{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LORIHOE22XEMMLYB4Z4IYJXIMP","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":"b9a0b356abc1be3b4cc1faa8eae37675045cfdefdc39f1d933b7962cb04dccaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-24T14:24:22Z","title_canon_sha256":"bae1bf20eb053ee32cffcfdceef1ad257e6de937c51dfce84327ac5d7e505d86"},"schema_version":"1.0","source":{"id":"1503.07054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07054","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07054v1","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07054","created_at":"2026-05-18T02:20:29Z"},{"alias_kind":"pith_short_12","alias_value":"LORIHOE22XEM","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LORIHOE22XEMMLYB","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LORIHOE2","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:48c95cd0317b91b70c9101828ef2e640e20b0a5e944caefcb0afdac838249518","target":"graph","created_at":"2026-05-18T02:20:29Z","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 is an introductory survey, from a geometric perspective, on the Singular Value Decomposition (SVD) for real matrices, focusing on the role of the Terracini Lemma. We extend this point of view to tensors, we define the singular space of a tensor as the space spanned by singular vector tuples and we study some of its basic properties.","authors_text":"Giorgio Ottaviani, Raffaella Paoletti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-24T14:24:22Z","title":"A Geometric Perspective on the Singular Value Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07054","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":"sha256:9e9984efde2a8e77405f71fd9dab863dc30d72779c141004c3367ed57cc6dcf7","target":"record","created_at":"2026-05-18T02:20:29Z","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":"b9a0b356abc1be3b4cc1faa8eae37675045cfdefdc39f1d933b7962cb04dccaa","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-03-24T14:24:22Z","title_canon_sha256":"bae1bf20eb053ee32cffcfdceef1ad257e6de937c51dfce84327ac5d7e505d86"},"schema_version":"1.0","source":{"id":"1503.07054","kind":"arxiv","version":1}},"canonical_sha256":"5ba283b89ad5c8c62f01e6788c26e863eff19c0e419709e68ee2a97307aaad1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ba283b89ad5c8c62f01e6788c26e863eff19c0e419709e68ee2a97307aaad1e","first_computed_at":"2026-05-18T02:20:29.470105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:20:29.470105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2H7sCIHhrK5W++qa/acxgMU7b45hO/bK1o9BNdyPdEnaJ/Y7t2fTGlNFuT9N53jXggAs/Yc6UPZ70Pi+7paXAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:20:29.470546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e9984efde2a8e77405f71fd9dab863dc30d72779c141004c3367ed57cc6dcf7","sha256:48c95cd0317b91b70c9101828ef2e640e20b0a5e944caefcb0afdac838249518"],"state_sha256":"fed3014affc2c3aa92b849aaeab31b501dec952b7ff79f35a170f6412bc10f20"}