{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GXTTB2NX3VKTLL5QTEN533RNEV","short_pith_number":"pith:GXTTB2NX","schema_version":"1.0","canonical_sha256":"35e730e9b7dd5535afb0991bddee2d2570addfd883f893b4a61f78512a4f49cf","source":{"kind":"arxiv","id":"1305.0644","version":1},"attestation_state":"computed","paper":{"title":"A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of Parseval's identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Takis Konstantopoulos","submitted_at":"2013-05-03T09:07:01Z","abstract_excerpt":"We give a short proof of the Cauchy-Binet determinantal formula using multilinear algebra by first generalizing it to an identity {\\em not} involving determinants. By extending the formula to abstract Hilbert spaces we obtain, as a corollary, a generalization of the classical Parseval identity."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.0644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-05-03T09:07:01Z","cross_cats_sorted":[],"title_canon_sha256":"5ecbb7f30abf10d526e96296a6c357d291f05ffef178e1f1430f683473f253b1","abstract_canon_sha256":"aef0deec71eebc0f964e04fd625e64ce9e6c6042f5799a99d4aa4f7105b18aad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:33.120211Z","signature_b64":"a7aOY1r6RBGcM6TgADVUTaFGbCpwvvg469l/XIvs3Mf6DYIY05+aR9THpE41eTH3Crcv9IbKAMlu8C6709uZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"35e730e9b7dd5535afb0991bddee2d2570addfd883f893b4a61f78512a4f49cf","last_reissued_at":"2026-05-18T03:26:33.119755Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:33.119755Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A multilinear algebra proof of the Cauchy-Binet formula and a multilinear version of Parseval's identity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Takis Konstantopoulos","submitted_at":"2013-05-03T09:07:01Z","abstract_excerpt":"We give a short proof of the Cauchy-Binet determinantal formula using multilinear algebra by first generalizing it to an identity {\\em not} involving determinants. By extending the formula to abstract Hilbert spaces we obtain, as a corollary, a generalization of the classical Parseval identity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0644","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1305.0644","created_at":"2026-05-18T03:26:33.119820+00:00"},{"alias_kind":"arxiv_version","alias_value":"1305.0644v1","created_at":"2026-05-18T03:26:33.119820+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0644","created_at":"2026-05-18T03:26:33.119820+00:00"},{"alias_kind":"pith_short_12","alias_value":"GXTTB2NX3VKT","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"GXTTB2NX3VKTLL5Q","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"GXTTB2NX","created_at":"2026-05-18T12:27:46.883200+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GXTTB2NX3VKTLL5QTEN533RNEV","json":"https://pith.science/pith/GXTTB2NX3VKTLL5QTEN533RNEV.json","graph_json":"https://pith.science/api/pith-number/GXTTB2NX3VKTLL5QTEN533RNEV/graph.json","events_json":"https://pith.science/api/pith-number/GXTTB2NX3VKTLL5QTEN533RNEV/events.json","paper":"https://pith.science/paper/GXTTB2NX"},"agent_actions":{"view_html":"https://pith.science/pith/GXTTB2NX3VKTLL5QTEN533RNEV","download_json":"https://pith.science/pith/GXTTB2NX3VKTLL5QTEN533RNEV.json","view_paper":"https://pith.science/paper/GXTTB2NX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1305.0644&json=true","fetch_graph":"https://pith.science/api/pith-number/GXTTB2NX3VKTLL5QTEN533RNEV/graph.json","fetch_events":"https://pith.science/api/pith-number/GXTTB2NX3VKTLL5QTEN533RNEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GXTTB2NX3VKTLL5QTEN533RNEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GXTTB2NX3VKTLL5QTEN533RNEV/action/storage_attestation","attest_author":"https://pith.science/pith/GXTTB2NX3VKTLL5QTEN533RNEV/action/author_attestation","sign_citation":"https://pith.science/pith/GXTTB2NX3VKTLL5QTEN533RNEV/action/citation_signature","submit_replication":"https://pith.science/pith/GXTTB2NX3VKTLL5QTEN533RNEV/action/replication_record"}},"created_at":"2026-05-18T03:26:33.119820+00:00","updated_at":"2026-05-18T03:26:33.119820+00:00"}