{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BSMODBPDGZ56B7IW3FDQY4MWCJ","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":"7f9a52796398a8244fe9ed03e868b0a6d09cf8bd5110c13014c10876aec50130","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-21T23:43:10Z","title_canon_sha256":"fccc395db9fad400205e2b8e58047afa37c23acc0a89a530dbf3961469302b58"},"schema_version":"1.0","source":{"id":"1503.06367","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.06367","created_at":"2026-05-18T01:02:57Z"},{"alias_kind":"arxiv_version","alias_value":"1503.06367v2","created_at":"2026-05-18T01:02:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06367","created_at":"2026-05-18T01:02:57Z"},{"alias_kind":"pith_short_12","alias_value":"BSMODBPDGZ56","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BSMODBPDGZ56B7IW","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BSMODBPD","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:09ec76ed28102a6c1faf1b91ea88f50aa2aaf8c1292904bd4504da2c53d2482e","target":"graph","created_at":"2026-05-18T01:02:57Z","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 look at the asymptotic behavior of the coefficients of the $q$-binomial coefficients (or Gaussian polynomials) $\\binom{a+k}{k}_q$, when $k$ is fixed. We give a number of results in this direction, some of which involve Eulerian polynomials and their generalizations.","authors_text":"Fabrizio Zanello, Richard P. Stanley","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-21T23:43:10Z","title":"Some asymptotic results on q-binomial coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06367","kind":"arxiv","version":2},"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":"sha256:61ed40652a54b306c793cc09455faa9c0e5c6fc2aa3b90122b52846cabca3105","target":"record","created_at":"2026-05-18T01:02:57Z","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":"7f9a52796398a8244fe9ed03e868b0a6d09cf8bd5110c13014c10876aec50130","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-03-21T23:43:10Z","title_canon_sha256":"fccc395db9fad400205e2b8e58047afa37c23acc0a89a530dbf3961469302b58"},"schema_version":"1.0","source":{"id":"1503.06367","kind":"arxiv","version":2}},"canonical_sha256":"0c98e185e3367be0fd16d9470c7196127d8a65285f0d19eb6d028b2bce0ff45b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c98e185e3367be0fd16d9470c7196127d8a65285f0d19eb6d028b2bce0ff45b","first_computed_at":"2026-05-18T01:02:57.058680Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:57.058680Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qv8WqPcNiONWeBrOjimbbauB+jEMNv/9ae9gMgf3zvGOGDIBBzD9qBofrnz1u3mL+0L7X7jf2N3mFRvTThOIDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:57.059242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.06367","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61ed40652a54b306c793cc09455faa9c0e5c6fc2aa3b90122b52846cabca3105","sha256:09ec76ed28102a6c1faf1b91ea88f50aa2aaf8c1292904bd4504da2c53d2482e"],"state_sha256":"4bd51bdf6b1b506692cd245db6de7f31526f3a7c3eccff9f06da0abeaef940ef"}