{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:NTHGHSVTUNYHOQFGSWM5O3PJYV","short_pith_number":"pith:NTHGHSVT","canonical_record":{"source":{"id":"1009.0806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-04T05:39:41Z","cross_cats_sorted":[],"title_canon_sha256":"c3abc47ad0a15451d25874c25c850a1723133fbffbd7251252c43e36666c0948","abstract_canon_sha256":"8e7f2b6cf08eed9725d93054b61cb2564359f536889b0e137ca3f7252d34007c"},"schema_version":"1.0"},"canonical_sha256":"6cce63cab3a3707740a69599d76de9c54cb70b250771c276936d4234c55ecc87","source":{"kind":"arxiv","id":"1009.0806","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0806","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0806v1","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0806","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"pith_short_12","alias_value":"NTHGHSVTUNYH","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NTHGHSVTUNYHOQFG","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NTHGHSVT","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:NTHGHSVTUNYHOQFGSWM5O3PJYV","target":"record","payload":{"canonical_record":{"source":{"id":"1009.0806","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-04T05:39:41Z","cross_cats_sorted":[],"title_canon_sha256":"c3abc47ad0a15451d25874c25c850a1723133fbffbd7251252c43e36666c0948","abstract_canon_sha256":"8e7f2b6cf08eed9725d93054b61cb2564359f536889b0e137ca3f7252d34007c"},"schema_version":"1.0"},"canonical_sha256":"6cce63cab3a3707740a69599d76de9c54cb70b250771c276936d4234c55ecc87","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:41:24.569989Z","signature_b64":"BkU13KUrJvEutLjBbXgtaKfxKhpD9PJ28dJ+jwHmqx4GKReSzE/VBwEl+U4sv9cKS5dyra2wOeqXtqDTgJztCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cce63cab3a3707740a69599d76de9c54cb70b250771c276936d4234c55ecc87","last_reissued_at":"2026-05-18T04:41:24.569374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:41:24.569374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.0806","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":"2026-05-18T04:41:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v5Ji8GwIcnXvNEV/QgxY/E1NRZVX6T3F07gLElcfdCigBjFTeaCr/FmgrqXWrKAalL+PeBwqvQFnDGuojhN9CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T12:29:06.542281Z"},"content_sha256":"6a37e9554d97f0f842375fa7a054f1b9c00890c6669e6f8d4e3bede0ec60dc9e","schema_version":"1.0","event_id":"sha256:6a37e9554d97f0f842375fa7a054f1b9c00890c6669e6f8d4e3bede0ec60dc9e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:NTHGHSVTUNYHOQFGSWM5O3PJYV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Quartic Kernel for Pathwidth-One Vertex Deletion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Geevarghese Philip, Venkatesh Raman, Yngve Villanger","submitted_at":"2010-09-04T05:39:41Z","abstract_excerpt":"The pathwidth of a graph is a measure of how path-like the graph is. Given a graph G and an integer k, the problem of finding whether there exist at most k vertices in G whose deletion results in a graph of pathwidth at most one is NP- complete. We initiate the study of the parameterized complexity of this problem, parameterized by k. We show that the problem has a quartic vertex-kernel: We show that, given an input instance (G = (V, E), k); |V| = n, we can construct, in polynomial time, an instance (G', k') such that (i) (G, k) is a YES instance if and only if (G', k') is a YES instance, (ii)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0806","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":"2026-05-18T04:41:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pNB72Zm6ghkUPh2FCe374dJSLBcFaT9VWC38vGhh11AfVAZE8b2XuqHF3ax7rnAblTLOSoDCVYybmBDipznwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T12:29:06.542860Z"},"content_sha256":"fbcfb9370910ffe3312e81ac67750c4e15bf3e49ffbde1af6cb970ceae9c16ff","schema_version":"1.0","event_id":"sha256:fbcfb9370910ffe3312e81ac67750c4e15bf3e49ffbde1af6cb970ceae9c16ff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NTHGHSVTUNYHOQFGSWM5O3PJYV/bundle.json","state_url":"https://pith.science/pith/NTHGHSVTUNYHOQFGSWM5O3PJYV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NTHGHSVTUNYHOQFGSWM5O3PJYV/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":"2026-05-22T12:29:06Z","links":{"resolver":"https://pith.science/pith/NTHGHSVTUNYHOQFGSWM5O3PJYV","bundle":"https://pith.science/pith/NTHGHSVTUNYHOQFGSWM5O3PJYV/bundle.json","state":"https://pith.science/pith/NTHGHSVTUNYHOQFGSWM5O3PJYV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NTHGHSVTUNYHOQFGSWM5O3PJYV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NTHGHSVTUNYHOQFGSWM5O3PJYV","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":"8e7f2b6cf08eed9725d93054b61cb2564359f536889b0e137ca3f7252d34007c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-04T05:39:41Z","title_canon_sha256":"c3abc47ad0a15451d25874c25c850a1723133fbffbd7251252c43e36666c0948"},"schema_version":"1.0","source":{"id":"1009.0806","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.0806","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"arxiv_version","alias_value":"1009.0806v1","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.0806","created_at":"2026-05-18T04:41:24Z"},{"alias_kind":"pith_short_12","alias_value":"NTHGHSVTUNYH","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"NTHGHSVTUNYHOQFG","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"NTHGHSVT","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:fbcfb9370910ffe3312e81ac67750c4e15bf3e49ffbde1af6cb970ceae9c16ff","target":"graph","created_at":"2026-05-18T04:41:24Z","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":"The pathwidth of a graph is a measure of how path-like the graph is. Given a graph G and an integer k, the problem of finding whether there exist at most k vertices in G whose deletion results in a graph of pathwidth at most one is NP- complete. We initiate the study of the parameterized complexity of this problem, parameterized by k. We show that the problem has a quartic vertex-kernel: We show that, given an input instance (G = (V, E), k); |V| = n, we can construct, in polynomial time, an instance (G', k') such that (i) (G, k) is a YES instance if and only if (G', k') is a YES instance, (ii)","authors_text":"Geevarghese Philip, Venkatesh Raman, Yngve Villanger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-04T05:39:41Z","title":"A Quartic Kernel for Pathwidth-One Vertex Deletion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0806","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":"sha256:6a37e9554d97f0f842375fa7a054f1b9c00890c6669e6f8d4e3bede0ec60dc9e","target":"record","created_at":"2026-05-18T04:41:24Z","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":"8e7f2b6cf08eed9725d93054b61cb2564359f536889b0e137ca3f7252d34007c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2010-09-04T05:39:41Z","title_canon_sha256":"c3abc47ad0a15451d25874c25c850a1723133fbffbd7251252c43e36666c0948"},"schema_version":"1.0","source":{"id":"1009.0806","kind":"arxiv","version":1}},"canonical_sha256":"6cce63cab3a3707740a69599d76de9c54cb70b250771c276936d4234c55ecc87","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6cce63cab3a3707740a69599d76de9c54cb70b250771c276936d4234c55ecc87","first_computed_at":"2026-05-18T04:41:24.569374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:41:24.569374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BkU13KUrJvEutLjBbXgtaKfxKhpD9PJ28dJ+jwHmqx4GKReSzE/VBwEl+U4sv9cKS5dyra2wOeqXtqDTgJztCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:41:24.569989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.0806","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a37e9554d97f0f842375fa7a054f1b9c00890c6669e6f8d4e3bede0ec60dc9e","sha256:fbcfb9370910ffe3312e81ac67750c4e15bf3e49ffbde1af6cb970ceae9c16ff"],"state_sha256":"fd76c8625f0556e518199a1366353482717e7dcdcb86d1fba6d152ac00756c9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n5NNcee/+BhUWby86Scp/AfWdEdo7/LgLj+ZuTjYyNwXtIhRKZveeoDcnDTwStNPXVmkEQ/1Kkl62tOosICQDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T12:29:06.545958Z","bundle_sha256":"db43380df247fe6c7810ccb7e1dc3fb8d3291cda1e1bd5f5a76e018931eba027"}}