{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:TGRT65ESM6VMGRKIHKPXOP43LJ","short_pith_number":"pith:TGRT65ES","schema_version":"1.0","canonical_sha256":"99a33f749267aac345483a9f773f9b5a70c1620aeaaed8a219b9efd9f5bddf0b","source":{"kind":"arxiv","id":"0904.0727","version":3},"attestation_state":"computed","paper":{"title":"(Meta) Kernelization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Daniel Lokshtanov, Dimitrios M. Thilikos, Eelko Penninkx, Fedor V. Fomin, Hans L. Bodlaender, Saket Saurabh","submitted_at":"2009-04-04T16:11:07Z","abstract_excerpt":"In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance I to a polynomial in k, while preserving the answer. In this work we give two meta-theorems on kernelzation. The first theorem says that all problems expressible in Counting Monadic Second Order Logic and satisfying a coverability property admit a polynomial kernel on graphs of bounded genus. Our second result is that all problems that have finite integer index and satisfy a weaker coverability property ad"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0904.0727","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2009-04-04T16:11:07Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"c1124fe9242bab0759a4e36cf6bbab5b9656858c465d05f08c89a99a423fffd1","abstract_canon_sha256":"ed705e9189f89c13327c50aa5efaf66ef83fac456daaea436366859e050c3501"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:23.043278Z","signature_b64":"Lfj4SCgmVS0P7Rm7qyK5JyE0Is1Y+ZE7FAFjrNIk/XXnauhjYOYLXJeDvn0rsb2W3VC2Mzy0DXgdBwO/FZX9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99a33f749267aac345483a9f773f9b5a70c1620aeaaed8a219b9efd9f5bddf0b","last_reissued_at":"2026-05-18T03:12:23.042502Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:23.042502Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"(Meta) Kernelization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Daniel Lokshtanov, Dimitrios M. Thilikos, Eelko Penninkx, Fedor V. Fomin, Hans L. Bodlaender, Saket Saurabh","submitted_at":"2009-04-04T16:11:07Z","abstract_excerpt":"In a parameterized problem, every instance I comes with a positive integer k. The problem is said to admit a polynomial kernel if, in polynomial time, one can reduce the size of the instance I to a polynomial in k, while preserving the answer. In this work we give two meta-theorems on kernelzation. The first theorem says that all problems expressible in Counting Monadic Second Order Logic and satisfying a coverability property admit a polynomial kernel on graphs of bounded genus. Our second result is that all problems that have finite integer index and satisfy a weaker coverability property ad"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0904.0727","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0904.0727","created_at":"2026-05-18T03:12:23.042654+00:00"},{"alias_kind":"arxiv_version","alias_value":"0904.0727v3","created_at":"2026-05-18T03:12:23.042654+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0904.0727","created_at":"2026-05-18T03:12:23.042654+00:00"},{"alias_kind":"pith_short_12","alias_value":"TGRT65ESM6VM","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_16","alias_value":"TGRT65ESM6VMGRKI","created_at":"2026-05-18T12:26:01.383474+00:00"},{"alias_kind":"pith_short_8","alias_value":"TGRT65ES","created_at":"2026-05-18T12:26:01.383474+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TGRT65ESM6VMGRKIHKPXOP43LJ","json":"https://pith.science/pith/TGRT65ESM6VMGRKIHKPXOP43LJ.json","graph_json":"https://pith.science/api/pith-number/TGRT65ESM6VMGRKIHKPXOP43LJ/graph.json","events_json":"https://pith.science/api/pith-number/TGRT65ESM6VMGRKIHKPXOP43LJ/events.json","paper":"https://pith.science/paper/TGRT65ES"},"agent_actions":{"view_html":"https://pith.science/pith/TGRT65ESM6VMGRKIHKPXOP43LJ","download_json":"https://pith.science/pith/TGRT65ESM6VMGRKIHKPXOP43LJ.json","view_paper":"https://pith.science/paper/TGRT65ES","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0904.0727&json=true","fetch_graph":"https://pith.science/api/pith-number/TGRT65ESM6VMGRKIHKPXOP43LJ/graph.json","fetch_events":"https://pith.science/api/pith-number/TGRT65ESM6VMGRKIHKPXOP43LJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TGRT65ESM6VMGRKIHKPXOP43LJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TGRT65ESM6VMGRKIHKPXOP43LJ/action/storage_attestation","attest_author":"https://pith.science/pith/TGRT65ESM6VMGRKIHKPXOP43LJ/action/author_attestation","sign_citation":"https://pith.science/pith/TGRT65ESM6VMGRKIHKPXOP43LJ/action/citation_signature","submit_replication":"https://pith.science/pith/TGRT65ESM6VMGRKIHKPXOP43LJ/action/replication_record"}},"created_at":"2026-05-18T03:12:23.042654+00:00","updated_at":"2026-05-18T03:12:23.042654+00:00"}