{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ISCF5I7OJHYWEJDVGAU7APXY3U","short_pith_number":"pith:ISCF5I7O","canonical_record":{"source":{"id":"1301.0172","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-02T06:42:20Z","cross_cats_sorted":[],"title_canon_sha256":"51ed2209047382041698361ba6697e08d87228e34b39c0abd15635fd4f177e12","abstract_canon_sha256":"5ab647d32be7a7f04f607e429caf3a28b0ba087fd3ea84b8ab17fdd538413c63"},"schema_version":"1.0"},"canonical_sha256":"44845ea3ee49f16224753029f03ef8dd1000a4dc0ce17ea90fdd4e5941c69526","source":{"kind":"arxiv","id":"1301.0172","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0172","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0172v3","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0172","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"pith_short_12","alias_value":"ISCF5I7OJHYW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"ISCF5I7OJHYWEJDV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"ISCF5I7O","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ISCF5I7OJHYWEJDVGAU7APXY3U","target":"record","payload":{"canonical_record":{"source":{"id":"1301.0172","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-02T06:42:20Z","cross_cats_sorted":[],"title_canon_sha256":"51ed2209047382041698361ba6697e08d87228e34b39c0abd15635fd4f177e12","abstract_canon_sha256":"5ab647d32be7a7f04f607e429caf3a28b0ba087fd3ea84b8ab17fdd538413c63"},"schema_version":"1.0"},"canonical_sha256":"44845ea3ee49f16224753029f03ef8dd1000a4dc0ce17ea90fdd4e5941c69526","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:42:29.157733Z","signature_b64":"3ofOa8v4vvOjUKTnTY/cxIqmphj9Iw/1lzFcUf920ps/IA+iu1i8y7YIFF7vL7wBWi6Y6VCYhY7wop+m/8isAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"44845ea3ee49f16224753029f03ef8dd1000a4dc0ce17ea90fdd4e5941c69526","last_reissued_at":"2026-05-18T02:42:29.156811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:42:29.156811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.0172","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:42:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jBfD6ZkKPECE853sAIityoIxYxZ9/YWDEeo2nHt5zG1VGzH1CuEU6oyOVUofsyQBQrzY8VDnUyLzOgfxwGNWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:26:45.811042Z"},"content_sha256":"3e59f8ece7f28eb224b11cfbcb7f6cb0911c7fd59021c316b18ef563ba2410a5","schema_version":"1.0","event_id":"sha256:3e59f8ece7f28eb224b11cfbcb7f6cb0911c7fd59021c316b18ef563ba2410a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ISCF5I7OJHYWEJDVGAU7APXY3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Framework of Constraint Preserving Update Schemes for Optimization on Stiefel Manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Jiang, Yu-Hong Dai","submitted_at":"2013-01-02T06:42:20Z","abstract_excerpt":"This paper considers optimization problems on the Stiefel manifold $X^{\\mathsf{T}}X=I_p$, where $X\\in \\mathbb{R}^{n \\times p}$ is the variable and $I_p$ is the $p$-by-$p$ identity matrix. A framework of constraint preserving update schemes is proposed by decomposing each feasible point into the range space of $X$ and the null space of $X^{\\mathsf{T}}$. While this general framework can unify many existing schemes, a new update scheme with low complexity cost is also discovered. Then we study a feasible Barzilai-Borwein-like method under the new update scheme. The global convergence of the metho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0172","kind":"arxiv","version":3},"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":"2026-05-18T02:42:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"srlsVxcfcTRhhpvUzmFsIi4h1OrW3Kc4t8+0rUjvWPo1zFweotq8OR57/37u+uO2XQhgqkxM15wGEGpwdGZDDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T16:26:45.811762Z"},"content_sha256":"ef8d120174c75e245094941e0d1c367d4a230cd7a471cc9369a71f304926787d","schema_version":"1.0","event_id":"sha256:ef8d120174c75e245094941e0d1c367d4a230cd7a471cc9369a71f304926787d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ISCF5I7OJHYWEJDVGAU7APXY3U/bundle.json","state_url":"https://pith.science/pith/ISCF5I7OJHYWEJDVGAU7APXY3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ISCF5I7OJHYWEJDVGAU7APXY3U/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":"2026-05-25T16:26:45Z","links":{"resolver":"https://pith.science/pith/ISCF5I7OJHYWEJDVGAU7APXY3U","bundle":"https://pith.science/pith/ISCF5I7OJHYWEJDVGAU7APXY3U/bundle.json","state":"https://pith.science/pith/ISCF5I7OJHYWEJDVGAU7APXY3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ISCF5I7OJHYWEJDVGAU7APXY3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ISCF5I7OJHYWEJDVGAU7APXY3U","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":"5ab647d32be7a7f04f607e429caf3a28b0ba087fd3ea84b8ab17fdd538413c63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-02T06:42:20Z","title_canon_sha256":"51ed2209047382041698361ba6697e08d87228e34b39c0abd15635fd4f177e12"},"schema_version":"1.0","source":{"id":"1301.0172","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.0172","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"arxiv_version","alias_value":"1301.0172v3","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.0172","created_at":"2026-05-18T02:42:29Z"},{"alias_kind":"pith_short_12","alias_value":"ISCF5I7OJHYW","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"ISCF5I7OJHYWEJDV","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"ISCF5I7O","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:ef8d120174c75e245094941e0d1c367d4a230cd7a471cc9369a71f304926787d","target":"graph","created_at":"2026-05-18T02:42:29Z","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":"This paper considers optimization problems on the Stiefel manifold $X^{\\mathsf{T}}X=I_p$, where $X\\in \\mathbb{R}^{n \\times p}$ is the variable and $I_p$ is the $p$-by-$p$ identity matrix. A framework of constraint preserving update schemes is proposed by decomposing each feasible point into the range space of $X$ and the null space of $X^{\\mathsf{T}}$. While this general framework can unify many existing schemes, a new update scheme with low complexity cost is also discovered. Then we study a feasible Barzilai-Borwein-like method under the new update scheme. The global convergence of the metho","authors_text":"Bo Jiang, Yu-Hong Dai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-02T06:42:20Z","title":"A Framework of Constraint Preserving Update Schemes for Optimization on Stiefel Manifold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0172","kind":"arxiv","version":3},"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":"sha256:3e59f8ece7f28eb224b11cfbcb7f6cb0911c7fd59021c316b18ef563ba2410a5","target":"record","created_at":"2026-05-18T02:42:29Z","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":"5ab647d32be7a7f04f607e429caf3a28b0ba087fd3ea84b8ab17fdd538413c63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2013-01-02T06:42:20Z","title_canon_sha256":"51ed2209047382041698361ba6697e08d87228e34b39c0abd15635fd4f177e12"},"schema_version":"1.0","source":{"id":"1301.0172","kind":"arxiv","version":3}},"canonical_sha256":"44845ea3ee49f16224753029f03ef8dd1000a4dc0ce17ea90fdd4e5941c69526","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"44845ea3ee49f16224753029f03ef8dd1000a4dc0ce17ea90fdd4e5941c69526","first_computed_at":"2026-05-18T02:42:29.156811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:42:29.156811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3ofOa8v4vvOjUKTnTY/cxIqmphj9Iw/1lzFcUf920ps/IA+iu1i8y7YIFF7vL7wBWi6Y6VCYhY7wop+m/8isAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:42:29.157733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.0172","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e59f8ece7f28eb224b11cfbcb7f6cb0911c7fd59021c316b18ef563ba2410a5","sha256:ef8d120174c75e245094941e0d1c367d4a230cd7a471cc9369a71f304926787d"],"state_sha256":"a1432f84d78af217296b4f606f3972a060fe2da90af0cccf81579fe43c0ca920"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"einFtgxnDZi9ldKLrXW7LNA+2Xv4sSBk0A1wJYpoPqJkJf9ASwgLER2bmUiGrWXWeXInwemJiNl+jIGtXIdPCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T16:26:45.815540Z","bundle_sha256":"34d4ff914c3f02a88bf38d60be823446d2809a45137c8f375a701d8339c6b49d"}}