{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TS6FCM7NJ3L4DRYVE4LOPHPHXK","short_pith_number":"pith:TS6FCM7N","canonical_record":{"source":{"id":"1811.01162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-03T05:05:51Z","cross_cats_sorted":[],"title_canon_sha256":"bda9baa1c4c5e15de10ee9828f98827052185f5d63b382d2479308deca2d6961","abstract_canon_sha256":"22949e0a31041aa1dc25a838ac0de8bf89d167a4e3ee169003db8afee0d82484"},"schema_version":"1.0"},"canonical_sha256":"9cbc5133ed4ed7c1c7152716e79de7ba91aa67a61262bf3b2d36502be2de2c85","source":{"kind":"arxiv","id":"1811.01162","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01162","created_at":"2026-05-18T00:01:35Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01162v1","created_at":"2026-05-18T00:01:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01162","created_at":"2026-05-18T00:01:35Z"},{"alias_kind":"pith_short_12","alias_value":"TS6FCM7NJ3L4","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TS6FCM7NJ3L4DRYV","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TS6FCM7N","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TS6FCM7NJ3L4DRYVE4LOPHPHXK","target":"record","payload":{"canonical_record":{"source":{"id":"1811.01162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-03T05:05:51Z","cross_cats_sorted":[],"title_canon_sha256":"bda9baa1c4c5e15de10ee9828f98827052185f5d63b382d2479308deca2d6961","abstract_canon_sha256":"22949e0a31041aa1dc25a838ac0de8bf89d167a4e3ee169003db8afee0d82484"},"schema_version":"1.0"},"canonical_sha256":"9cbc5133ed4ed7c1c7152716e79de7ba91aa67a61262bf3b2d36502be2de2c85","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:35.179980Z","signature_b64":"koLMch99zfWqM9LVm+iOe72CQmqlsS8QTPwfumBY24Qy/3YuB/odTg0rSh14Nsx3+qv2Y8FE2wgU5cfWNLGuDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cbc5133ed4ed7c1c7152716e79de7ba91aa67a61262bf3b2d36502be2de2c85","last_reissued_at":"2026-05-18T00:01:35.179457Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:35.179457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.01162","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":"2026-05-18T00:01:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9VtgxG9Vlvhs5bKraqrUtRzSpibX7tYSUv9KwbMJ3poICxloP6XxWXer8mJUYfgw7ItqEToO51zcfZHhrzeMAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T21:07:57.263851Z"},"content_sha256":"310700cce232189677b9ad607d7b24c1ccb0ce7cbe21cb471de21cc5bdb76910","schema_version":"1.0","event_id":"sha256:310700cce232189677b9ad607d7b24c1ccb0ce7cbe21cb471de21cc5bdb76910"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TS6FCM7NJ3L4DRYVE4LOPHPHXK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Improved approximation algorithms for path vertex covers in regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"An Zhang, Guohui Lin, Yong Chen, Zhi-Zhong Chen","submitted_at":"2018-11-03T05:05:51Z","abstract_excerpt":"Given a simple graph $G = (V, E)$ and a constant integer $k \\ge 2$, the $k$-path vertex cover problem ({\\sc P$k$VC}) asks for a minimum subset $F \\subseteq V$ of vertices such that the induced subgraph $G[V - F]$ does not contain any path of order $k$. When $k = 2$, this turns out to be the classic vertex cover ({\\sc VC}) problem, which admits a $\\left(2 - {\\rm \\Theta}\\left(\\frac 1{\\log|V|}\\right)\\right)$-approximation. The general {\\sc P$k$VC} admits a trivial $k$-approximation; when $k = 3$ and $k = 4$, the best known approximation results for {\\sc P$3$VC} and {\\sc P$4$VC} are a $2$-approxim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01162","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":"2026-05-18T00:01:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ztJ/xCVaCVRO6Phx7T4XAO7DAshHHsOlWD0CMWDjEiXK38QICfPoJhMiVVkbKGUD0rqEWouFJy7X0ZDon5ixCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T21:07:57.264213Z"},"content_sha256":"554a855817022b8b561ff6885371af249572a789578b5afb4acf3c85c6669fef","schema_version":"1.0","event_id":"sha256:554a855817022b8b561ff6885371af249572a789578b5afb4acf3c85c6669fef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TS6FCM7NJ3L4DRYVE4LOPHPHXK/bundle.json","state_url":"https://pith.science/pith/TS6FCM7NJ3L4DRYVE4LOPHPHXK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TS6FCM7NJ3L4DRYVE4LOPHPHXK/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":"2026-05-23T21:07:57Z","links":{"resolver":"https://pith.science/pith/TS6FCM7NJ3L4DRYVE4LOPHPHXK","bundle":"https://pith.science/pith/TS6FCM7NJ3L4DRYVE4LOPHPHXK/bundle.json","state":"https://pith.science/pith/TS6FCM7NJ3L4DRYVE4LOPHPHXK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TS6FCM7NJ3L4DRYVE4LOPHPHXK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TS6FCM7NJ3L4DRYVE4LOPHPHXK","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":"22949e0a31041aa1dc25a838ac0de8bf89d167a4e3ee169003db8afee0d82484","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-03T05:05:51Z","title_canon_sha256":"bda9baa1c4c5e15de10ee9828f98827052185f5d63b382d2479308deca2d6961"},"schema_version":"1.0","source":{"id":"1811.01162","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.01162","created_at":"2026-05-18T00:01:35Z"},{"alias_kind":"arxiv_version","alias_value":"1811.01162v1","created_at":"2026-05-18T00:01:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.01162","created_at":"2026-05-18T00:01:35Z"},{"alias_kind":"pith_short_12","alias_value":"TS6FCM7NJ3L4","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TS6FCM7NJ3L4DRYV","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TS6FCM7N","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:554a855817022b8b561ff6885371af249572a789578b5afb4acf3c85c6669fef","target":"graph","created_at":"2026-05-18T00:01:35Z","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":"Given a simple graph $G = (V, E)$ and a constant integer $k \\ge 2$, the $k$-path vertex cover problem ({\\sc P$k$VC}) asks for a minimum subset $F \\subseteq V$ of vertices such that the induced subgraph $G[V - F]$ does not contain any path of order $k$. When $k = 2$, this turns out to be the classic vertex cover ({\\sc VC}) problem, which admits a $\\left(2 - {\\rm \\Theta}\\left(\\frac 1{\\log|V|}\\right)\\right)$-approximation. The general {\\sc P$k$VC} admits a trivial $k$-approximation; when $k = 3$ and $k = 4$, the best known approximation results for {\\sc P$3$VC} and {\\sc P$4$VC} are a $2$-approxim","authors_text":"An Zhang, Guohui Lin, Yong Chen, Zhi-Zhong Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-03T05:05:51Z","title":"Improved approximation algorithms for path vertex covers in regular graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.01162","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":"sha256:310700cce232189677b9ad607d7b24c1ccb0ce7cbe21cb471de21cc5bdb76910","target":"record","created_at":"2026-05-18T00:01:35Z","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":"22949e0a31041aa1dc25a838ac0de8bf89d167a4e3ee169003db8afee0d82484","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-11-03T05:05:51Z","title_canon_sha256":"bda9baa1c4c5e15de10ee9828f98827052185f5d63b382d2479308deca2d6961"},"schema_version":"1.0","source":{"id":"1811.01162","kind":"arxiv","version":1}},"canonical_sha256":"9cbc5133ed4ed7c1c7152716e79de7ba91aa67a61262bf3b2d36502be2de2c85","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cbc5133ed4ed7c1c7152716e79de7ba91aa67a61262bf3b2d36502be2de2c85","first_computed_at":"2026-05-18T00:01:35.179457Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:35.179457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"koLMch99zfWqM9LVm+iOe72CQmqlsS8QTPwfumBY24Qy/3YuB/odTg0rSh14Nsx3+qv2Y8FE2wgU5cfWNLGuDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:35.179980Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.01162","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:310700cce232189677b9ad607d7b24c1ccb0ce7cbe21cb471de21cc5bdb76910","sha256:554a855817022b8b561ff6885371af249572a789578b5afb4acf3c85c6669fef"],"state_sha256":"be50f4a61f771814b62a20778ce47caf60abceb721e98e0f75759b69eb5e8b15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YdOg2AcDAl/u95TafjkG8DmNFj3yIvEwz/Cr5qJQ7VVs49vfMkEirlTH27KZXzlFNpy1K4EnXR3fpyFE94MtDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T21:07:57.266948Z","bundle_sha256":"4470c0c27434d1452967b4a26d164450a7023b3b137261ca59334f10d30cf96f"}}