{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VVUJZMODOPUKSOFOLNH4BAYS5Q","short_pith_number":"pith:VVUJZMOD","schema_version":"1.0","canonical_sha256":"ad689cb1c373e8a938ae5b4fc08312ec137600a4baa0c260d51c0a6986fc76a5","source":{"kind":"arxiv","id":"1701.05805","version":1},"attestation_state":"computed","paper":{"title":"Structured low rank decomposition of multivariate Hankel matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AG","authors_text":"Bernard Mourrain (AROMATH), Houssam Khalil, Jouhayna Harmouch (AROMATH)","submitted_at":"2017-01-19T14:19:27Z","abstract_excerpt":"We study the decomposition of a multivariate Hankel matrix H\\_$\\sigma$ as a sum of Hankel matrices of small rank in correlation with the decomposition of its symbol $\\sigma$ as a sum of polynomial-exponential series. We present a new algorithm to compute the low rank decomposition of the Hankel operator and the decomposition of its symbol exploiting the properties of the associated Artinian Gorenstein quotient algebra A\\_$\\sigma$. A basis of A\\_$\\sigma$ is computed from the Singular Value Decomposition of a sub-matrix of the Hankel matrix H\\_$\\sigma$. The frequencies and the weights are deduce"},"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":"1701.05805","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-01-19T14:19:27Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"4630ca495ac76d8fa20139993bcf37560456c81623a1bdf998068c3715e16da1","abstract_canon_sha256":"a175d7687205a9dfde13a68dcd16cfc4ee92f7e369f71c22053dbf89fd675902"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:24.708388Z","signature_b64":"2oObWvR/9SO6nNpUhS5dyBH0y/5c+NGYa3w5zbkXeuBnlD/XGRlrk/WqZt46it6OPAxL5BSe7Y9yV3AvzbjTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad689cb1c373e8a938ae5b4fc08312ec137600a4baa0c260d51c0a6986fc76a5","last_reissued_at":"2026-05-18T00:52:24.707718Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:24.707718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Structured low rank decomposition of multivariate Hankel matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AG","authors_text":"Bernard Mourrain (AROMATH), Houssam Khalil, Jouhayna Harmouch (AROMATH)","submitted_at":"2017-01-19T14:19:27Z","abstract_excerpt":"We study the decomposition of a multivariate Hankel matrix H\\_$\\sigma$ as a sum of Hankel matrices of small rank in correlation with the decomposition of its symbol $\\sigma$ as a sum of polynomial-exponential series. We present a new algorithm to compute the low rank decomposition of the Hankel operator and the decomposition of its symbol exploiting the properties of the associated Artinian Gorenstein quotient algebra A\\_$\\sigma$. A basis of A\\_$\\sigma$ is computed from the Singular Value Decomposition of a sub-matrix of the Hankel matrix H\\_$\\sigma$. The frequencies and the weights are deduce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05805","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":"1701.05805","created_at":"2026-05-18T00:52:24.707802+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.05805v1","created_at":"2026-05-18T00:52:24.707802+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05805","created_at":"2026-05-18T00:52:24.707802+00:00"},{"alias_kind":"pith_short_12","alias_value":"VVUJZMODOPUK","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VVUJZMODOPUKSOFO","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VVUJZMOD","created_at":"2026-05-18T12:31:49.984773+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/VVUJZMODOPUKSOFOLNH4BAYS5Q","json":"https://pith.science/pith/VVUJZMODOPUKSOFOLNH4BAYS5Q.json","graph_json":"https://pith.science/api/pith-number/VVUJZMODOPUKSOFOLNH4BAYS5Q/graph.json","events_json":"https://pith.science/api/pith-number/VVUJZMODOPUKSOFOLNH4BAYS5Q/events.json","paper":"https://pith.science/paper/VVUJZMOD"},"agent_actions":{"view_html":"https://pith.science/pith/VVUJZMODOPUKSOFOLNH4BAYS5Q","download_json":"https://pith.science/pith/VVUJZMODOPUKSOFOLNH4BAYS5Q.json","view_paper":"https://pith.science/paper/VVUJZMOD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.05805&json=true","fetch_graph":"https://pith.science/api/pith-number/VVUJZMODOPUKSOFOLNH4BAYS5Q/graph.json","fetch_events":"https://pith.science/api/pith-number/VVUJZMODOPUKSOFOLNH4BAYS5Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VVUJZMODOPUKSOFOLNH4BAYS5Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VVUJZMODOPUKSOFOLNH4BAYS5Q/action/storage_attestation","attest_author":"https://pith.science/pith/VVUJZMODOPUKSOFOLNH4BAYS5Q/action/author_attestation","sign_citation":"https://pith.science/pith/VVUJZMODOPUKSOFOLNH4BAYS5Q/action/citation_signature","submit_replication":"https://pith.science/pith/VVUJZMODOPUKSOFOLNH4BAYS5Q/action/replication_record"}},"created_at":"2026-05-18T00:52:24.707802+00:00","updated_at":"2026-05-18T00:52:24.707802+00:00"}