRMQU4K7D/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":"2026-05-25T22:47:47Z","links":{"resolver":"https://pith.science/pith/E3WTRICJ6ABC5X26TCRMQU4K7D","bundle":"https://pith.science/pith/E3WTRICJ6ABC5X26TCRMQU4K7D/bundle.json","state":"https://pith.science/pith/E3WTRICJ6ABC5X26TCRMQU4K7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E3WTRICJ6ABC5X26TCRMQU4K7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E3WTRICJ6ABC5X26TCRMQU4K7D","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":"b567ed8bf81f8cbbfc72607da55a62ea2b614a139658e6a1dfa0c370afb8c30f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-09T20:53:18Z","title_canon_sha256":"006799453f34587bf1f2af6ef07f53cca970dd88dfcac22a8e50af5fa3cb3f27"},"schema_version":"1.0","source":{"id":"1204.1989","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1989","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1989v1","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1989","created_at":"2026-05-18T03:58:13Z"},{"alias_kind":"pith_short_12","alias_value":"E3WTRICJ6ABC","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E3WTRICJ6ABC5X26","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E3WTRICJ","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:37a4f09c8ef789e3a33090f7fb8c7dfb655e7ea961eb4b2af9a2177dfe071d0d","target":"graph","created_at":"2026-05-18T03:58:13Z","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":"A permutation graph is a cubic graph admitting a 1-factor M whose complement consists of two chordless cycles. Extending results of Ellingham and of Goldwasser and Zhang, we prove that if e is an edge of M such that every 4-cycle containing an edge of M contains e, then e is contained in a subdivision of the Petersen graph of a special type. In particular, if the graph is cyclically 5-edge-connected, then every edge of M is contained in such a subdivision. Our proof is based on a characterization of cographs in terms of twin vertices. We infer a linear lower bound on the number of Petersen sub","authors_text":"Jean-S\\'ebastien Sereni, Tom\\'a\\v{s} Kaiser, Zelealem Yilma","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-09T20:53:18Z","title":"Multiple Petersen subdivisions in permutation graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1989","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":"sha256:9b54af08a926438f182c63956cf7f253118a30fbf366d543575e2e998bcc6aa8","target":"record","created_at":"2026-05-18T03:58:13Z","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":"b567ed8bf81f8cbbfc72607da55a62ea2b614a139658e6a1dfa0c370afb8c30f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-04-09T20:53:18Z","title_canon_sha256":"006799453f34587bf1f2af6ef07f53cca970dd88dfcac22a8e50af5fa3cb3f27"},"schema_version":"1.0","source":{"id":"1204.1989","kind":"arxiv","version":1}},"canonical_sha256":"26ed38a049f0022edf5e98a2c8538af8d37a818d1bfbbd13e2eaef07edb9b33e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26ed38a049f0022edf5e98a2c8538af8d37a818d1bfbbd13e2eaef07edb9b33e","first_computed_at":"2026-05-18T03:58:13.580334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:13.580334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HXbEPY12sEG9ZtuOWle5S6Nfa2Jxm8W3VL/gRtBKwMGF/PDG/OpUIYxwSBXI0Bz4zeHrckbomiyb0L0VJUuNBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:13.580772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1989","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b54af08a926438f182c63956cf7f253118a30fbf366d543575e2e998bcc6aa8","sha256:37a4f09c8ef789e3a33090f7fb8c7dfb655e7ea961eb4b2af9a2177dfe071d0d"],"state_sha256":"309e67db77f1e1e040f6c7a66fbfb61066beecb66b5aead6c734bf5c62ba86f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PkR1SD1i51+xz/hEOQ2Bqmi5R2KNn9Q8M3ckheNTP1wXxd/iDZKYNmP9lDiWJPVfRN3PVbWg1jubFjLY7GXxDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:47:47.854650Z","bundle_sha256":"47d084902f177fe58fc8758e034560e175f6f552c68db18a08d9a1ae758c98b8"}}