{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:OZUFVBBM4XXZIG6G33FKPLS5EC","short_pith_number":"pith:OZUFVBBM","canonical_record":{"source":{"id":"0901.3706","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2009-01-23T16:21:18Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"98e30cba65459a9f8ea655f74f950b00e53b2e9f8ce054b96069decc0afb7749","abstract_canon_sha256":"532948d01cd9c9831f19f8f5e880bb5eeab8b49636b5516591a6a439d400dfd7"},"schema_version":"1.0"},"canonical_sha256":"76685a842ce5ef941bc6decaa7ae5d20843d49ef9be607c308b3131e8aef2952","source":{"kind":"arxiv","id":"0901.3706","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.3706","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"0901.3706v2","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.3706","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"OZUFVBBM4XXZ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OZUFVBBM4XXZIG6G","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OZUFVBBM","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:OZUFVBBM4XXZIG6G33FKPLS5EC","target":"record","payload":{"canonical_record":{"source":{"id":"0901.3706","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2009-01-23T16:21:18Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"98e30cba65459a9f8ea655f74f950b00e53b2e9f8ce054b96069decc0afb7749","abstract_canon_sha256":"532948d01cd9c9831f19f8f5e880bb5eeab8b49636b5516591a6a439d400dfd7"},"schema_version":"1.0"},"canonical_sha256":"76685a842ce5ef941bc6decaa7ae5d20843d49ef9be607c308b3131e8aef2952","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:46.362826Z","signature_b64":"YTJPzhIxDGVQc9IoC6eVS5pZ5H5shZ16tGhmo2DvkoSEEKK1QWJkOLBIGTIBd3ZI7uCghVrBcwgSbh0hTnMHAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"76685a842ce5ef941bc6decaa7ae5d20843d49ef9be607c308b3131e8aef2952","last_reissued_at":"2026-05-18T04:34:46.362253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:46.362253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0901.3706","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:34:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nac11emQ1nlXI9+VMrP0XEjE3UKIgNBmZtz2LVLm4YB3E0B426k3sBjTfI671F69rMeKkBBBrlAo9xkzbUzLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T13:20:29.593662Z"},"content_sha256":"3babf3afec8546dc9a262af708a75f362c508773ea585b8eebd6aff2157cce9f","schema_version":"1.0","event_id":"sha256:3babf3afec8546dc9a262af708a75f362c508773ea585b8eebd6aff2157cce9f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:OZUFVBBM4XXZIG6G33FKPLS5EC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetric tensor decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"cs.SC","authors_text":"Bernard Mourrain (INRIA Sophia Antipolis), Elias Tsigaridas (INRIA Sophia Antipolis), Jerome Brachat (INRIA Sophia Antipolis), Pierre Comon (I3S)","submitted_at":"2009-01-23T16:21:18Z","abstract_excerpt":"We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables of total degree d as a sum of powers of linear forms (Waring's problem), incidence properties on secant varieties of the Veronese Variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester's approach from the dual point of view. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3706","kind":"arxiv","version":2},"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":"2026-05-18T04:34:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xw7R/7yRGkdwoQ3MXU+tadyJ4KJ5NbGcfdMItzpUX1pMSfQwkpaH+9EKubCaUt+W5WqYO60ysjHb6WHPm0PVCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T13:20:29.594007Z"},"content_sha256":"3c382c32d8ce80e0004bd3bedec97a8ae2726272745ae375f7125aa8df8043e8","schema_version":"1.0","event_id":"sha256:3c382c32d8ce80e0004bd3bedec97a8ae2726272745ae375f7125aa8df8043e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC/bundle.json","state_url":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OZUFVBBM4XXZIG6G33FKPLS5EC/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":"2026-06-20T13:20:29Z","links":{"resolver":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC","bundle":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC/bundle.json","state":"https://pith.science/pith/OZUFVBBM4XXZIG6G33FKPLS5EC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OZUFVBBM4XXZIG6G33FKPLS5EC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OZUFVBBM4XXZIG6G33FKPLS5EC","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":"532948d01cd9c9831f19f8f5e880bb5eeab8b49636b5516591a6a439d400dfd7","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2009-01-23T16:21:18Z","title_canon_sha256":"98e30cba65459a9f8ea655f74f950b00e53b2e9f8ce054b96069decc0afb7749"},"schema_version":"1.0","source":{"id":"0901.3706","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.3706","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"arxiv_version","alias_value":"0901.3706v2","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.3706","created_at":"2026-05-18T04:34:46Z"},{"alias_kind":"pith_short_12","alias_value":"OZUFVBBM4XXZ","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OZUFVBBM4XXZIG6G","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OZUFVBBM","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:3c382c32d8ce80e0004bd3bedec97a8ae2726272745ae375f7125aa8df8043e8","target":"graph","created_at":"2026-05-18T04:34:46Z","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":"We present an algorithm for decomposing a symmetric tensor, of dimension n and order d as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables of total degree d as a sum of powers of linear forms (Waring's problem), incidence properties on secant varieties of the Veronese Variety and the representation of linear forms as a linear combination of evaluations at distinct points. Then we reformulate Sylvester's approach from the dual point of view. ","authors_text":"Bernard Mourrain (INRIA Sophia Antipolis), Elias Tsigaridas (INRIA Sophia Antipolis), Jerome Brachat (INRIA Sophia Antipolis), Pierre Comon (I3S)","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2009-01-23T16:21:18Z","title":"Symmetric tensor decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.3706","kind":"arxiv","version":2},"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":"sha256:3babf3afec8546dc9a262af708a75f362c508773ea585b8eebd6aff2157cce9f","target":"record","created_at":"2026-05-18T04:34:46Z","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":"532948d01cd9c9831f19f8f5e880bb5eeab8b49636b5516591a6a439d400dfd7","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2009-01-23T16:21:18Z","title_canon_sha256":"98e30cba65459a9f8ea655f74f950b00e53b2e9f8ce054b96069decc0afb7749"},"schema_version":"1.0","source":{"id":"0901.3706","kind":"arxiv","version":2}},"canonical_sha256":"76685a842ce5ef941bc6decaa7ae5d20843d49ef9be607c308b3131e8aef2952","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"76685a842ce5ef941bc6decaa7ae5d20843d49ef9be607c308b3131e8aef2952","first_computed_at":"2026-05-18T04:34:46.362253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:46.362253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YTJPzhIxDGVQc9IoC6eVS5pZ5H5shZ16tGhmo2DvkoSEEKK1QWJkOLBIGTIBd3ZI7uCghVrBcwgSbh0hTnMHAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:46.362826Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.3706","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3babf3afec8546dc9a262af708a75f362c508773ea585b8eebd6aff2157cce9f","sha256:3c382c32d8ce80e0004bd3bedec97a8ae2726272745ae375f7125aa8df8043e8"],"state_sha256":"1173be414eaa9ae437c5c6542328b431a3f60bb35677ea8076e0cfc8313f0406"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TJCpgyDIfqCUrKFRc/w1vs748zpyuqqaKRH0Yg/znHJ9KhMkIrfOuKXeRQyT+1O8NKZztDGMAVQZd3maDnVPAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T13:20:29.596047Z","bundle_sha256":"da909450d1eb137f71e878515e63502d8875788d57de2dc2dc53f214eb595dc1"}}