{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:D5R66RUQL3LCZSCOTLJHMYLC2J","short_pith_number":"pith:D5R66RUQ","canonical_record":{"source":{"id":"2106.04756","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-09T00:59:33Z","cross_cats_sorted":[],"title_canon_sha256":"2f9e5ce2c2f16372332acd86ea8d9fd9fe1cbb421e3a400af183242f434d182e","abstract_canon_sha256":"b44ae47afacd5c5734b5eb5553e599cc565303aa78be67e7ebeb872539f00795"},"schema_version":"1.0"},"canonical_sha256":"1f63ef46905ed62cc84e9ad2766162d24d03bbfa20f52f6fb1d54604a103a694","source":{"kind":"arxiv","id":"2106.04756","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.04756","created_at":"2026-07-05T03:46:34Z"},{"alias_kind":"arxiv_version","alias_value":"2106.04756v2","created_at":"2026-07-05T03:46:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.04756","created_at":"2026-07-05T03:46:34Z"},{"alias_kind":"pith_short_12","alias_value":"D5R66RUQL3LC","created_at":"2026-07-05T03:46:34Z"},{"alias_kind":"pith_short_16","alias_value":"D5R66RUQL3LCZSCO","created_at":"2026-07-05T03:46:34Z"},{"alias_kind":"pith_short_8","alias_value":"D5R66RUQ","created_at":"2026-07-05T03:46:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:D5R66RUQL3LCZSCOTLJHMYLC2J","target":"record","payload":{"canonical_record":{"source":{"id":"2106.04756","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-09T00:59:33Z","cross_cats_sorted":[],"title_canon_sha256":"2f9e5ce2c2f16372332acd86ea8d9fd9fe1cbb421e3a400af183242f434d182e","abstract_canon_sha256":"b44ae47afacd5c5734b5eb5553e599cc565303aa78be67e7ebeb872539f00795"},"schema_version":"1.0"},"canonical_sha256":"1f63ef46905ed62cc84e9ad2766162d24d03bbfa20f52f6fb1d54604a103a694","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:46:34.979950Z","signature_b64":"Mfnq+2qQAb1sS2Fjz/NPskJQPi9z2cQkOnx6klYD6vQm+MKmFIherBs8KcyMdtYmQDpnpurS9nLh3OJUxf6cAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f63ef46905ed62cc84e9ad2766162d24d03bbfa20f52f6fb1d54604a103a694","last_reissued_at":"2026-07-05T03:46:34.979324Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:46:34.979324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2106.04756","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":"2026-07-05T03:46:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Up7C1h307ZJJhBvuoEVx9wAucPPgBOXJSipGKqiW7Cyioo+JufSdFCQsTY2X5pGnMkQ8DiPwZrCZ172oJZJiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:03:20.441229Z"},"content_sha256":"1f4dfcf95eb6f2097ff73e63fae16eab4c53296b636de54e43e8c3349399620c","schema_version":"1.0","event_id":"sha256:1f4dfcf95eb6f2097ff73e63fae16eab4c53296b636de54e43e8c3349399620c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:D5R66RUQL3LCZSCOTLJHMYLC2J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Practical Large-Scale Linear Programming using Primal-Dual Hybrid Gradient","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Brendan O'Donoghue, David Applegate, Haihao Lu, Mateo D\\'iaz, Miles Lubin, Oliver Hinder, Warren Schudy","submitted_at":"2021-06-09T00:59:33Z","abstract_excerpt":"We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core operation is matrix-vector multiplications. PDLP is derived by applying the primal-dual hybrid gradient (PDHG) method, popularized by Chambolle and Pock (2011), to a saddle-point formulation of LP. PDLP enhances PDHG for LP by combining several new techniques with older tricks from the literature; the enhancements include diagonal preconditioning, presolving, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.04756","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/2106.04756/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":"2026-07-05T03:46:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kS81KgVlbNucRUlWhfXAi3tDOImgqCI6Sd+Dyqn03BREstim7h727UuBUxJF+fWdiRrdRyE2EmrZzYgP4Yh/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:03:20.442175Z"},"content_sha256":"b23cc833d40a4a18fb9cc425f01d0a6b6f4d1a16b6b2a10191f7d954ad2605ae","schema_version":"1.0","event_id":"sha256:b23cc833d40a4a18fb9cc425f01d0a6b6f4d1a16b6b2a10191f7d954ad2605ae"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D5R66RUQL3LCZSCOTLJHMYLC2J/bundle.json","state_url":"https://pith.science/pith/D5R66RUQL3LCZSCOTLJHMYLC2J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D5R66RUQL3LCZSCOTLJHMYLC2J/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":"2026-08-11T00:03:20Z","links":{"resolver":"https://pith.science/pith/D5R66RUQL3LCZSCOTLJHMYLC2J","bundle":"https://pith.science/pith/D5R66RUQL3LCZSCOTLJHMYLC2J/bundle.json","state":"https://pith.science/pith/D5R66RUQL3LCZSCOTLJHMYLC2J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D5R66RUQL3LCZSCOTLJHMYLC2J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:D5R66RUQL3LCZSCOTLJHMYLC2J","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":"b44ae47afacd5c5734b5eb5553e599cc565303aa78be67e7ebeb872539f00795","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-09T00:59:33Z","title_canon_sha256":"2f9e5ce2c2f16372332acd86ea8d9fd9fe1cbb421e3a400af183242f434d182e"},"schema_version":"1.0","source":{"id":"2106.04756","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2106.04756","created_at":"2026-07-05T03:46:34Z"},{"alias_kind":"arxiv_version","alias_value":"2106.04756v2","created_at":"2026-07-05T03:46:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2106.04756","created_at":"2026-07-05T03:46:34Z"},{"alias_kind":"pith_short_12","alias_value":"D5R66RUQL3LC","created_at":"2026-07-05T03:46:34Z"},{"alias_kind":"pith_short_16","alias_value":"D5R66RUQL3LCZSCO","created_at":"2026-07-05T03:46:34Z"},{"alias_kind":"pith_short_8","alias_value":"D5R66RUQ","created_at":"2026-07-05T03:46:34Z"}],"graph_snapshots":[{"event_id":"sha256:b23cc833d40a4a18fb9cc425f01d0a6b6f4d1a16b6b2a10191f7d954ad2605ae","target":"graph","created_at":"2026-07-05T03:46:34Z","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/2106.04756/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present PDLP, a practical first-order method for linear programming (LP) that can solve to the high levels of accuracy that are expected in traditional LP applications. In addition, it can scale to very large problems because its core operation is matrix-vector multiplications. PDLP is derived by applying the primal-dual hybrid gradient (PDHG) method, popularized by Chambolle and Pock (2011), to a saddle-point formulation of LP. PDLP enhances PDHG for LP by combining several new techniques with older tricks from the literature; the enhancements include diagonal preconditioning, presolving, ","authors_text":"Brendan O'Donoghue, David Applegate, Haihao Lu, Mateo D\\'iaz, Miles Lubin, Oliver Hinder, Warren Schudy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-09T00:59:33Z","title":"Practical Large-Scale Linear Programming using Primal-Dual Hybrid Gradient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.04756","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":"sha256:1f4dfcf95eb6f2097ff73e63fae16eab4c53296b636de54e43e8c3349399620c","target":"record","created_at":"2026-07-05T03:46:34Z","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":"b44ae47afacd5c5734b5eb5553e599cc565303aa78be67e7ebeb872539f00795","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-06-09T00:59:33Z","title_canon_sha256":"2f9e5ce2c2f16372332acd86ea8d9fd9fe1cbb421e3a400af183242f434d182e"},"schema_version":"1.0","source":{"id":"2106.04756","kind":"arxiv","version":2}},"canonical_sha256":"1f63ef46905ed62cc84e9ad2766162d24d03bbfa20f52f6fb1d54604a103a694","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f63ef46905ed62cc84e9ad2766162d24d03bbfa20f52f6fb1d54604a103a694","first_computed_at":"2026-07-05T03:46:34.979324Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:46:34.979324Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mfnq+2qQAb1sS2Fjz/NPskJQPi9z2cQkOnx6klYD6vQm+MKmFIherBs8KcyMdtYmQDpnpurS9nLh3OJUxf6cAw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:46:34.979950Z","signed_message":"canonical_sha256_bytes"},"source_id":"2106.04756","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f4dfcf95eb6f2097ff73e63fae16eab4c53296b636de54e43e8c3349399620c","sha256:b23cc833d40a4a18fb9cc425f01d0a6b6f4d1a16b6b2a10191f7d954ad2605ae"],"state_sha256":"8dde431d0128e6f88caa06d3b1fd77894b77e0ed7100f8e6e97b067684901141"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rV7tElFeLSqcg8kcKAPH9EIIeejKiWbOqVEfb77/ZrNfli5fas392vZP9AhcNCFfCWI3Ag/if5q2+oaY2pMeCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T00:03:20.450036Z","bundle_sha256":"e58a6eeafeca79657fe3b7b762aef06402808d7296c3e8ae6fa37518a74421a4"}}