{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:7MPJVHD44ENB5VAQB5T46AJJMY","short_pith_number":"pith:7MPJVHD4","schema_version":"1.0","canonical_sha256":"fb1e9a9c7ce11a1ed4100f67cf0129663ef3e9890cc0a7645d10c0974b9a0c68","source":{"kind":"arxiv","id":"1203.1843","version":3},"attestation_state":"computed","paper":{"title":"Quantitative equidistribution for the solutions of systems of sparse polynomial equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CV","authors_text":"Andr\\'e Galligo, Carlos D'Andrea, Mart\\'in Sombra","submitted_at":"2012-03-08T16:32:26Z","abstract_excerpt":"For a system of Laurent polynomials f_1,..., f_n \\in C[x_1^{\\pm1},..., x_n^{\\pm1}] whose coefficients are not too big with respect to its directional resultants, we show that the solutions in the algebraic n-th dimensional complex torus of the system of equations f_1=\\dots=f_n=0, are approximately equidistributed near the unit polycircle. This generalizes to the multivariate case a classical result due to Erdos and Turan on the distribution of the arguments of the roots of a univariate polynomial. We apply this result to bound the number of real roots of a system of Laurent polynomials, and to"},"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":"1203.1843","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-08T16:32:26Z","cross_cats_sorted":["math.AC","math.AG"],"title_canon_sha256":"507f3d837615c22a133ec1a007fe88a5df7fe3877efffdd61524db5d0dbdfcb4","abstract_canon_sha256":"c9cff7fee6c2506e2b6a2727fb312e7685d0ba03041826e3a79fdfc006ce9d67"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:48.855282Z","signature_b64":"Rq4GU+pGY9czYGxt7jrgN9N+4iRPCwfcTNZravz6GEflltYBP+vRFIb/Na3nFFDwWNuWipke1RqD+eK3zKKsAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb1e9a9c7ce11a1ed4100f67cf0129663ef3e9890cc0a7645d10c0974b9a0c68","last_reissued_at":"2026-05-18T02:45:48.854836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:48.854836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quantitative equidistribution for the solutions of systems of sparse polynomial equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG"],"primary_cat":"math.CV","authors_text":"Andr\\'e Galligo, Carlos D'Andrea, Mart\\'in Sombra","submitted_at":"2012-03-08T16:32:26Z","abstract_excerpt":"For a system of Laurent polynomials f_1,..., f_n \\in C[x_1^{\\pm1},..., x_n^{\\pm1}] whose coefficients are not too big with respect to its directional resultants, we show that the solutions in the algebraic n-th dimensional complex torus of the system of equations f_1=\\dots=f_n=0, are approximately equidistributed near the unit polycircle. This generalizes to the multivariate case a classical result due to Erdos and Turan on the distribution of the arguments of the roots of a univariate polynomial. We apply this result to bound the number of real roots of a system of Laurent polynomials, and to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1843","kind":"arxiv","version":3},"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":"1203.1843","created_at":"2026-05-18T02:45:48.854905+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.1843v3","created_at":"2026-05-18T02:45:48.854905+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1843","created_at":"2026-05-18T02:45:48.854905+00:00"},{"alias_kind":"pith_short_12","alias_value":"7MPJVHD44ENB","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_16","alias_value":"7MPJVHD44ENB5VAQ","created_at":"2026-05-18T12:26:58.693483+00:00"},{"alias_kind":"pith_short_8","alias_value":"7MPJVHD4","created_at":"2026-05-18T12:26:58.693483+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/7MPJVHD44ENB5VAQB5T46AJJMY","json":"https://pith.science/pith/7MPJVHD44ENB5VAQB5T46AJJMY.json","graph_json":"https://pith.science/api/pith-number/7MPJVHD44ENB5VAQB5T46AJJMY/graph.json","events_json":"https://pith.science/api/pith-number/7MPJVHD44ENB5VAQB5T46AJJMY/events.json","paper":"https://pith.science/paper/7MPJVHD4"},"agent_actions":{"view_html":"https://pith.science/pith/7MPJVHD44ENB5VAQB5T46AJJMY","download_json":"https://pith.science/pith/7MPJVHD44ENB5VAQB5T46AJJMY.json","view_paper":"https://pith.science/paper/7MPJVHD4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.1843&json=true","fetch_graph":"https://pith.science/api/pith-number/7MPJVHD44ENB5VAQB5T46AJJMY/graph.json","fetch_events":"https://pith.science/api/pith-number/7MPJVHD44ENB5VAQB5T46AJJMY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7MPJVHD44ENB5VAQB5T46AJJMY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7MPJVHD44ENB5VAQB5T46AJJMY/action/storage_attestation","attest_author":"https://pith.science/pith/7MPJVHD44ENB5VAQB5T46AJJMY/action/author_attestation","sign_citation":"https://pith.science/pith/7MPJVHD44ENB5VAQB5T46AJJMY/action/citation_signature","submit_replication":"https://pith.science/pith/7MPJVHD44ENB5VAQB5T46AJJMY/action/replication_record"}},"created_at":"2026-05-18T02:45:48.854905+00:00","updated_at":"2026-05-18T02:45:48.854905+00:00"}