{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SJM3ZEPAJ22HO3GGM6EE6URTWO","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":"841fabfe355aa0902eb1663069f2f212afd5175003f80ac5e98dbb9fe3444cad","cross_cats_sorted":["cs.DS","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-19T18:01:23Z","title_canon_sha256":"d94a0eb1e1e96e3f0dd430e09798eb52c463541ccdb317961dba76c46c9ff75d"},"schema_version":"1.0","source":{"id":"1806.07404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07404","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07404v1","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07404","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"pith_short_12","alias_value":"SJM3ZEPAJ22H","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SJM3ZEPAJ22HO3GG","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SJM3ZEPA","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:f990e16ef08d61dd411024686aabb61b6bfe5e5f960db82bf3710cf3f0411f3b","target":"graph","created_at":"2026-05-18T00:12:47Z","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":"Let $p(x)=a_0 + a_1 x + \\ldots + a_n x^n$ be a polynomial with all roots real and satisfying $x \\leq -\\delta$ for some $0<\\delta <1$. We show that for any $0 < \\epsilon <1$, the value of $p(1)$ is determined within relative error $\\epsilon$ by the coefficients $a_k$ with $k \\leq {c \\over \\sqrt{\\delta}} \\ln {n \\over \\epsilon \\sqrt{ \\delta}}$ for some absolute constant $c > 0$. Consequently, if $m_k(G)$ is the number of matchings with $k$ edges in a graph $G$, then for any $0 < \\epsilon < 1$, the total number $M(G)=m_0(G)+m_1(G) + \\ldots $ of matchings is determined within relative error $\\epsil","authors_text":"Alexander Barvinok","cross_cats":["cs.DS","math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-19T18:01:23Z","title":"Approximating real-rooted and stable polynomials, with combinatorial applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07404","kind":"arxiv","version":1},"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:b253b4eb3ae4fbd5c9a217ceea71fc55f198a668f2872b0dc96a0b59671ab816","target":"record","created_at":"2026-05-18T00:12:47Z","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":"841fabfe355aa0902eb1663069f2f212afd5175003f80ac5e98dbb9fe3444cad","cross_cats_sorted":["cs.DS","math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-19T18:01:23Z","title_canon_sha256":"d94a0eb1e1e96e3f0dd430e09798eb52c463541ccdb317961dba76c46c9ff75d"},"schema_version":"1.0","source":{"id":"1806.07404","kind":"arxiv","version":1}},"canonical_sha256":"9259bc91e04eb4776cc667884f5233b3ba67426a6a95c59a9aec8b06974e35df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9259bc91e04eb4776cc667884f5233b3ba67426a6a95c59a9aec8b06974e35df","first_computed_at":"2026-05-18T00:12:47.843270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:47.843270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SdST83eAejP2vU5U9bxWRJegre1mLDXBM70ds54Qd5nPpuIJuO6SVZxWF5C6rRYpxYDSoM+yGEVz+3CCKF9rCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:47.843796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b253b4eb3ae4fbd5c9a217ceea71fc55f198a668f2872b0dc96a0b59671ab816","sha256:f990e16ef08d61dd411024686aabb61b6bfe5e5f960db82bf3710cf3f0411f3b"],"state_sha256":"8465352809200b3ace1ca34235d4dc2a15da938421cf2f365eb895c9866b48f2"}