{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:MDL3DITC3ER7ZAYIICWSU3LWUO","short_pith_number":"pith:MDL3DITC","canonical_record":{"source":{"id":"1902.01635","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-05T10:42:00Z","cross_cats_sorted":["cs.DS","cs.LG","cs.NA","math.OC"],"title_canon_sha256":"50734d28e9718917e6d63970aa59a7ea25ec5dd398b7fee16dc58771c17e6cc2","abstract_canon_sha256":"8b51e59a2bcdeee7d0fd29b8bb76de7ba825d87172f1d10a8832d5513ff8fc9f"},"schema_version":"1.0"},"canonical_sha256":"60d7b1a262d923fc830840ad2a6d76a3b7ee902c8c6d75336898e873e93c05af","source":{"kind":"arxiv","id":"1902.01635","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01635","created_at":"2026-07-05T05:28:03Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01635v4","created_at":"2026-07-05T05:28:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01635","created_at":"2026-07-05T05:28:03Z"},{"alias_kind":"pith_short_12","alias_value":"MDL3DITC3ER7","created_at":"2026-07-05T05:28:03Z"},{"alias_kind":"pith_short_16","alias_value":"MDL3DITC3ER7ZAYI","created_at":"2026-07-05T05:28:03Z"},{"alias_kind":"pith_short_8","alias_value":"MDL3DITC","created_at":"2026-07-05T05:28:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:MDL3DITC3ER7ZAYIICWSU3LWUO","target":"record","payload":{"canonical_record":{"source":{"id":"1902.01635","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-05T10:42:00Z","cross_cats_sorted":["cs.DS","cs.LG","cs.NA","math.OC"],"title_canon_sha256":"50734d28e9718917e6d63970aa59a7ea25ec5dd398b7fee16dc58771c17e6cc2","abstract_canon_sha256":"8b51e59a2bcdeee7d0fd29b8bb76de7ba825d87172f1d10a8832d5513ff8fc9f"},"schema_version":"1.0"},"canonical_sha256":"60d7b1a262d923fc830840ad2a6d76a3b7ee902c8c6d75336898e873e93c05af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:28:03.485498Z","signature_b64":"GW/bZURENQcnahvqN89vJA1vBPOjoujiHS5EOFuMqPrr/s/0aPo5SzDuYLvTKLFBzgqSLujA2/U4a2V+7JyoBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60d7b1a262d923fc830840ad2a6d76a3b7ee902c8c6d75336898e873e93c05af","last_reissued_at":"2026-07-05T05:28:03.485133Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:28:03.485133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.01635","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T05:28:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pDzByQfHuUZxZJ+2jXz8gtdQ6wVjUnjt3JfSc/oeGmiGPC+J+Cf4vdNt34fj1xEs8XCw0LHLMgFsJQEO8GvcAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T00:38:27.619606Z"},"content_sha256":"8fa03cd523e99504884a3f94967caf009de8e18bfef498fa9f891b06cd88e7aa","schema_version":"1.0","event_id":"sha256:8fa03cd523e99504884a3f94967caf009de8e18bfef498fa9f891b06cd88e7aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:MDL3DITC3ER7ZAYIICWSU3LWUO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riemannian optimization with a preconditioning scheme on the generalized Stiefel manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS","cs.LG","cs.NA","math.OC"],"primary_cat":"math.NA","authors_text":"Boris Shustin, Haim Avron","submitted_at":"2019-02-05T10:42:00Z","abstract_excerpt":"Optimization problems on the generalized Stiefel manifold (and products of it) are prevalent across science and engineering. For example, in computational science they arise in symmetric (generalized) eigenvalue problems, in nonlinear eigenvalue problems, and in electronic structures computations, to name a few problems. In statistics and machine learning, they arise, for example, in various dimensionality reduction techniques such as canonical correlation analysis. In deep learning, regularization and improved stability can be obtained by constraining some layers to have parameter matrices th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01635","kind":"arxiv","version":4},"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/1902.01635/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":"2026-07-05T05:28:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bzjA5KhdpAxspZGhDhsdTwVYveXIeFVVxk5xJBCAVv9DQ9QaE7spnacwo0aoEfCAjX0+TU8tKo5r83rc3BE/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T00:38:27.620193Z"},"content_sha256":"c2061ac58e789681e1bfe18c043903cb270b3de4c49df574e8a63b04360537b4","schema_version":"1.0","event_id":"sha256:c2061ac58e789681e1bfe18c043903cb270b3de4c49df574e8a63b04360537b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MDL3DITC3ER7ZAYIICWSU3LWUO/bundle.json","state_url":"https://pith.science/pith/MDL3DITC3ER7ZAYIICWSU3LWUO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MDL3DITC3ER7ZAYIICWSU3LWUO/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":"2026-08-15T00:38:27Z","links":{"resolver":"https://pith.science/pith/MDL3DITC3ER7ZAYIICWSU3LWUO","bundle":"https://pith.science/pith/MDL3DITC3ER7ZAYIICWSU3LWUO/bundle.json","state":"https://pith.science/pith/MDL3DITC3ER7ZAYIICWSU3LWUO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MDL3DITC3ER7ZAYIICWSU3LWUO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MDL3DITC3ER7ZAYIICWSU3LWUO","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":"8b51e59a2bcdeee7d0fd29b8bb76de7ba825d87172f1d10a8832d5513ff8fc9f","cross_cats_sorted":["cs.DS","cs.LG","cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-05T10:42:00Z","title_canon_sha256":"50734d28e9718917e6d63970aa59a7ea25ec5dd398b7fee16dc58771c17e6cc2"},"schema_version":"1.0","source":{"id":"1902.01635","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.01635","created_at":"2026-07-05T05:28:03Z"},{"alias_kind":"arxiv_version","alias_value":"1902.01635v4","created_at":"2026-07-05T05:28:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.01635","created_at":"2026-07-05T05:28:03Z"},{"alias_kind":"pith_short_12","alias_value":"MDL3DITC3ER7","created_at":"2026-07-05T05:28:03Z"},{"alias_kind":"pith_short_16","alias_value":"MDL3DITC3ER7ZAYI","created_at":"2026-07-05T05:28:03Z"},{"alias_kind":"pith_short_8","alias_value":"MDL3DITC","created_at":"2026-07-05T05:28:03Z"}],"graph_snapshots":[{"event_id":"sha256:c2061ac58e789681e1bfe18c043903cb270b3de4c49df574e8a63b04360537b4","target":"graph","created_at":"2026-07-05T05:28:03Z","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/1902.01635/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Optimization problems on the generalized Stiefel manifold (and products of it) are prevalent across science and engineering. For example, in computational science they arise in symmetric (generalized) eigenvalue problems, in nonlinear eigenvalue problems, and in electronic structures computations, to name a few problems. In statistics and machine learning, they arise, for example, in various dimensionality reduction techniques such as canonical correlation analysis. In deep learning, regularization and improved stability can be obtained by constraining some layers to have parameter matrices th","authors_text":"Boris Shustin, Haim Avron","cross_cats":["cs.DS","cs.LG","cs.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-05T10:42:00Z","title":"Riemannian optimization with a preconditioning scheme on the generalized Stiefel manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01635","kind":"arxiv","version":4},"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":"sha256:8fa03cd523e99504884a3f94967caf009de8e18bfef498fa9f891b06cd88e7aa","target":"record","created_at":"2026-07-05T05:28:03Z","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":"8b51e59a2bcdeee7d0fd29b8bb76de7ba825d87172f1d10a8832d5513ff8fc9f","cross_cats_sorted":["cs.DS","cs.LG","cs.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-02-05T10:42:00Z","title_canon_sha256":"50734d28e9718917e6d63970aa59a7ea25ec5dd398b7fee16dc58771c17e6cc2"},"schema_version":"1.0","source":{"id":"1902.01635","kind":"arxiv","version":4}},"canonical_sha256":"60d7b1a262d923fc830840ad2a6d76a3b7ee902c8c6d75336898e873e93c05af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60d7b1a262d923fc830840ad2a6d76a3b7ee902c8c6d75336898e873e93c05af","first_computed_at":"2026-07-05T05:28:03.485133Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:28:03.485133Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GW/bZURENQcnahvqN89vJA1vBPOjoujiHS5EOFuMqPrr/s/0aPo5SzDuYLvTKLFBzgqSLujA2/U4a2V+7JyoBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T05:28:03.485498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.01635","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8fa03cd523e99504884a3f94967caf009de8e18bfef498fa9f891b06cd88e7aa","sha256:c2061ac58e789681e1bfe18c043903cb270b3de4c49df574e8a63b04360537b4"],"state_sha256":"5b2737515116a37088c557768145cd96fcd7c9c6ba3d7bfacb41a16913088a15"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ujceHEo2wGefra9UanaBSZAQZ10AE+0kvCmfUwtbY62rWP+EIfjRFVkKehifiTiyX4Z0r57h1ffQyMpl4cbAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T00:38:27.625985Z","bundle_sha256":"26efff3621383e8b106cf55ed895a3a38b86e08fcceee220495b7287e8b4eb75"}}