{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:VZ7G6XPRDQCN2KKKZAAXAPFVVQ","short_pith_number":"pith:VZ7G6XPR","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"},"canonical_sha256":"ae7e6f5df11c04dd294ac801703cb5ac3f31f9bebfa062e9ee7096dec022da4a","source":{"kind":"arxiv","id":"2403.06335","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.06335","created_at":"2026-07-05T08:27:06Z"},{"alias_kind":"arxiv_version","alias_value":"2403.06335v2","created_at":"2026-07-05T08:27:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06335","created_at":"2026-07-05T08:27:06Z"},{"alias_kind":"pith_short_12","alias_value":"VZ7G6XPRDQCN","created_at":"2026-07-05T08:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"VZ7G6XPRDQCN2KKK","created_at":"2026-07-05T08:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"VZ7G6XPR","created_at":"2026-07-05T08:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:VZ7G6XPRDQCN2KKKZAAXAPFVVQ","target":"record","payload":{"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"},"canonical_sha256":"ae7e6f5df11c04dd294ac801703cb5ac3f31f9bebfa062e9ee7096dec022da4a","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"},"source_kind":"arxiv","source_id":"2403.06335","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":"2026-07-05T08:27:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DkvNFCLG+y4bsujC1+QYgjll/t8XYAhxpCTA4Zo2o0NZ5jMUvEv0p92rRVQfUSuUdoiHRUTeWUvWnSvxun+JDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T16:16:30.079314Z"},"content_sha256":"11171931b82a72eb4bd56479e27f2a61d215fe062dca7cdb3776fd3d61fde7f9","schema_version":"1.0","event_id":"sha256:11171931b82a72eb4bd56479e27f2a61d215fe062dca7cdb3776fd3d61fde7f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:VZ7G6XPRDQCN2KKKZAAXAPFVVQ","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:27:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"76KlYpxg9Sjp3oBtpsZoIsZrG5vJdnGAbLHqt3e07EWGRw6rI4tsk8dBnaL3nG3vneqrM8yci+yxGHtpXdZkDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-23T16:16:30.079877Z"},"content_sha256":"0c1051ccbad94cee235f4acc1f5667d419438a73bf1764de2fe674f0824a2528","schema_version":"1.0","event_id":"sha256:0c1051ccbad94cee235f4acc1f5667d419438a73bf1764de2fe674f0824a2528"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/bundle.json","state_url":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/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":"2026-08-23T16:16:30Z","links":{"resolver":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ","bundle":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/bundle.json","state":"https://pith.science/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VZ7G6XPRDQCN2KKKZAAXAPFVVQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:VZ7G6XPRDQCN2KKKZAAXAPFVVQ","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":"ef1026073dbbc974d8ef20f771a18e2781ebbe12f69eca423db5c12213952d65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-03-10T22:54:06Z","title_canon_sha256":"65e7adf38ed7906be1628de25e03afcd9e7d28226a12a06c1965fe524d90d512"},"schema_version":"1.0","source":{"id":"2403.06335","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.06335","created_at":"2026-07-05T08:27:06Z"},{"alias_kind":"arxiv_version","alias_value":"2403.06335v2","created_at":"2026-07-05T08:27:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.06335","created_at":"2026-07-05T08:27:06Z"},{"alias_kind":"pith_short_12","alias_value":"VZ7G6XPRDQCN","created_at":"2026-07-05T08:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"VZ7G6XPRDQCN2KKK","created_at":"2026-07-05T08:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"VZ7G6XPR","created_at":"2026-07-05T08:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:0c1051ccbad94cee235f4acc1f5667d419438a73bf1764de2fe674f0824a2528","target":"graph","created_at":"2026-07-05T08:27:06Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.06335/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Pasin Manurangsi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-03-10T22:54:06Z","title":"Improved FPT Approximation Scheme and Approximate Kernel for Biclique-Free Max k-Weight SAT: Greedy Strikes Back"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.06335","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":"sha256:11171931b82a72eb4bd56479e27f2a61d215fe062dca7cdb3776fd3d61fde7f9","target":"record","created_at":"2026-07-05T08:27:06Z","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":"ef1026073dbbc974d8ef20f771a18e2781ebbe12f69eca423db5c12213952d65","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2024-03-10T22:54:06Z","title_canon_sha256":"65e7adf38ed7906be1628de25e03afcd9e7d28226a12a06c1965fe524d90d512"},"schema_version":"1.0","source":{"id":"2403.06335","kind":"arxiv","version":2}},"canonical_sha256":"ae7e6f5df11c04dd294ac801703cb5ac3f31f9bebfa062e9ee7096dec022da4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae7e6f5df11c04dd294ac801703cb5ac3f31f9bebfa062e9ee7096dec022da4a","first_computed_at":"2026-07-05T08:27:06.157800Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:27:06.157800Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PUwQIfiyzjve23BenIqNWhh3NharKrlt04M6zWQ6GT4pOKgv84iJiomb+BP7426SkD60oVa/Tq6FABAf7vXrAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:27:06.158143Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.06335","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:11171931b82a72eb4bd56479e27f2a61d215fe062dca7cdb3776fd3d61fde7f9","sha256:0c1051ccbad94cee235f4acc1f5667d419438a73bf1764de2fe674f0824a2528"],"state_sha256":"2d92c81e3cc53360fe8180e38f39858e0dc62c4bbe267317f933b95ddaf62264"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i9vb6sb/BlCwOTcJ2ZPnPOd0sqy902v/r6NogFiyC6xKgj9/KI4PACP0Ajh718VkSnr/ZX4vWouEO9pzJt7hBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-23T16:16:30.084279Z","bundle_sha256":"173b49808c01d64e8cd661f52ef4c9a5e8f8c940e7e6530904ad88d1eea88bf6"}}