{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SBOPALI4WGERJKMRCPENEXUCTT","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":"cb19888399acf12aae13affbce08a991e890c2cb6e466ba5d7d789ae46b64624","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-19T17:56:48Z","title_canon_sha256":"e0705806701ac8cc2ffd0b6e2bf7a2c1014623a0a6e7828bbff1ea511e6f24b9"},"schema_version":"1.0","source":{"id":"1310.5256","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.5256","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"arxiv_version","alias_value":"1310.5256v3","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5256","created_at":"2026-05-18T02:57:43Z"},{"alias_kind":"pith_short_12","alias_value":"SBOPALI4WGER","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SBOPALI4WGERJKMR","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SBOPALI4","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:6fae8ba5c87bceb5087c9fba517a2ee2b45ea30e3e95075bded2cc881c606eff","target":"graph","created_at":"2026-05-18T02:57:43Z","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":"We prove a conjecture by Brown, Dilcher and Manna on the asymptotic behavior of sparse binomial-type polynomials arising naturally in a graph theoretical context in connection with the expected number of independent sets of a graph.","authors_text":"Thorsten Neuschel, Wolfgang Gawronski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-19T17:56:48Z","title":"On a conjecture on sparse binomial-type polynomials by Brown, Dilcher and Manna"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5256","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:a71334465bdadd626fbeccfd0e1623018ee72589662b6e7807c379edab646372","target":"record","created_at":"2026-05-18T02:57:43Z","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":"cb19888399acf12aae13affbce08a991e890c2cb6e466ba5d7d789ae46b64624","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-10-19T17:56:48Z","title_canon_sha256":"e0705806701ac8cc2ffd0b6e2bf7a2c1014623a0a6e7828bbff1ea511e6f24b9"},"schema_version":"1.0","source":{"id":"1310.5256","kind":"arxiv","version":3}},"canonical_sha256":"905cf02d1cb18914a99113c8d25e829cdb2437e0ffbca5604aa6c124e8682ea0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"905cf02d1cb18914a99113c8d25e829cdb2437e0ffbca5604aa6c124e8682ea0","first_computed_at":"2026-05-18T02:57:43.429720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:43.429720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eV5vcwpafJZ09nj4Czbu55jV+T72Wixqn14bsDyGGslNbat3Nz1CmfNGnsSVd/hNc2NoG/dKkRtq6IxAgkOjBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:43.430348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.5256","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a71334465bdadd626fbeccfd0e1623018ee72589662b6e7807c379edab646372","sha256:6fae8ba5c87bceb5087c9fba517a2ee2b45ea30e3e95075bded2cc881c606eff"],"state_sha256":"5db9069b2bf5d56e34519226958edd7d5ebbbe236008aed45603e1dbada9ac9b"}