{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:IVZLMSGA4ZYCK6PTOI6OJBMBQ4","short_pith_number":"pith:IVZLMSGA","canonical_record":{"source":{"id":"1311.1612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-07T09:09:05Z","cross_cats_sorted":[],"title_canon_sha256":"ea973a292e5e50bbc042343c5be4353f7467f756d3768945d2ecbf0a7222577f","abstract_canon_sha256":"18782de52ca84ce7808b01c1791d5d40c7a9e02ee499698281650e2790a12916"},"schema_version":"1.0"},"canonical_sha256":"4572b648c0e6702579f3723ce48581871b72b8a104495636292a157e7f1bbfa6","source":{"kind":"arxiv","id":"1311.1612","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1612","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1612v1","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1612","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"IVZLMSGA4ZYC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IVZLMSGA4ZYCK6PT","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IVZLMSGA","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:IVZLMSGA4ZYCK6PTOI6OJBMBQ4","target":"record","payload":{"canonical_record":{"source":{"id":"1311.1612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-07T09:09:05Z","cross_cats_sorted":[],"title_canon_sha256":"ea973a292e5e50bbc042343c5be4353f7467f756d3768945d2ecbf0a7222577f","abstract_canon_sha256":"18782de52ca84ce7808b01c1791d5d40c7a9e02ee499698281650e2790a12916"},"schema_version":"1.0"},"canonical_sha256":"4572b648c0e6702579f3723ce48581871b72b8a104495636292a157e7f1bbfa6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:22.192448Z","signature_b64":"vG0wRJEqQROnVwnOaUTHFSDgSl8RighpnXpqXetpgbSUiRS9h+3GSokUN9ARzpb6zyRP7cddFw6j/PLaQ8prDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4572b648c0e6702579f3723ce48581871b72b8a104495636292a157e7f1bbfa6","last_reissued_at":"2026-05-18T00:42:22.191690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:22.191690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.1612","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":"2026-05-18T00:42:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v0WV3cjvQ5HvO2IRoZSD1WeX8ZIs3LRecfP8WFD2sDmuSvyFXEEQnGS6PNv0JZarzKNqkBj1Ij1snqlmB9vsAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:06:09.043377Z"},"content_sha256":"2acdff0ec5a660da435aa19b4e7c80ddc82a81901b5e1d890ba3a9e5f6ff9d09","schema_version":"1.0","event_id":"sha256:2acdff0ec5a660da435aa19b4e7c80ddc82a81901b5e1d890ba3a9e5f6ff9d09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:IVZLMSGA4ZYCK6PTOI6OJBMBQ4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear Extensions of N-free Orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Stefan Felsner, Thibault Manneville","submitted_at":"2013-11-07T09:09:05Z","abstract_excerpt":"We consider the number of linear extensions of an N-free order P. We give upper and lower bounds on this number in terms of parameters of the corresponding arc diagram. We propose a dynamic programming algorithm to calculate the number. The algorithm is polynomial if a new parameter called activity is bounded by a constant. The activity can be bounded in terms of parameters of the arc diagram."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1612","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":"2026-05-18T00:42:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1a3Ct2K2NTfr/D8M3TEO4ITp/ddx/w94QL+KxQ1ILNvGI0hkwpyxCYc/Jiz/YJkSpVzMWZGGAsQNHAACIoqDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T14:06:09.044043Z"},"content_sha256":"42e72fbe4a2f2efed2e0b0dd2405a8fe5d6ab8e5227d502d09422bcb9e6e37d5","schema_version":"1.0","event_id":"sha256:42e72fbe4a2f2efed2e0b0dd2405a8fe5d6ab8e5227d502d09422bcb9e6e37d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IVZLMSGA4ZYCK6PTOI6OJBMBQ4/bundle.json","state_url":"https://pith.science/pith/IVZLMSGA4ZYCK6PTOI6OJBMBQ4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IVZLMSGA4ZYCK6PTOI6OJBMBQ4/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":"2026-06-07T14:06:09Z","links":{"resolver":"https://pith.science/pith/IVZLMSGA4ZYCK6PTOI6OJBMBQ4","bundle":"https://pith.science/pith/IVZLMSGA4ZYCK6PTOI6OJBMBQ4/bundle.json","state":"https://pith.science/pith/IVZLMSGA4ZYCK6PTOI6OJBMBQ4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IVZLMSGA4ZYCK6PTOI6OJBMBQ4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IVZLMSGA4ZYCK6PTOI6OJBMBQ4","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":"18782de52ca84ce7808b01c1791d5d40c7a9e02ee499698281650e2790a12916","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-07T09:09:05Z","title_canon_sha256":"ea973a292e5e50bbc042343c5be4353f7467f756d3768945d2ecbf0a7222577f"},"schema_version":"1.0","source":{"id":"1311.1612","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1612","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1612v1","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1612","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"IVZLMSGA4ZYC","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IVZLMSGA4ZYCK6PT","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IVZLMSGA","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:42e72fbe4a2f2efed2e0b0dd2405a8fe5d6ab8e5227d502d09422bcb9e6e37d5","target":"graph","created_at":"2026-05-18T00:42:22Z","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 consider the number of linear extensions of an N-free order P. We give upper and lower bounds on this number in terms of parameters of the corresponding arc diagram. We propose a dynamic programming algorithm to calculate the number. The algorithm is polynomial if a new parameter called activity is bounded by a constant. The activity can be bounded in terms of parameters of the arc diagram.","authors_text":"Stefan Felsner, Thibault Manneville","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-07T09:09:05Z","title":"Linear Extensions of N-free Orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1612","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":"sha256:2acdff0ec5a660da435aa19b4e7c80ddc82a81901b5e1d890ba3a9e5f6ff9d09","target":"record","created_at":"2026-05-18T00:42:22Z","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":"18782de52ca84ce7808b01c1791d5d40c7a9e02ee499698281650e2790a12916","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-11-07T09:09:05Z","title_canon_sha256":"ea973a292e5e50bbc042343c5be4353f7467f756d3768945d2ecbf0a7222577f"},"schema_version":"1.0","source":{"id":"1311.1612","kind":"arxiv","version":1}},"canonical_sha256":"4572b648c0e6702579f3723ce48581871b72b8a104495636292a157e7f1bbfa6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4572b648c0e6702579f3723ce48581871b72b8a104495636292a157e7f1bbfa6","first_computed_at":"2026-05-18T00:42:22.191690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:22.191690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vG0wRJEqQROnVwnOaUTHFSDgSl8RighpnXpqXetpgbSUiRS9h+3GSokUN9ARzpb6zyRP7cddFw6j/PLaQ8prDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:22.192448Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1612","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2acdff0ec5a660da435aa19b4e7c80ddc82a81901b5e1d890ba3a9e5f6ff9d09","sha256:42e72fbe4a2f2efed2e0b0dd2405a8fe5d6ab8e5227d502d09422bcb9e6e37d5"],"state_sha256":"d0a3e5c2e6f52a59cc4b5fbbb64a3926788f9e700888f0eb12b959441fb4cc39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QTAPWZtJm74ebq/zblRDJMxtIY5f3jDL/1Lx9F9b1pRDF/F9edsZVsHxrJDvkxR02pppQHoQ6TUdxt189ZpZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T14:06:09.047659Z","bundle_sha256":"4652b574f8621a5c3d981339d52d98462d5ace840d2c72249af46787e2613e77"}}