{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:VNVDOKCWV7AJG76HYKU2KWM2TT","short_pith_number":"pith:VNVDOKCW","canonical_record":{"source":{"id":"1909.02659","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2019-09-04T09:34:15Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","cs.LG","cs.NA","quant-ph","stat.ML"],"title_canon_sha256":"85cf34f843d90cb07f73e4bd1111e4fb48260d4b35aa6f46f82ab51f3762e357","abstract_canon_sha256":"9d60242e35002719ce6bd43cd4c01d416de2ae061647b0fce7a9c9cccf8f10a1"},"schema_version":"1.0"},"canonical_sha256":"ab6a372856afc0937fc7c2a9a5599a9cdf9dd942ca20bd7b8e292812c9b4d49b","source":{"kind":"arxiv","id":"1909.02659","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.02659","created_at":"2026-07-05T00:17:28Z"},{"alias_kind":"arxiv_version","alias_value":"1909.02659v3","created_at":"2026-07-05T00:17:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.02659","created_at":"2026-07-05T00:17:28Z"},{"alias_kind":"pith_short_12","alias_value":"VNVDOKCWV7AJ","created_at":"2026-07-05T00:17:28Z"},{"alias_kind":"pith_short_16","alias_value":"VNVDOKCWV7AJG76H","created_at":"2026-07-05T00:17:28Z"},{"alias_kind":"pith_short_8","alias_value":"VNVDOKCW","created_at":"2026-07-05T00:17:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:VNVDOKCWV7AJG76HYKU2KWM2TT","target":"record","payload":{"canonical_record":{"source":{"id":"1909.02659","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2019-09-04T09:34:15Z","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","cs.LG","cs.NA","quant-ph","stat.ML"],"title_canon_sha256":"85cf34f843d90cb07f73e4bd1111e4fb48260d4b35aa6f46f82ab51f3762e357","abstract_canon_sha256":"9d60242e35002719ce6bd43cd4c01d416de2ae061647b0fce7a9c9cccf8f10a1"},"schema_version":"1.0"},"canonical_sha256":"ab6a372856afc0937fc7c2a9a5599a9cdf9dd942ca20bd7b8e292812c9b4d49b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:17:28.949710Z","signature_b64":"sOJSiSfqnlkoS/jpIZhIIh0oIOKYv0j16VJwyLe1ArPT4WxChtjNFZQqthpyQ8uuq2YExQYGABCXk1V+PcVwDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab6a372856afc0937fc7c2a9a5599a9cdf9dd942ca20bd7b8e292812c9b4d49b","last_reissued_at":"2026-07-05T00:17:28.949209Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:17:28.949209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1909.02659","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":"2026-07-05T00:17:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ELMKQoADB7Q6tnMz3iMBQ7jKRG237kayYqOKpbzaEMieJMrfduxMs95hlAjXmtcD84lM92Zy9RtOeV8iHEhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T02:25:52.879848Z"},"content_sha256":"8b9b60282319b8cb6bf80f164bbed83afb980cd37fe5c1c4082cf9615ffa3824","schema_version":"1.0","event_id":"sha256:8b9b60282319b8cb6bf80f164bbed83afb980cd37fe5c1c4082cf9615ffa3824"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:VNVDOKCWV7AJG76HYKU2KWM2TT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Automatic Differentiation for Complex Valued SVD","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","cs.LG","cs.NA","quant-ph","stat.ML"],"primary_cat":"math.NA","authors_text":"Shi-Xin Zhang, Zhou-Quan Wan","submitted_at":"2019-09-04T09:34:15Z","abstract_excerpt":"In this note, we report the back propagation formula for complex valued singular value decompositions (SVD). This formula is an important ingredient for a complete automatic differentiation(AD) infrastructure in terms of complex numbers, and it is also the key to understand and utilize AD in tensor networks."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.02659","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1909.02659/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":"2026-07-05T00:17:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"34T7a+uY7tEbxoCpvmaamQqmbIacgvjTtXN8W/8fU7w6+uZpgdZkmISqrYDNdOmbfZmnaX7kERi0X0cZo93wAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T02:25:52.880527Z"},"content_sha256":"3829362474add31d0bc02d958ed8a037a8d78a18eb02209687c7392eeccf2e11","schema_version":"1.0","event_id":"sha256:3829362474add31d0bc02d958ed8a037a8d78a18eb02209687c7392eeccf2e11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VNVDOKCWV7AJG76HYKU2KWM2TT/bundle.json","state_url":"https://pith.science/pith/VNVDOKCWV7AJG76HYKU2KWM2TT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VNVDOKCWV7AJG76HYKU2KWM2TT/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":"2026-08-04T02:25:52Z","links":{"resolver":"https://pith.science/pith/VNVDOKCWV7AJG76HYKU2KWM2TT","bundle":"https://pith.science/pith/VNVDOKCWV7AJG76HYKU2KWM2TT/bundle.json","state":"https://pith.science/pith/VNVDOKCWV7AJG76HYKU2KWM2TT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VNVDOKCWV7AJG76HYKU2KWM2TT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:VNVDOKCWV7AJG76HYKU2KWM2TT","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":"9d60242e35002719ce6bd43cd4c01d416de2ae061647b0fce7a9c9cccf8f10a1","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","cs.LG","cs.NA","quant-ph","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2019-09-04T09:34:15Z","title_canon_sha256":"85cf34f843d90cb07f73e4bd1111e4fb48260d4b35aa6f46f82ab51f3762e357"},"schema_version":"1.0","source":{"id":"1909.02659","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1909.02659","created_at":"2026-07-05T00:17:28Z"},{"alias_kind":"arxiv_version","alias_value":"1909.02659v3","created_at":"2026-07-05T00:17:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1909.02659","created_at":"2026-07-05T00:17:28Z"},{"alias_kind":"pith_short_12","alias_value":"VNVDOKCWV7AJ","created_at":"2026-07-05T00:17:28Z"},{"alias_kind":"pith_short_16","alias_value":"VNVDOKCWV7AJG76H","created_at":"2026-07-05T00:17:28Z"},{"alias_kind":"pith_short_8","alias_value":"VNVDOKCW","created_at":"2026-07-05T00:17:28Z"}],"graph_snapshots":[{"event_id":"sha256:3829362474add31d0bc02d958ed8a037a8d78a18eb02209687c7392eeccf2e11","target":"graph","created_at":"2026-07-05T00:17:28Z","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/1909.02659/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this note, we report the back propagation formula for complex valued singular value decompositions (SVD). This formula is an important ingredient for a complete automatic differentiation(AD) infrastructure in terms of complex numbers, and it is also the key to understand and utilize AD in tensor networks.","authors_text":"Shi-Xin Zhang, Zhou-Quan Wan","cross_cats":["cond-mat.stat-mech","cond-mat.str-el","cs.LG","cs.NA","quant-ph","stat.ML"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2019-09-04T09:34:15Z","title":"Automatic Differentiation for Complex Valued SVD"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.02659","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":"sha256:8b9b60282319b8cb6bf80f164bbed83afb980cd37fe5c1c4082cf9615ffa3824","target":"record","created_at":"2026-07-05T00:17:28Z","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":"9d60242e35002719ce6bd43cd4c01d416de2ae061647b0fce7a9c9cccf8f10a1","cross_cats_sorted":["cond-mat.stat-mech","cond-mat.str-el","cs.LG","cs.NA","quant-ph","stat.ML"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.NA","submitted_at":"2019-09-04T09:34:15Z","title_canon_sha256":"85cf34f843d90cb07f73e4bd1111e4fb48260d4b35aa6f46f82ab51f3762e357"},"schema_version":"1.0","source":{"id":"1909.02659","kind":"arxiv","version":3}},"canonical_sha256":"ab6a372856afc0937fc7c2a9a5599a9cdf9dd942ca20bd7b8e292812c9b4d49b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab6a372856afc0937fc7c2a9a5599a9cdf9dd942ca20bd7b8e292812c9b4d49b","first_computed_at":"2026-07-05T00:17:28.949209Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:17:28.949209Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sOJSiSfqnlkoS/jpIZhIIh0oIOKYv0j16VJwyLe1ArPT4WxChtjNFZQqthpyQ8uuq2YExQYGABCXk1V+PcVwDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:17:28.949710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1909.02659","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b9b60282319b8cb6bf80f164bbed83afb980cd37fe5c1c4082cf9615ffa3824","sha256:3829362474add31d0bc02d958ed8a037a8d78a18eb02209687c7392eeccf2e11"],"state_sha256":"9220bb52e545d16c03ac9dd9a43c6ed27e68e2ed9bb2eea16713bf417495fe3e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bD9aMY/AEEWssrL+ByUAr7+uChazX0PbxsIOFs2Pc5krsL65AP454OMAjaZ4ZzbvCMt6lyiTt2H3fBstscX7Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T02:25:52.885459Z","bundle_sha256":"183cf1ea573483270f6a4926b9a06876a643fc774d9031a5552038ab87eeede6"}}