{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Q4GILI56CIWBYVKA4XEO5ZCTTE","short_pith_number":"pith:Q4GILI56","canonical_record":{"source":{"id":"1507.07459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-27T15:51:50Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"a61501f19585b3b9dd003e474976e15f6da10fbf11b80bb02a4d5b7e5e04d4bf","abstract_canon_sha256":"37e492535fcc273b0ae5bb5013f26d9c96243fb69ff5bf2a5ff064473c9d495e"},"schema_version":"1.0"},"canonical_sha256":"870c85a3be122c1c5540e5c8eee4539901a05258ca65b901bb4319eb1f0fd98c","source":{"kind":"arxiv","id":"1507.07459","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07459","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07459v1","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07459","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"pith_short_12","alias_value":"Q4GILI56CIWB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q4GILI56CIWBYVKA","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q4GILI56","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Q4GILI56CIWBYVKA4XEO5ZCTTE","target":"record","payload":{"canonical_record":{"source":{"id":"1507.07459","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-27T15:51:50Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"a61501f19585b3b9dd003e474976e15f6da10fbf11b80bb02a4d5b7e5e04d4bf","abstract_canon_sha256":"37e492535fcc273b0ae5bb5013f26d9c96243fb69ff5bf2a5ff064473c9d495e"},"schema_version":"1.0"},"canonical_sha256":"870c85a3be122c1c5540e5c8eee4539901a05258ca65b901bb4319eb1f0fd98c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:16.360013Z","signature_b64":"/Nk8o8ujyJDN2jZ8Up1C4fqf69SPJZmOTtjj+MZf0Yr1DsKIvxmrVIq88k4+J6J377DOw9wzjeaa1q+bYZIkCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"870c85a3be122c1c5540e5c8eee4539901a05258ca65b901bb4319eb1f0fd98c","last_reissued_at":"2026-05-18T01:36:16.359395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:16.359395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.07459","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":"2026-05-18T01:36:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YBsuuEjZczJeB9xShpKtSEoPcL0pJO0H6zCFPZ8SVXHP42f2h2DnSNkgf4MJZjBQvuv1OS3R9xkyRi9q4gHJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:10:04.284140Z"},"content_sha256":"e7644417eacb72f4d0fc1488ef5bd550ef7a18896bcdbe41247fa037eaf68a4f","schema_version":"1.0","event_id":"sha256:e7644417eacb72f4d0fc1488ef5bd550ef7a18896bcdbe41247fa037eaf68a4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Q4GILI56CIWBYVKA4XEO5ZCTTE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On local search and LP and SDP relaxations for k-Set Packing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.CO","authors_text":"Tim Oosterwijk","submitted_at":"2015-07-27T15:51:50Z","abstract_excerpt":"Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set problem. In this thesis we study the k-set packing problem where given a universe U and a collection C of subsets over U, each of cardinality k, one needs to find the maximum collection of mutually disjoint subsets. Local search techniques have proved to be successful in the search for approximation algorithms, both for the unweighted and the weighted version o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07459","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":"2026-05-18T01:36:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sQYR5WhSY+k7dUjshHZ+2+F3m4As0qYFwpo/FPZXIzsah9Kul3+kX1S9sAMSwRQNIyOnu+446HoXVIz6pzIABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:10:04.284503Z"},"content_sha256":"ccb9aefc2a34b0cfb487cc87c7e82aa1f73438b706f60e4214e1c79d871f10f2","schema_version":"1.0","event_id":"sha256:ccb9aefc2a34b0cfb487cc87c7e82aa1f73438b706f60e4214e1c79d871f10f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4GILI56CIWBYVKA4XEO5ZCTTE/bundle.json","state_url":"https://pith.science/pith/Q4GILI56CIWBYVKA4XEO5ZCTTE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4GILI56CIWBYVKA4XEO5ZCTTE/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":"2026-06-23T14:10:04Z","links":{"resolver":"https://pith.science/pith/Q4GILI56CIWBYVKA4XEO5ZCTTE","bundle":"https://pith.science/pith/Q4GILI56CIWBYVKA4XEO5ZCTTE/bundle.json","state":"https://pith.science/pith/Q4GILI56CIWBYVKA4XEO5ZCTTE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4GILI56CIWBYVKA4XEO5ZCTTE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Q4GILI56CIWBYVKA4XEO5ZCTTE","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":"37e492535fcc273b0ae5bb5013f26d9c96243fb69ff5bf2a5ff064473c9d495e","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-27T15:51:50Z","title_canon_sha256":"a61501f19585b3b9dd003e474976e15f6da10fbf11b80bb02a4d5b7e5e04d4bf"},"schema_version":"1.0","source":{"id":"1507.07459","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.07459","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"arxiv_version","alias_value":"1507.07459v1","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.07459","created_at":"2026-05-18T01:36:16Z"},{"alias_kind":"pith_short_12","alias_value":"Q4GILI56CIWB","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q4GILI56CIWBYVKA","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q4GILI56","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:ccb9aefc2a34b0cfb487cc87c7e82aa1f73438b706f60e4214e1c79d871f10f2","target":"graph","created_at":"2026-05-18T01:36:16Z","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":"Set packing is a fundamental problem that generalises some well-known combinatorial optimization problems and knows a lot of applications. It is equivalent to hypergraph matching and it is strongly related to the maximum independent set problem. In this thesis we study the k-set packing problem where given a universe U and a collection C of subsets over U, each of cardinality k, one needs to find the maximum collection of mutually disjoint subsets. Local search techniques have proved to be successful in the search for approximation algorithms, both for the unweighted and the weighted version o","authors_text":"Tim Oosterwijk","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-27T15:51:50Z","title":"On local search and LP and SDP relaxations for k-Set Packing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.07459","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:e7644417eacb72f4d0fc1488ef5bd550ef7a18896bcdbe41247fa037eaf68a4f","target":"record","created_at":"2026-05-18T01:36:16Z","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":"37e492535fcc273b0ae5bb5013f26d9c96243fb69ff5bf2a5ff064473c9d495e","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-07-27T15:51:50Z","title_canon_sha256":"a61501f19585b3b9dd003e474976e15f6da10fbf11b80bb02a4d5b7e5e04d4bf"},"schema_version":"1.0","source":{"id":"1507.07459","kind":"arxiv","version":1}},"canonical_sha256":"870c85a3be122c1c5540e5c8eee4539901a05258ca65b901bb4319eb1f0fd98c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"870c85a3be122c1c5540e5c8eee4539901a05258ca65b901bb4319eb1f0fd98c","first_computed_at":"2026-05-18T01:36:16.359395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:16.359395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/Nk8o8ujyJDN2jZ8Up1C4fqf69SPJZmOTtjj+MZf0Yr1DsKIvxmrVIq88k4+J6J377DOw9wzjeaa1q+bYZIkCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:16.360013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.07459","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7644417eacb72f4d0fc1488ef5bd550ef7a18896bcdbe41247fa037eaf68a4f","sha256:ccb9aefc2a34b0cfb487cc87c7e82aa1f73438b706f60e4214e1c79d871f10f2"],"state_sha256":"22fd83d1e6db376ff63d99bb8e435c30a9217e9d3a7a4386d6cb63d75938bde0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MXhRG2wQ5o/7+xmbSPdmpk3+jXimREPZLrsPBLt3QLCYMZ8ZRQ2zII+fCK0SH7QdP1CuT/p7qCiTHrFwmVieAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:10:04.286432Z","bundle_sha256":"f0741471490dca54d3d754e48c09b02e4394a1e0a2883f9ca46017d0fc8256cd"}}