{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:F3NK4QMFHOUUPRYHPNPVC55AL5","short_pith_number":"pith:F3NK4QMF","canonical_record":{"source":{"id":"1301.5953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-25T02:24:26Z","cross_cats_sorted":[],"title_canon_sha256":"afe8a8046f475342ba0f2caca48474a8b36f46476f318fb3774a5ef574ba78f4","abstract_canon_sha256":"277d04879ab71890d7c4cf177ee0ac7bd983be6cb06c1771168d37e005502f90"},"schema_version":"1.0"},"canonical_sha256":"2edaae41853ba947c7077b5f5177a05f48ba7ea3f44423a14cb704eab03354dd","source":{"kind":"arxiv","id":"1301.5953","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5953","created_at":"2026-05-18T03:35:27Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5953v1","created_at":"2026-05-18T03:35:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5953","created_at":"2026-05-18T03:35:27Z"},{"alias_kind":"pith_short_12","alias_value":"F3NK4QMFHOUU","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"F3NK4QMFHOUUPRYH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"F3NK4QMF","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:F3NK4QMFHOUUPRYHPNPVC55AL5","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5953","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-25T02:24:26Z","cross_cats_sorted":[],"title_canon_sha256":"afe8a8046f475342ba0f2caca48474a8b36f46476f318fb3774a5ef574ba78f4","abstract_canon_sha256":"277d04879ab71890d7c4cf177ee0ac7bd983be6cb06c1771168d37e005502f90"},"schema_version":"1.0"},"canonical_sha256":"2edaae41853ba947c7077b5f5177a05f48ba7ea3f44423a14cb704eab03354dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:35:27.508261Z","signature_b64":"d5lLeYkdLprdtH2o5QRx/18Gn7SPmLLd9De5a5UgkxPO3OV4xTk09TB6Bv+bWbijBL0WwBP7b9fH+L3g2huaCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2edaae41853ba947c7077b5f5177a05f48ba7ea3f44423a14cb704eab03354dd","last_reissued_at":"2026-05-18T03:35:27.507609Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:35:27.507609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5953","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":"2026-05-18T03:35:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5/IdzZb/OrCJnf3+VYGjlx9zvWOYgk71l1YX+xTsNskai8XGw3JEApnO9GMN3xtcL0QLQd/i2K93ffBjLNFjAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:52:53.803661Z"},"content_sha256":"1a4ad46411c0472eea188270f70736d927ddab2dcea85fa87771b29256f5cf0b","schema_version":"1.0","event_id":"sha256:1a4ad46411c0472eea188270f70736d927ddab2dcea85fa87771b29256f5cf0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:F3NK4QMFHOUUPRYHPNPVC55AL5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Andrzej Proskurowski, Dani\\\"el Paulusma, Hajo Broersma, Ji\\v{r}\\'i Fiala, Petr A. Golovach, Tom\\'a\\v{s} Kaiser","submitted_at":"2013-01-25T02:24:26Z","abstract_excerpt":"Hung and Chang showed that for all k>=1 an interval graph has a path cover of size at most k if and only if its scattering number is at most k. They also showed that an interval graph has a Hamilton cycle if and only if its scattering number is at most 0. We complete this characterization by proving that for all k<=-1 an interval graph is -(k+1)-Hamilton-connected if and only if its scattering number is at most k. We also give an O(m+n) time algorithm for computing the scattering number of an interval graph with n vertices an m edges, which improves the O(n^4) time bound of Kratsch, Kloks and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5953","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":"2026-05-18T03:35:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wlvcBLh6kH9Q7VKPJyUaFiuDgEyQ5TbPNb4XVWktOjhyYPGRctC6wPEeTf2peyXzz8PO+bGj0fRkgjDqrkVCDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:52:53.804299Z"},"content_sha256":"b68b1bf48492fa31ddf0f588e880c8256902d9f20d895329168d6bcc5d32554d","schema_version":"1.0","event_id":"sha256:b68b1bf48492fa31ddf0f588e880c8256902d9f20d895329168d6bcc5d32554d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5/bundle.json","state_url":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F3NK4QMFHOUUPRYHPNPVC55AL5/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":"2026-05-25T16:52:53Z","links":{"resolver":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5","bundle":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5/bundle.json","state":"https://pith.science/pith/F3NK4QMFHOUUPRYHPNPVC55AL5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F3NK4QMFHOUUPRYHPNPVC55AL5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:F3NK4QMFHOUUPRYHPNPVC55AL5","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":"277d04879ab71890d7c4cf177ee0ac7bd983be6cb06c1771168d37e005502f90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-25T02:24:26Z","title_canon_sha256":"afe8a8046f475342ba0f2caca48474a8b36f46476f318fb3774a5ef574ba78f4"},"schema_version":"1.0","source":{"id":"1301.5953","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5953","created_at":"2026-05-18T03:35:27Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5953v1","created_at":"2026-05-18T03:35:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5953","created_at":"2026-05-18T03:35:27Z"},{"alias_kind":"pith_short_12","alias_value":"F3NK4QMFHOUU","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"F3NK4QMFHOUUPRYH","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"F3NK4QMF","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:b68b1bf48492fa31ddf0f588e880c8256902d9f20d895329168d6bcc5d32554d","target":"graph","created_at":"2026-05-18T03:35:27Z","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"},"paper":{"abstract_excerpt":"Hung and Chang showed that for all k>=1 an interval graph has a path cover of size at most k if and only if its scattering number is at most k. They also showed that an interval graph has a Hamilton cycle if and only if its scattering number is at most 0. We complete this characterization by proving that for all k<=-1 an interval graph is -(k+1)-Hamilton-connected if and only if its scattering number is at most k. We also give an O(m+n) time algorithm for computing the scattering number of an interval graph with n vertices an m edges, which improves the O(n^4) time bound of Kratsch, Kloks and ","authors_text":"Andrzej Proskurowski, Dani\\\"el Paulusma, Hajo Broersma, Ji\\v{r}\\'i Fiala, Petr A. Golovach, Tom\\'a\\v{s} Kaiser","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-25T02:24:26Z","title":"Linear-Time Algorithms for Scattering Number and Hamilton-Connectivity of Interval Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5953","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":"sha256:1a4ad46411c0472eea188270f70736d927ddab2dcea85fa87771b29256f5cf0b","target":"record","created_at":"2026-05-18T03:35:27Z","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":"277d04879ab71890d7c4cf177ee0ac7bd983be6cb06c1771168d37e005502f90","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-01-25T02:24:26Z","title_canon_sha256":"afe8a8046f475342ba0f2caca48474a8b36f46476f318fb3774a5ef574ba78f4"},"schema_version":"1.0","source":{"id":"1301.5953","kind":"arxiv","version":1}},"canonical_sha256":"2edaae41853ba947c7077b5f5177a05f48ba7ea3f44423a14cb704eab03354dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2edaae41853ba947c7077b5f5177a05f48ba7ea3f44423a14cb704eab03354dd","first_computed_at":"2026-05-18T03:35:27.507609Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:27.507609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d5lLeYkdLprdtH2o5QRx/18Gn7SPmLLd9De5a5UgkxPO3OV4xTk09TB6Bv+bWbijBL0WwBP7b9fH+L3g2huaCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:27.508261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5953","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a4ad46411c0472eea188270f70736d927ddab2dcea85fa87771b29256f5cf0b","sha256:b68b1bf48492fa31ddf0f588e880c8256902d9f20d895329168d6bcc5d32554d"],"state_sha256":"ca9f837cca7b7d04d8951c27f9d2cce09e203f4c34f9479fd77b7d96f3d35ebf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+n49DtDSnC+/NoVzRhcU/dFuUXIZEFZqYWuT83tK3sXE/7vriMUTHUT9X3ijPXZkpFJNLvCyena4xhrdEAy1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:52:53.807235Z","bundle_sha256":"8bdbeaae4c54ef445c051b6fb633f7beefcd125507350d21bc07d95bec1035b9"}}