{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7MPJVHD44ENB5VAQB5T46AJJMY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c9cff7fee6c2506e2b6a2727fb312e7685d0ba03041826e3a79fdfc006ce9d67","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-08T16:32:26Z","title_canon_sha256":"507f3d837615c22a133ec1a007fe88a5df7fe3877efffdd61524db5d0dbdfcb4"},"schema_version":"1.0","source":{"id":"1203.1843","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.1843","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"arxiv_version","alias_value":"1203.1843v3","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.1843","created_at":"2026-05-18T02:45:48Z"},{"alias_kind":"pith_short_12","alias_value":"7MPJVHD44ENB","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7MPJVHD44ENB5VAQ","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7MPJVHD4","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:7aec489faf1a517b4a700609c2f36d7eeb52061c1e79205a7e93ee36f5b51713","target":"graph","created_at":"2026-05-18T02:45:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Andr\\'e Galligo, Carlos D'Andrea, Mart\\'in Sombra","cross_cats":["math.AC","math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-08T16:32:26Z","title":"Quantitative equidistribution for the solutions of systems of sparse polynomial equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.1843","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:895a1cbcb27e4c78479ba537797294a5b0cf78f1ee1f482c429b0037ddd1cd2a","target":"record","created_at":"2026-05-18T02:45:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c9cff7fee6c2506e2b6a2727fb312e7685d0ba03041826e3a79fdfc006ce9d67","cross_cats_sorted":["math.AC","math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-03-08T16:32:26Z","title_canon_sha256":"507f3d837615c22a133ec1a007fe88a5df7fe3877efffdd61524db5d0dbdfcb4"},"schema_version":"1.0","source":{"id":"1203.1843","kind":"arxiv","version":3}},"canonical_sha256":"fb1e9a9c7ce11a1ed4100f67cf0129663ef3e9890cc0a7645d10c0974b9a0c68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb1e9a9c7ce11a1ed4100f67cf0129663ef3e9890cc0a7645d10c0974b9a0c68","first_computed_at":"2026-05-18T02:45:48.854836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:48.854836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Rq4GU+pGY9czYGxt7jrgN9N+4iRPCwfcTNZravz6GEflltYBP+vRFIb/Na3nFFDwWNuWipke1RqD+eK3zKKsAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:48.855282Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.1843","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:895a1cbcb27e4c78479ba537797294a5b0cf78f1ee1f482c429b0037ddd1cd2a","sha256:7aec489faf1a517b4a700609c2f36d7eeb52061c1e79205a7e93ee36f5b51713"],"state_sha256":"289ca94c38acc360bdf5a39d07f18adaf2817f7bb047fa1e2d57080a456bc7fb"}