{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:MFDNZPG6M7ZT6GPBIFLG6RX2MD","short_pith_number":"pith:MFDNZPG6","canonical_record":{"source":{"id":"2004.02244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-04-05T16:14:41Z","cross_cats_sorted":[],"title_canon_sha256":"bd0bbe82a2a39b17c6a060747bd495657c5162b93df5e7d7fe5d499f7f17a293","abstract_canon_sha256":"56836c7660ea0142f26c554aed5110898466732f801315376ab75a4e432fede5"},"schema_version":"1.0"},"canonical_sha256":"6146dcbcde67f33f19e141566f46fa60e6b71d970b2172e81446022660b8b90a","source":{"kind":"arxiv","id":"2004.02244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.02244","created_at":"2026-07-05T03:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"2004.02244v1","created_at":"2026-07-05T03:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.02244","created_at":"2026-07-05T03:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"MFDNZPG6M7ZT","created_at":"2026-07-05T03:31:52Z"},{"alias_kind":"pith_short_16","alias_value":"MFDNZPG6M7ZT6GPB","created_at":"2026-07-05T03:31:52Z"},{"alias_kind":"pith_short_8","alias_value":"MFDNZPG6","created_at":"2026-07-05T03:31:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:MFDNZPG6M7ZT6GPBIFLG6RX2MD","target":"record","payload":{"canonical_record":{"source":{"id":"2004.02244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-04-05T16:14:41Z","cross_cats_sorted":[],"title_canon_sha256":"bd0bbe82a2a39b17c6a060747bd495657c5162b93df5e7d7fe5d499f7f17a293","abstract_canon_sha256":"56836c7660ea0142f26c554aed5110898466732f801315376ab75a4e432fede5"},"schema_version":"1.0"},"canonical_sha256":"6146dcbcde67f33f19e141566f46fa60e6b71d970b2172e81446022660b8b90a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:31:52.243201Z","signature_b64":"V3od1UBMSTNpazrQIgzpqVwU6DONk3rMUSU2seaaTJiivY4OVwfjiaO0d8ujXo4AkzUgmZbbzU5IwjdSXfxuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6146dcbcde67f33f19e141566f46fa60e6b71d970b2172e81446022660b8b90a","last_reissued_at":"2026-07-05T03:31:52.242752Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:31:52.242752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.02244","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":"2026-07-05T03:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gXQLiyIe9EAPRLoQ2x6hJoq8J1LdbRGZZALPom2ihQNhgwwzpCOwY13V20y2g0SzQc1aTRNVY+vb4/FYLEsFDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:22:29.094871Z"},"content_sha256":"06a25871265a077aee71d64d2e5037b1afa3f1457d7f442c21eb9bbeff229c87","schema_version":"1.0","event_id":"sha256:06a25871265a077aee71d64d2e5037b1afa3f1457d7f442c21eb9bbeff229c87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:MFDNZPG6M7ZT6GPBIFLG6RX2MD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Newton Hard Thresholding Pursuit for Sparse LCP via A New Merit Function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Lili Pan, Meijuan Shang, Mu Li, Shenglong Zhou","submitted_at":"2020-04-05T16:14:41Z","abstract_excerpt":"Solutions to the linear complementarity problem (LCP) are naturally sparse in many applications such as bimatrix games and portfolio section problems. Despite that it gives rise to the hardness, sparsity makes optimization faster and enables relatively large scale computation. Motivated by this, we take the sparse LCP into consideration, investigating the existence and boundedness of its solution set as well as introducing a new merit function, which allows us to convert the problem into a sparsity constrained optimization. The function turns out to be continuously differentiable and twice con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.02244","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.02244/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":"2026-07-05T03:31:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nYiRQx63kVBydp33JxwoHfW05xS+gQp5n3SFKzRZK9Yj5goO1mwGMIUUzjuqfC+wawgkVn5AWS0FsXFW26YGCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T01:22:29.095441Z"},"content_sha256":"943a907daa9a5a2a6db7b8d9becb55786d4a55d40e3808df1c843999a4cd6a90","schema_version":"1.0","event_id":"sha256:943a907daa9a5a2a6db7b8d9becb55786d4a55d40e3808df1c843999a4cd6a90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFDNZPG6M7ZT6GPBIFLG6RX2MD/bundle.json","state_url":"https://pith.science/pith/MFDNZPG6M7ZT6GPBIFLG6RX2MD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFDNZPG6M7ZT6GPBIFLG6RX2MD/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":"2026-08-09T01:22:29Z","links":{"resolver":"https://pith.science/pith/MFDNZPG6M7ZT6GPBIFLG6RX2MD","bundle":"https://pith.science/pith/MFDNZPG6M7ZT6GPBIFLG6RX2MD/bundle.json","state":"https://pith.science/pith/MFDNZPG6M7ZT6GPBIFLG6RX2MD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFDNZPG6M7ZT6GPBIFLG6RX2MD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:MFDNZPG6M7ZT6GPBIFLG6RX2MD","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":"56836c7660ea0142f26c554aed5110898466732f801315376ab75a4e432fede5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-04-05T16:14:41Z","title_canon_sha256":"bd0bbe82a2a39b17c6a060747bd495657c5162b93df5e7d7fe5d499f7f17a293"},"schema_version":"1.0","source":{"id":"2004.02244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.02244","created_at":"2026-07-05T03:31:52Z"},{"alias_kind":"arxiv_version","alias_value":"2004.02244v1","created_at":"2026-07-05T03:31:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.02244","created_at":"2026-07-05T03:31:52Z"},{"alias_kind":"pith_short_12","alias_value":"MFDNZPG6M7ZT","created_at":"2026-07-05T03:31:52Z"},{"alias_kind":"pith_short_16","alias_value":"MFDNZPG6M7ZT6GPB","created_at":"2026-07-05T03:31:52Z"},{"alias_kind":"pith_short_8","alias_value":"MFDNZPG6","created_at":"2026-07-05T03:31:52Z"}],"graph_snapshots":[{"event_id":"sha256:943a907daa9a5a2a6db7b8d9becb55786d4a55d40e3808df1c843999a4cd6a90","target":"graph","created_at":"2026-07-05T03:31:52Z","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/2004.02244/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Solutions to the linear complementarity problem (LCP) are naturally sparse in many applications such as bimatrix games and portfolio section problems. Despite that it gives rise to the hardness, sparsity makes optimization faster and enables relatively large scale computation. Motivated by this, we take the sparse LCP into consideration, investigating the existence and boundedness of its solution set as well as introducing a new merit function, which allows us to convert the problem into a sparsity constrained optimization. The function turns out to be continuously differentiable and twice con","authors_text":"Lili Pan, Meijuan Shang, Mu Li, Shenglong Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-04-05T16:14:41Z","title":"Newton Hard Thresholding Pursuit for Sparse LCP via A New Merit Function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.02244","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":"sha256:06a25871265a077aee71d64d2e5037b1afa3f1457d7f442c21eb9bbeff229c87","target":"record","created_at":"2026-07-05T03:31:52Z","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":"56836c7660ea0142f26c554aed5110898466732f801315376ab75a4e432fede5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2020-04-05T16:14:41Z","title_canon_sha256":"bd0bbe82a2a39b17c6a060747bd495657c5162b93df5e7d7fe5d499f7f17a293"},"schema_version":"1.0","source":{"id":"2004.02244","kind":"arxiv","version":1}},"canonical_sha256":"6146dcbcde67f33f19e141566f46fa60e6b71d970b2172e81446022660b8b90a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6146dcbcde67f33f19e141566f46fa60e6b71d970b2172e81446022660b8b90a","first_computed_at":"2026-07-05T03:31:52.242752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:31:52.242752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V3od1UBMSTNpazrQIgzpqVwU6DONk3rMUSU2seaaTJiivY4OVwfjiaO0d8ujXo4AkzUgmZbbzU5IwjdSXfxuBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:31:52.243201Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.02244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06a25871265a077aee71d64d2e5037b1afa3f1457d7f442c21eb9bbeff229c87","sha256:943a907daa9a5a2a6db7b8d9becb55786d4a55d40e3808df1c843999a4cd6a90"],"state_sha256":"7f3f1fc3556a4fdb29a1459c820140f6a5d4effbb35a46729fc389e3c3250a21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kB7iX3oN7hQtizXs9M/l4k7LJ3QsInMOdn7BbkQUfSGyjZrj40YdJLcdD/hiC3rpzp62K6HNlP3Xd88u/JAuDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T01:22:29.101151Z","bundle_sha256":"f723ba4b5c000f6bb126a9ac5a4b295b8bc14c7d6e7d68143ac0976583db6b91"}}