{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:NDV4KBYPY4QCY7UTWX45SYJQ2X","short_pith_number":"pith:NDV4KBYP","schema_version":"1.0","canonical_sha256":"68ebc5070fc7202c7e93b5f9d96130d5d942efb9d9aa11727a160e7ada196f29","source":{"kind":"arxiv","id":"1603.04279","version":1},"attestation_state":"computed","paper":{"title":"Non-symmetric polarization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Defant, Sunke Schl\\\"uters","submitted_at":"2016-03-14T14:41:44Z","abstract_excerpt":"Let $P$ be an $m$-homogeneous polynomial in $n$-complex variables $x_1, \\dotsc, x_n$. Clearly, $P$ has a unique representation in the form \\begin{equation*} P(x)= \\sum_{1 \\leq j_1 \\leq \\dotsc \\leq j_m \\leq n} c_{(j_1, \\dotsc, j_m)} \\, x_{j_1} \\dotsb x_{j_m} \\,, \\end{equation*} and the $m$\"~form \\begin{equation*} L_P(x^{(1)}, \\dotsc, x^{(m)})= \\sum_{1 \\leq j_1 \\leq \\dotsc \\leq j_m \\leq n} c_{(j_1, \\dotsc, j_m)} \\, x^{(1)}_{j_1} \\dotsb x^{(m)}_{j_m} \\end{equation*} satisfies $L_P(x,\\dotsc, x) = P(x)$ for every $x\\in\\mathbb{C}^n$. We show that, although $L_P$ in general is non-symmetric, for a la"},"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":"1603.04279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-03-14T14:41:44Z","cross_cats_sorted":[],"title_canon_sha256":"af1a87e13e10587ebf7e7ed36902226a2fb46cf3d28af4d30c8d6197735fbeda","abstract_canon_sha256":"3e83730ddd9f395cc26d2fb119583b79d57f8bd830ec19663dbc3e6da2788646"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:08.917733Z","signature_b64":"+mTGlXigXQBRM/+ZqEXKCp8+/+TT4AjQyGK+I7u728qzB74e60VP+FmsFyCNaRGVPHiirgqD2VwYsKpnJSiVCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68ebc5070fc7202c7e93b5f9d96130d5d942efb9d9aa11727a160e7ada196f29","last_reissued_at":"2026-05-18T01:19:08.916987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:08.916987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-symmetric polarization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andreas Defant, Sunke Schl\\\"uters","submitted_at":"2016-03-14T14:41:44Z","abstract_excerpt":"Let $P$ be an $m$-homogeneous polynomial in $n$-complex variables $x_1, \\dotsc, x_n$. Clearly, $P$ has a unique representation in the form \\begin{equation*} P(x)= \\sum_{1 \\leq j_1 \\leq \\dotsc \\leq j_m \\leq n} c_{(j_1, \\dotsc, j_m)} \\, x_{j_1} \\dotsb x_{j_m} \\,, \\end{equation*} and the $m$\"~form \\begin{equation*} L_P(x^{(1)}, \\dotsc, x^{(m)})= \\sum_{1 \\leq j_1 \\leq \\dotsc \\leq j_m \\leq n} c_{(j_1, \\dotsc, j_m)} \\, x^{(1)}_{j_1} \\dotsb x^{(m)}_{j_m} \\end{equation*} satisfies $L_P(x,\\dotsc, x) = P(x)$ for every $x\\in\\mathbb{C}^n$. We show that, although $L_P$ in general is non-symmetric, for a la"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04279","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":"1603.04279","created_at":"2026-05-18T01:19:08.917107+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.04279v1","created_at":"2026-05-18T01:19:08.917107+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04279","created_at":"2026-05-18T01:19:08.917107+00:00"},{"alias_kind":"pith_short_12","alias_value":"NDV4KBYPY4QC","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_16","alias_value":"NDV4KBYPY4QCY7UT","created_at":"2026-05-18T12:30:32.724797+00:00"},{"alias_kind":"pith_short_8","alias_value":"NDV4KBYP","created_at":"2026-05-18T12:30:32.724797+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/NDV4KBYPY4QCY7UTWX45SYJQ2X","json":"https://pith.science/pith/NDV4KBYPY4QCY7UTWX45SYJQ2X.json","graph_json":"https://pith.science/api/pith-number/NDV4KBYPY4QCY7UTWX45SYJQ2X/graph.json","events_json":"https://pith.science/api/pith-number/NDV4KBYPY4QCY7UTWX45SYJQ2X/events.json","paper":"https://pith.science/paper/NDV4KBYP"},"agent_actions":{"view_html":"https://pith.science/pith/NDV4KBYPY4QCY7UTWX45SYJQ2X","download_json":"https://pith.science/pith/NDV4KBYPY4QCY7UTWX45SYJQ2X.json","view_paper":"https://pith.science/paper/NDV4KBYP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.04279&json=true","fetch_graph":"https://pith.science/api/pith-number/NDV4KBYPY4QCY7UTWX45SYJQ2X/graph.json","fetch_events":"https://pith.science/api/pith-number/NDV4KBYPY4QCY7UTWX45SYJQ2X/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NDV4KBYPY4QCY7UTWX45SYJQ2X/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NDV4KBYPY4QCY7UTWX45SYJQ2X/action/storage_attestation","attest_author":"https://pith.science/pith/NDV4KBYPY4QCY7UTWX45SYJQ2X/action/author_attestation","sign_citation":"https://pith.science/pith/NDV4KBYPY4QCY7UTWX45SYJQ2X/action/citation_signature","submit_replication":"https://pith.science/pith/NDV4KBYPY4QCY7UTWX45SYJQ2X/action/replication_record"}},"created_at":"2026-05-18T01:19:08.917107+00:00","updated_at":"2026-05-18T01:19:08.917107+00:00"}