{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:RB53BPQ7EXWAM75V4KQQ6GHDUY","short_pith_number":"pith:RB53BPQ7","canonical_record":{"source":{"id":"1705.02822","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2017-05-08T10:56:28Z","cross_cats_sorted":[],"title_canon_sha256":"62154846e329f2f5de14d0ab6dd49a51da77ed25dfe20f17ca2a2cbc63803ade","abstract_canon_sha256":"4d23d2a4d3b77b584fb80794f3951181629baaff7a46c868da4fde88a2fbf2a5"},"schema_version":"1.0"},"canonical_sha256":"887bb0be1f25ec067fb5e2a10f18e3a61fed49f8ed77c03f1430b2a249ee3570","source":{"kind":"arxiv","id":"1705.02822","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02822","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02822v2","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02822","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"pith_short_12","alias_value":"RB53BPQ7EXWA","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RB53BPQ7EXWAM75V","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RB53BPQ7","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:RB53BPQ7EXWAM75V4KQQ6GHDUY","target":"record","payload":{"canonical_record":{"source":{"id":"1705.02822","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2017-05-08T10:56:28Z","cross_cats_sorted":[],"title_canon_sha256":"62154846e329f2f5de14d0ab6dd49a51da77ed25dfe20f17ca2a2cbc63803ade","abstract_canon_sha256":"4d23d2a4d3b77b584fb80794f3951181629baaff7a46c868da4fde88a2fbf2a5"},"schema_version":"1.0"},"canonical_sha256":"887bb0be1f25ec067fb5e2a10f18e3a61fed49f8ed77c03f1430b2a249ee3570","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:43.844489Z","signature_b64":"lSJERX5JM9c24Tt8146Mxx8kbcjryTbGV7JVyRJED5nIe7xnimneTaGbV6wdnzXD4YwysDwofYXeLQiAQ7pEBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"887bb0be1f25ec067fb5e2a10f18e3a61fed49f8ed77c03f1430b2a249ee3570","last_reissued_at":"2026-05-18T00:44:43.843852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:43.843852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.02822","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iaNRcUITNgRTtTjYL653G2ieuZC51Z783HLkCGSwjyLeI+av6lCMYyfCRV03EcFBF8UD0P7FIT6OXgqbLqiTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:45:01.288780Z"},"content_sha256":"9227d46afd5c01d4402371c51c4f82b68344ab7a6cfabf21aca3a69065e74f7a","schema_version":"1.0","event_id":"sha256:9227d46afd5c01d4402371c51c4f82b68344ab7a6cfabf21aca3a69065e74f7a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:RB53BPQ7EXWAM75V4KQQ6GHDUY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rank Vertex Cover as a Natural Problem for Algebraic Compression","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Fahad Panolan, Meirav Zehavi, Saket Saurabh, Syed Mohammad Meesum","submitted_at":"2017-05-08T10:56:28Z","abstract_excerpt":"The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem has been a longstanding, notorious open problem in Parameterized Complexity. Five years ago, the breakthrough work by Kratsch and Wahlstrom on representative sets has finally answered this question in the affirmative [FOCS 2012]. In this paper, we present an alternative, algebraic compression of the Vertex Cover Above LP problem into the Rank Vertex Cover problem. Here, the input consists of a graph G, a parameter k, and a bijection between V (G) and the set of columns of a representation of a matr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02822","kind":"arxiv","version":2},"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":"2026-05-18T00:44:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jJsbD1Q5sX5BKNTKZQgyzZwZ2sRFrH+llqT9Zbvet3hioYJUwhKOtKlJHmPW7iQD7g/10pbvsH1y4ejF6W6ECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:45:01.289140Z"},"content_sha256":"e5336dd74003b16beb0f17f91f5726d6b9eab549313b12e539783633ff47c8fc","schema_version":"1.0","event_id":"sha256:e5336dd74003b16beb0f17f91f5726d6b9eab549313b12e539783633ff47c8fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RB53BPQ7EXWAM75V4KQQ6GHDUY/bundle.json","state_url":"https://pith.science/pith/RB53BPQ7EXWAM75V4KQQ6GHDUY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RB53BPQ7EXWAM75V4KQQ6GHDUY/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":"2026-05-30T10:45:01Z","links":{"resolver":"https://pith.science/pith/RB53BPQ7EXWAM75V4KQQ6GHDUY","bundle":"https://pith.science/pith/RB53BPQ7EXWAM75V4KQQ6GHDUY/bundle.json","state":"https://pith.science/pith/RB53BPQ7EXWAM75V4KQQ6GHDUY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RB53BPQ7EXWAM75V4KQQ6GHDUY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:RB53BPQ7EXWAM75V4KQQ6GHDUY","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":"4d23d2a4d3b77b584fb80794f3951181629baaff7a46c868da4fde88a2fbf2a5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2017-05-08T10:56:28Z","title_canon_sha256":"62154846e329f2f5de14d0ab6dd49a51da77ed25dfe20f17ca2a2cbc63803ade"},"schema_version":"1.0","source":{"id":"1705.02822","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02822","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02822v2","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02822","created_at":"2026-05-18T00:44:43Z"},{"alias_kind":"pith_short_12","alias_value":"RB53BPQ7EXWA","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"RB53BPQ7EXWAM75V","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"RB53BPQ7","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:e5336dd74003b16beb0f17f91f5726d6b9eab549313b12e539783633ff47c8fc","target":"graph","created_at":"2026-05-18T00:44:43Z","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 question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem has been a longstanding, notorious open problem in Parameterized Complexity. Five years ago, the breakthrough work by Kratsch and Wahlstrom on representative sets has finally answered this question in the affirmative [FOCS 2012]. In this paper, we present an alternative, algebraic compression of the Vertex Cover Above LP problem into the Rank Vertex Cover problem. Here, the input consists of a graph G, a parameter k, and a bijection between V (G) and the set of columns of a representation of a matr","authors_text":"Fahad Panolan, Meirav Zehavi, Saket Saurabh, Syed Mohammad Meesum","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2017-05-08T10:56:28Z","title":"Rank Vertex Cover as a Natural Problem for Algebraic Compression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02822","kind":"arxiv","version":2},"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":"sha256:9227d46afd5c01d4402371c51c4f82b68344ab7a6cfabf21aca3a69065e74f7a","target":"record","created_at":"2026-05-18T00:44:43Z","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":"4d23d2a4d3b77b584fb80794f3951181629baaff7a46c868da4fde88a2fbf2a5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"cs.DS","submitted_at":"2017-05-08T10:56:28Z","title_canon_sha256":"62154846e329f2f5de14d0ab6dd49a51da77ed25dfe20f17ca2a2cbc63803ade"},"schema_version":"1.0","source":{"id":"1705.02822","kind":"arxiv","version":2}},"canonical_sha256":"887bb0be1f25ec067fb5e2a10f18e3a61fed49f8ed77c03f1430b2a249ee3570","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"887bb0be1f25ec067fb5e2a10f18e3a61fed49f8ed77c03f1430b2a249ee3570","first_computed_at":"2026-05-18T00:44:43.843852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:43.843852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lSJERX5JM9c24Tt8146Mxx8kbcjryTbGV7JVyRJED5nIe7xnimneTaGbV6wdnzXD4YwysDwofYXeLQiAQ7pEBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:43.844489Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02822","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9227d46afd5c01d4402371c51c4f82b68344ab7a6cfabf21aca3a69065e74f7a","sha256:e5336dd74003b16beb0f17f91f5726d6b9eab549313b12e539783633ff47c8fc"],"state_sha256":"4a7e0ed6546b1852fdf4053017dff6f7bdea088db15ba9af71ba30d600fa9ff3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"05Ss90RVVVF0VHa0R+EgOlvkxMPG6ldYdmAKewwuFrmKqiuDO5pgcDsi3T+1c+XahOBUMDRYh02uFxOMrau2Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:45:01.291572Z","bundle_sha256":"f39d5067d4de72c9efb5279381b349d7961102525b5b423509130bf10f9d98a2"}}