{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:FCKK7H2SYU5J5OOQTKN56PTNWK","short_pith_number":"pith:FCKK7H2S","canonical_record":{"source":{"id":"2406.01908","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-04T02:39:42Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4a37c51297db503270c80a2af89028fae8d9af109b154459af843135a796d38f","abstract_canon_sha256":"47ec2ec07cc52ab724c9427ca2a0a7adbaf955146bad984d610c881a337572a2"},"schema_version":"1.0"},"canonical_sha256":"2894af9f52c53a9eb9d09a9bdf3e6db2abf3774dc1ab88f1f8cb8311015e3a96","source":{"kind":"arxiv","id":"2406.01908","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.01908","created_at":"2026-07-05T08:28:11Z"},{"alias_kind":"arxiv_version","alias_value":"2406.01908v2","created_at":"2026-07-05T08:28:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.01908","created_at":"2026-07-05T08:28:11Z"},{"alias_kind":"pith_short_12","alias_value":"FCKK7H2SYU5J","created_at":"2026-07-05T08:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"FCKK7H2SYU5J5OOQ","created_at":"2026-07-05T08:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"FCKK7H2S","created_at":"2026-07-05T08:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:FCKK7H2SYU5J5OOQTKN56PTNWK","target":"record","payload":{"canonical_record":{"source":{"id":"2406.01908","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-04T02:39:42Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"4a37c51297db503270c80a2af89028fae8d9af109b154459af843135a796d38f","abstract_canon_sha256":"47ec2ec07cc52ab724c9427ca2a0a7adbaf955146bad984d610c881a337572a2"},"schema_version":"1.0"},"canonical_sha256":"2894af9f52c53a9eb9d09a9bdf3e6db2abf3774dc1ab88f1f8cb8311015e3a96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:28:11.303336Z","signature_b64":"MHT5oSg1OodV0gyW2KEgz+HtThQ8hrKG4NMT+xLzALKOveT4AJyzHdobLqRyKDK5w4u/6l75fV6cBxGcuALFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2894af9f52c53a9eb9d09a9bdf3e6db2abf3774dc1ab88f1f8cb8311015e3a96","last_reissued_at":"2026-07-05T08:28:11.302836Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:28:11.302836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2406.01908","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":"2026-07-05T08:28:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r+jdMRTnoC7hzX2y/GZ4MV6On11v/atMk3vfHyBFnRGP5bV3ab0nNCTSgM6Jqaw3SA2mWM9pMH9YkSzLZEZ5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:03:51.613747Z"},"content_sha256":"47c144615df3e0ea9cc8d008156ce7277ddddf18b6a5122a45120da3568645bc","schema_version":"1.0","event_id":"sha256:47c144615df3e0ea9cc8d008156ce7277ddddf18b6a5122a45120da3568645bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:FCKK7H2SYU5J5OOQTKN56PTNWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.LG","authors_text":"Akang Wang, Bingheng Li, Haitao Mao, Jiliang Tang, Linxin Yang, Qian Chen, Ruoyu Sun, Senmiao Wang, Tian Ding, Yao Ma, YuPeng Chen","submitted_at":"2024-06-04T02:39:42Z","abstract_excerpt":"Solving large-scale linear programming (LP) problems is an important task in various areas such as communication networks, power systems, finance and logistics. Recently, two distinct approaches have emerged to expedite LP solving: (i) First-order methods (FOMs); (ii) Learning to optimize (L2O). In this work, we propose an FOM-unrolled neural network (NN) called PDHG-Net, and propose a two-stage L2O method to solve large-scale LP problems. The new architecture PDHG-Net is designed by unrolling the recently emerged PDHG method into a neural network, combined with channel-expansion techniques bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01908","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/2406.01908/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":"2026-07-05T08:28:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MCfRReF/fTW8Z2lEWYdRCmcfwU0rcYxBhttGzyj4JdSV+o81FlInDUISBjxHQV7kue8UMPR8ATzS/+YwEVDDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:03:51.614285Z"},"content_sha256":"9dd34640c66b19b106ed2b7dbd1753d7bb735a5dc86efac9c835dac74297d534","schema_version":"1.0","event_id":"sha256:9dd34640c66b19b106ed2b7dbd1753d7bb735a5dc86efac9c835dac74297d534"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FCKK7H2SYU5J5OOQTKN56PTNWK/bundle.json","state_url":"https://pith.science/pith/FCKK7H2SYU5J5OOQTKN56PTNWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FCKK7H2SYU5J5OOQTKN56PTNWK/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":"2026-08-12T14:03:51Z","links":{"resolver":"https://pith.science/pith/FCKK7H2SYU5J5OOQTKN56PTNWK","bundle":"https://pith.science/pith/FCKK7H2SYU5J5OOQTKN56PTNWK/bundle.json","state":"https://pith.science/pith/FCKK7H2SYU5J5OOQTKN56PTNWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FCKK7H2SYU5J5OOQTKN56PTNWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:FCKK7H2SYU5J5OOQTKN56PTNWK","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":"47ec2ec07cc52ab724c9427ca2a0a7adbaf955146bad984d610c881a337572a2","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-04T02:39:42Z","title_canon_sha256":"4a37c51297db503270c80a2af89028fae8d9af109b154459af843135a796d38f"},"schema_version":"1.0","source":{"id":"2406.01908","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.01908","created_at":"2026-07-05T08:28:11Z"},{"alias_kind":"arxiv_version","alias_value":"2406.01908v2","created_at":"2026-07-05T08:28:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.01908","created_at":"2026-07-05T08:28:11Z"},{"alias_kind":"pith_short_12","alias_value":"FCKK7H2SYU5J","created_at":"2026-07-05T08:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"FCKK7H2SYU5J5OOQ","created_at":"2026-07-05T08:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"FCKK7H2S","created_at":"2026-07-05T08:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:9dd34640c66b19b106ed2b7dbd1753d7bb735a5dc86efac9c835dac74297d534","target":"graph","created_at":"2026-07-05T08:28:11Z","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/2406.01908/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Solving large-scale linear programming (LP) problems is an important task in various areas such as communication networks, power systems, finance and logistics. Recently, two distinct approaches have emerged to expedite LP solving: (i) First-order methods (FOMs); (ii) Learning to optimize (L2O). In this work, we propose an FOM-unrolled neural network (NN) called PDHG-Net, and propose a two-stage L2O method to solve large-scale LP problems. The new architecture PDHG-Net is designed by unrolling the recently emerged PDHG method into a neural network, combined with channel-expansion techniques bo","authors_text":"Akang Wang, Bingheng Li, Haitao Mao, Jiliang Tang, Linxin Yang, Qian Chen, Ruoyu Sun, Senmiao Wang, Tian Ding, Yao Ma, YuPeng Chen","cross_cats":["math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-04T02:39:42Z","title":"PDHG-Unrolled Learning-to-Optimize Method for Large-Scale Linear Programming"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.01908","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":"sha256:47c144615df3e0ea9cc8d008156ce7277ddddf18b6a5122a45120da3568645bc","target":"record","created_at":"2026-07-05T08:28:11Z","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":"47ec2ec07cc52ab724c9427ca2a0a7adbaf955146bad984d610c881a337572a2","cross_cats_sorted":["math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2024-06-04T02:39:42Z","title_canon_sha256":"4a37c51297db503270c80a2af89028fae8d9af109b154459af843135a796d38f"},"schema_version":"1.0","source":{"id":"2406.01908","kind":"arxiv","version":2}},"canonical_sha256":"2894af9f52c53a9eb9d09a9bdf3e6db2abf3774dc1ab88f1f8cb8311015e3a96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2894af9f52c53a9eb9d09a9bdf3e6db2abf3774dc1ab88f1f8cb8311015e3a96","first_computed_at":"2026-07-05T08:28:11.302836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:28:11.302836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MHT5oSg1OodV0gyW2KEgz+HtThQ8hrKG4NMT+xLzALKOveT4AJyzHdobLqRyKDK5w4u/6l75fV6cBxGcuALFCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:28:11.303336Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.01908","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47c144615df3e0ea9cc8d008156ce7277ddddf18b6a5122a45120da3568645bc","sha256:9dd34640c66b19b106ed2b7dbd1753d7bb735a5dc86efac9c835dac74297d534"],"state_sha256":"c65a130814b12084b763170f7dbed5f0b0477057352105cb0f78207945be5c8c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLF+ksXD/7XL7NQfNSinGh2MUBQfbGFMl5nJYiFPHdD36rVM+xgSZ4d61/uMWsax5QdFQxthuWnwUMspL5X5CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T14:03:51.618329Z","bundle_sha256":"f1c3fe0006e72a98523f32fbc7c49bda4fcdd0dc9b0026767c9825686b460fc8"}}