{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:VDVJCBR3LLBZTK36HCSGDHKHSL","short_pith_number":"pith:VDVJCBR3","schema_version":"1.0","canonical_sha256":"a8ea91063b5ac399ab7e38a4619d4792c8cb6ad0aec160b73a73c21f8cd1d4ff","source":{"kind":"arxiv","id":"1509.05707","version":1},"attestation_state":"computed","paper":{"title":"Symmetric multilinear forms and polarization of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ale\\v{s} Dr\\'apal, Petr Vojt\\v{e}chovsk\\'y","submitted_at":"2015-09-18T17:14:02Z","abstract_excerpt":"We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in $n$ variables. The main tool is combinatorial polarization, and the approach is applicable even when $n!$ is not invertible in the underlying field."},"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":"1509.05707","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-09-18T17:14:02Z","cross_cats_sorted":[],"title_canon_sha256":"7c534fbe9ea15d9f668ef202261f4367617b309da6d5c66e9896d2c803ad039e","abstract_canon_sha256":"e67850d66c8b4264eb344d298a25aeac29d600e4ce6aa1f5ea0abad8f5302c6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:42.553261Z","signature_b64":"p8eWZoahTyca5eZYrh4IxT5sSaklAE1YchSx6Cur+B9fA7BowpDoK0pz67pL8KlZZMz2jPQa/gYEzI+j6EbwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8ea91063b5ac399ab7e38a4619d4792c8cb6ad0aec160b73a73c21f8cd1d4ff","last_reissued_at":"2026-05-18T01:32:42.552735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:42.552735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetric multilinear forms and polarization of polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ale\\v{s} Dr\\'apal, Petr Vojt\\v{e}chovsk\\'y","submitted_at":"2015-09-18T17:14:02Z","abstract_excerpt":"We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in $n$ variables. The main tool is combinatorial polarization, and the approach is applicable even when $n!$ is not invertible in the underlying field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.05707","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":"1509.05707","created_at":"2026-05-18T01:32:42.552810+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.05707v1","created_at":"2026-05-18T01:32:42.552810+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.05707","created_at":"2026-05-18T01:32:42.552810+00:00"},{"alias_kind":"pith_short_12","alias_value":"VDVJCBR3LLBZ","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"VDVJCBR3LLBZTK36","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"VDVJCBR3","created_at":"2026-05-18T12:29:44.643036+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/VDVJCBR3LLBZTK36HCSGDHKHSL","json":"https://pith.science/pith/VDVJCBR3LLBZTK36HCSGDHKHSL.json","graph_json":"https://pith.science/api/pith-number/VDVJCBR3LLBZTK36HCSGDHKHSL/graph.json","events_json":"https://pith.science/api/pith-number/VDVJCBR3LLBZTK36HCSGDHKHSL/events.json","paper":"https://pith.science/paper/VDVJCBR3"},"agent_actions":{"view_html":"https://pith.science/pith/VDVJCBR3LLBZTK36HCSGDHKHSL","download_json":"https://pith.science/pith/VDVJCBR3LLBZTK36HCSGDHKHSL.json","view_paper":"https://pith.science/paper/VDVJCBR3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.05707&json=true","fetch_graph":"https://pith.science/api/pith-number/VDVJCBR3LLBZTK36HCSGDHKHSL/graph.json","fetch_events":"https://pith.science/api/pith-number/VDVJCBR3LLBZTK36HCSGDHKHSL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VDVJCBR3LLBZTK36HCSGDHKHSL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VDVJCBR3LLBZTK36HCSGDHKHSL/action/storage_attestation","attest_author":"https://pith.science/pith/VDVJCBR3LLBZTK36HCSGDHKHSL/action/author_attestation","sign_citation":"https://pith.science/pith/VDVJCBR3LLBZTK36HCSGDHKHSL/action/citation_signature","submit_replication":"https://pith.science/pith/VDVJCBR3LLBZTK36HCSGDHKHSL/action/replication_record"}},"created_at":"2026-05-18T01:32:42.552810+00:00","updated_at":"2026-05-18T01:32:42.552810+00:00"}