{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:PIWB3BBIU5NVOBSQET4GEYWMST","short_pith_number":"pith:PIWB3BBI","schema_version":"1.0","canonical_sha256":"7a2c1d8428a75b57065024f86262cc94e422e12fde2a197e869caa91e46b8649","source":{"kind":"arxiv","id":"1112.1012","version":1},"attestation_state":"computed","paper":{"title":"Mixed Discriminants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.CO"],"primary_cat":"math.AG","authors_text":"Alicia Dickenstein, Bernd Sturmfels, Eduardo Cattani, Maria Angelica Cueto, Sandra Di Rocco","submitted_at":"2011-12-05T17:39:08Z","abstract_excerpt":"The mixed discriminant of n Laurent polynomials in n variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick expresses the mixed discriminant as an A-discriminant. We show that the degree of the mixed discriminant is a piecewise linear function in the Plucker coordinates of a mixed Grassmannian. An explicit degree formula is given for the case of plane curves."},"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":"1112.1012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-12-05T17:39:08Z","cross_cats_sorted":["cs.SC","math.CO"],"title_canon_sha256":"45fabde5b1ab747168521873719d3acf6423d28ce84b516cb5346937c36de531","abstract_canon_sha256":"46d86ba2fdc5fa30040e8ecc60b74a9a8765edf86168d4c80c8df5f6a3a520cf"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:57.234911Z","signature_b64":"Cyv2Anf79W6+CulDMoclsNw5JxD16vC/AeSIFJXrXHZSI63fpTOO7R5wknM5dcnMhIZ16B9CPVddgXRyeN2+DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7a2c1d8428a75b57065024f86262cc94e422e12fde2a197e869caa91e46b8649","last_reissued_at":"2026-05-18T04:06:57.234198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:57.234198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mixed Discriminants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.CO"],"primary_cat":"math.AG","authors_text":"Alicia Dickenstein, Bernd Sturmfels, Eduardo Cattani, Maria Angelica Cueto, Sandra Di Rocco","submitted_at":"2011-12-05T17:39:08Z","abstract_excerpt":"The mixed discriminant of n Laurent polynomials in n variables is the irreducible polynomial in the coefficients which vanishes whenever two of the roots coincide. The Cayley trick expresses the mixed discriminant as an A-discriminant. We show that the degree of the mixed discriminant is a piecewise linear function in the Plucker coordinates of a mixed Grassmannian. An explicit degree formula is given for the case of plane curves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1012","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":"1112.1012","created_at":"2026-05-18T04:06:57.234301+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.1012v1","created_at":"2026-05-18T04:06:57.234301+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1012","created_at":"2026-05-18T04:06:57.234301+00:00"},{"alias_kind":"pith_short_12","alias_value":"PIWB3BBIU5NV","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"PIWB3BBIU5NVOBSQ","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"PIWB3BBI","created_at":"2026-05-18T12:26:39.201973+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/PIWB3BBIU5NVOBSQET4GEYWMST","json":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST.json","graph_json":"https://pith.science/api/pith-number/PIWB3BBIU5NVOBSQET4GEYWMST/graph.json","events_json":"https://pith.science/api/pith-number/PIWB3BBIU5NVOBSQET4GEYWMST/events.json","paper":"https://pith.science/paper/PIWB3BBI"},"agent_actions":{"view_html":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST","download_json":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST.json","view_paper":"https://pith.science/paper/PIWB3BBI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.1012&json=true","fetch_graph":"https://pith.science/api/pith-number/PIWB3BBIU5NVOBSQET4GEYWMST/graph.json","fetch_events":"https://pith.science/api/pith-number/PIWB3BBIU5NVOBSQET4GEYWMST/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST/action/storage_attestation","attest_author":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST/action/author_attestation","sign_citation":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST/action/citation_signature","submit_replication":"https://pith.science/pith/PIWB3BBIU5NVOBSQET4GEYWMST/action/replication_record"}},"created_at":"2026-05-18T04:06:57.234301+00:00","updated_at":"2026-05-18T04:06:57.234301+00:00"}