{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:VZ7G6XPRDQCN2KKKZAAXAPFVVQ","short_pith_number":"pith:VZ7G6XPR","schema_version":"1.0","canonical_sha256":"ae7e6f5df11c04dd294ac801703cb5ac3f31f9bebfa062e9ee7096dec022da4a","source":{"kind":"arxiv","id":"2403.06335","version":2},"attestation_state":"computed","paper":{"title":"Improved FPT Approximation Scheme and Approximate Kernel for Biclique-Free Max k-Weight SAT: Greedy Strikes Back","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Pasin Manurangsi","submitted_at":"2024-03-10T22:54:06Z","abstract_excerpt":"In the Max $k$-Weight SAT (aka Max SAT with Cardinality Constraint) problem, we are given a CNF formula with $n$ variables and $m$ clauses together with a positive integer $k$. The goal is to find an assignment where at most $k$ variables are set to one that satisfies as many constraints as possible. Recently, Jain et al. [SODA'23] gave an FPT approximation scheme (FPT-AS) with running time $2^{O\\left(\\left(dk/\\epsilon\\right)^d\\right)} \\cdot (n + m)^{O(1)}$ for Max $k$-Weight SAT when the incidence graph is $K_{d,d}$-free. They asked whether a polynomial-size approximate kernel exists. In this"},"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":"2403.06335","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-03-10T22:54:06Z","cross_cats_sorted":[],"title_canon_sha256":"65e7adf38ed7906be1628de25e03afcd9e7d28226a12a06c1965fe524d90d512","abstract_canon_sha256":"ef1026073dbbc974d8ef20f771a18e2781ebbe12f69eca423db5c12213952d65"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:27:06.158143Z","signature_b64":"PUwQIfiyzjve23BenIqNWhh3NharKrlt04M6zWQ6GT4pOKgv84iJiomb+BP7426SkD60oVa/Tq6FABAf7vXrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae7e6f5df11c04dd294ac801703cb5ac3f31f9bebfa062e9ee7096dec022da4a","last_reissued_at":"2026-07-05T08:27:06.157800Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:27:06.157800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved FPT Approximation Scheme and Approximate Kernel for Biclique-Free Max k-Weight SAT: Greedy Strikes Back","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Pasin Manurangsi","submitted_at":"2024-03-10T22:54:06Z","abstract_excerpt":"In the Max $k$-Weight SAT (aka Max SAT with Cardinality Constraint) problem, we are given a CNF formula with $n$ variables and $m$ clauses together with a positive integer $k$. The goal is to find an assignment where at most $k$ variables are set to one that satisfies as many constraints as possible. Recently, Jain et al. [SODA'23] gave an FPT approximation scheme (FPT-AS) with running time $2^{O\\left(\\left(dk/\\epsilon\\right)^d\\right)} \\cdot (n + m)^{O(1)}$ for Max $k$-Weight SAT when the incidence graph is $K_{d,d}$-free. They asked whether a polynomial-size approximate kernel exists. In this"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06335","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.06335/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2403.06335","created_at":"2026-07-05T08:27:06.157855+00:00"},{"alias_kind":"arxiv_version","alias_value":"2403.06335v2","created_at":"2026-07-05T08:27:06.157855+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06335","created_at":"2026-07-05T08:27:06.157855+00:00"},{"alias_kind":"pith_short_12","alias_value":"VZ7G6XPRDQCN","created_at":"2026-07-05T08:27:06.157855+00:00"},{"alias_kind":"pith_short_16","alias_value":"VZ7G6XPRDQCN2KKK","created_at":"2026-07-05T08:27:06.157855+00:00"},{"alias_kind":"pith_short_8","alias_value":"VZ7G6XPR","created_at":"2026-07-05T08:27:06.157855+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.12699","citing_title":"More Efforts Towards Fixed-Parameter Approximability of Multiwinner Rules","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ","json":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ.json","graph_json":"https://pith.science/api/pith-number/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/graph.json","events_json":"https://pith.science/api/pith-number/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/events.json","paper":"https://pith.science/paper/VZ7G6XPR"},"agent_actions":{"view_html":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ","download_json":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ.json","view_paper":"https://pith.science/paper/VZ7G6XPR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2403.06335&json=true","fetch_graph":"https://pith.science/api/pith-number/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/graph.json","fetch_events":"https://pith.science/api/pith-number/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/action/storage_attestation","attest_author":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/action/author_attestation","sign_citation":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/action/citation_signature","submit_replication":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/action/replication_record"}},"created_at":"2026-07-05T08:27:06.157855+00:00","updated_at":"2026-07-05T08:27:06.157855+00:00"}