{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ROBRIVLHYZV3HONBFGRZTM6YGH","short_pith_number":"pith:ROBRIVLH","canonical_record":{"source":{"id":"1802.09013","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-25T14:15:25Z","cross_cats_sorted":[],"title_canon_sha256":"486b80b63502ff0e77e86172dbcf51d1f1d20890cd011321820af53e0a865e5b","abstract_canon_sha256":"5b3e5f4e82f6249fcedf1f452e4dff45a9b2e1d6b28cd7cd006738c857decb89"},"schema_version":"1.0"},"canonical_sha256":"8b83145567c66bb3b9a129a399b3d831e24d4ff4ef6093c357a46899ac2ec4f3","source":{"kind":"arxiv","id":"1802.09013","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09013","created_at":"2026-05-18T00:22:35Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09013v1","created_at":"2026-05-18T00:22:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09013","created_at":"2026-05-18T00:22:35Z"},{"alias_kind":"pith_short_12","alias_value":"ROBRIVLHYZV3","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"ROBRIVLHYZV3HONB","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"ROBRIVLH","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ROBRIVLHYZV3HONBFGRZTM6YGH","target":"record","payload":{"canonical_record":{"source":{"id":"1802.09013","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-25T14:15:25Z","cross_cats_sorted":[],"title_canon_sha256":"486b80b63502ff0e77e86172dbcf51d1f1d20890cd011321820af53e0a865e5b","abstract_canon_sha256":"5b3e5f4e82f6249fcedf1f452e4dff45a9b2e1d6b28cd7cd006738c857decb89"},"schema_version":"1.0"},"canonical_sha256":"8b83145567c66bb3b9a129a399b3d831e24d4ff4ef6093c357a46899ac2ec4f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:35.787608Z","signature_b64":"ACFquMscUWSbg/CCf/TI8QY2XIBe/94heKFHotzl9yEPcbJKV+R1go7mjknNkH4PYegKQErGM5ARjylGOu+wAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b83145567c66bb3b9a129a399b3d831e24d4ff4ef6093c357a46899ac2ec4f3","last_reissued_at":"2026-05-18T00:22:35.786920Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:35.786920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.09013","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:22:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6GssQvZKZ4S0sFnTg6GZMWI/EZ/W0M4toax+pji0l1ofUY8g1w4nXJTnw/KgkSRNOVD3cUtfXCMdmfY4PQ+iCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:22:11.421187Z"},"content_sha256":"20c0537a9d3368a5838bc94db9a4aadfe8c0f99562d491b160b0395ea2fde98a","schema_version":"1.0","event_id":"sha256:20c0537a9d3368a5838bc94db9a4aadfe8c0f99562d491b160b0395ea2fde98a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ROBRIVLHYZV3HONBFGRZTM6YGH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On decompositions and approximations of conjugate partial-symmetric complex tensors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Bo Jiang, Taoran Fu, Zhening Li","submitted_at":"2018-02-25T14:15:25Z","abstract_excerpt":"Conjugate partial-symmetric (CPS) tensors are the high-order generalization of Hermitian matrices. As the role played by Hermitian matrices in matrix theory and quadratic optimization, CPS tensors have shown growing interest recently in tensor theory and optimization, particularly in many application-driven complex polynomial optimization problems. In this paper, we study CPS tensors with a focus on ranks, rank-one decompositions and approximations, as well as their applications. The analysis is conducted along side with a more general class of complex tensors called partial-symmetric tensors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09013","kind":"arxiv","version":1},"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":"2026-05-18T00:22:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Or6W45xueZ7PbZ35SCa6Wi0xA7nWvg79DEFPBeVNf8G+14p0MKYFsN/GdtkJVvURN5mAnR/N8FBryjPQm8e5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:22:11.421777Z"},"content_sha256":"b173236e068d5bcebbf53ab804ec7f63bf18d48eab4d70e524e5d05042a9eaf7","schema_version":"1.0","event_id":"sha256:b173236e068d5bcebbf53ab804ec7f63bf18d48eab4d70e524e5d05042a9eaf7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ROBRIVLHYZV3HONBFGRZTM6YGH/bundle.json","state_url":"https://pith.science/pith/ROBRIVLHYZV3HONBFGRZTM6YGH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ROBRIVLHYZV3HONBFGRZTM6YGH/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":"2026-08-04T05:22:11Z","links":{"resolver":"https://pith.science/pith/ROBRIVLHYZV3HONBFGRZTM6YGH","bundle":"https://pith.science/pith/ROBRIVLHYZV3HONBFGRZTM6YGH/bundle.json","state":"https://pith.science/pith/ROBRIVLHYZV3HONBFGRZTM6YGH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ROBRIVLHYZV3HONBFGRZTM6YGH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ROBRIVLHYZV3HONBFGRZTM6YGH","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":"5b3e5f4e82f6249fcedf1f452e4dff45a9b2e1d6b28cd7cd006738c857decb89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-25T14:15:25Z","title_canon_sha256":"486b80b63502ff0e77e86172dbcf51d1f1d20890cd011321820af53e0a865e5b"},"schema_version":"1.0","source":{"id":"1802.09013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.09013","created_at":"2026-05-18T00:22:35Z"},{"alias_kind":"arxiv_version","alias_value":"1802.09013v1","created_at":"2026-05-18T00:22:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.09013","created_at":"2026-05-18T00:22:35Z"},{"alias_kind":"pith_short_12","alias_value":"ROBRIVLHYZV3","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"ROBRIVLHYZV3HONB","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"ROBRIVLH","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:b173236e068d5bcebbf53ab804ec7f63bf18d48eab4d70e524e5d05042a9eaf7","target":"graph","created_at":"2026-05-18T00:22:35Z","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":"Conjugate partial-symmetric (CPS) tensors are the high-order generalization of Hermitian matrices. As the role played by Hermitian matrices in matrix theory and quadratic optimization, CPS tensors have shown growing interest recently in tensor theory and optimization, particularly in many application-driven complex polynomial optimization problems. In this paper, we study CPS tensors with a focus on ranks, rank-one decompositions and approximations, as well as their applications. The analysis is conducted along side with a more general class of complex tensors called partial-symmetric tensors.","authors_text":"Bo Jiang, Taoran Fu, Zhening Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-25T14:15:25Z","title":"On decompositions and approximations of conjugate partial-symmetric complex tensors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.09013","kind":"arxiv","version":1},"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":"sha256:20c0537a9d3368a5838bc94db9a4aadfe8c0f99562d491b160b0395ea2fde98a","target":"record","created_at":"2026-05-18T00:22:35Z","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":"5b3e5f4e82f6249fcedf1f452e4dff45a9b2e1d6b28cd7cd006738c857decb89","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-02-25T14:15:25Z","title_canon_sha256":"486b80b63502ff0e77e86172dbcf51d1f1d20890cd011321820af53e0a865e5b"},"schema_version":"1.0","source":{"id":"1802.09013","kind":"arxiv","version":1}},"canonical_sha256":"8b83145567c66bb3b9a129a399b3d831e24d4ff4ef6093c357a46899ac2ec4f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b83145567c66bb3b9a129a399b3d831e24d4ff4ef6093c357a46899ac2ec4f3","first_computed_at":"2026-05-18T00:22:35.786920Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:35.786920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ACFquMscUWSbg/CCf/TI8QY2XIBe/94heKFHotzl9yEPcbJKV+R1go7mjknNkH4PYegKQErGM5ARjylGOu+wAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:35.787608Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.09013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20c0537a9d3368a5838bc94db9a4aadfe8c0f99562d491b160b0395ea2fde98a","sha256:b173236e068d5bcebbf53ab804ec7f63bf18d48eab4d70e524e5d05042a9eaf7"],"state_sha256":"c674baae27d231bba7286ac419db41fe5b63ebde229eede023e2b8bbf1ccd13d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T1KajWjuFtkkW+gWFNR2rp/edFsSzSLkfnXaIum1LwT0eaOdmOk0pVguTw6VL2IQUWpvv30/hRpch8fxQl4LBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T05:22:11.427356Z","bundle_sha256":"6b5b5189110341a449e517a6ade7690f7505872bdb9b1b4f02be6916ddb07249"}}