{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:M5XC66YXGGEYBLHIYPXB6BUSTK","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":"978ce26fe0523e69eb3c31f151aac23532257e39dbe27899b8867c4988d15fe2","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1997-10-21T07:48:59Z","title_canon_sha256":"e53c3cd7718f122a639939b9fe144b9954de491f3a29f1c2a431cc9247554e1f"},"schema_version":"1.0","source":{"id":"q-alg/9710025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9710025","created_at":"2026-05-18T01:05:07Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9710025v1","created_at":"2026-05-18T01:05:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9710025","created_at":"2026-05-18T01:05:07Z"},{"alias_kind":"pith_short_12","alias_value":"M5XC66YXGGEY","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"M5XC66YXGGEYBLHI","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"M5XC66YX","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:5c3cde73cd22682ffdc00b9378f056feb7181e0e0230b7570fe7db333c41fe59","target":"graph","created_at":"2026-05-18T01:05:07Z","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":"Using a summation formula due to Burge, and a combinatorial identity between partition pairs, we obtain an infinite tree of q-polynomial identities for the Virasoro characters \\chi^{p, p'}_{r, s}, dependent on two finite size parameters M and N, in the cases where:\n  (i) p and p' are coprime integers that satisfy 0 < p < p'.\n  (ii) If the pair (p', p) has a continued fraction (c_1, c_2, ... , c_{t-1}, c_t+2), where t >= 1, then the pair (s, r) has a continued fraction (c_1, c_2, ... , c_{u-1}, d), where 1 =< u =< t, and 1 =< d =< c_{u}.\n  The limit M -> infinity, for fixed N, and the limit N -","authors_text":"Australia.), Keith S. M. Lee, Omar Foda, Statistics, Trevor A. Welsh (Department of Mathematics, University of Melbourne","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"q-alg","submitted_at":"1997-10-21T07:48:59Z","title":"A Burge tree of Virasoro-type polynomial identities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9710025","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:dbc643990892cd769ff6bcf2fd0f7f0c41251e435e47bc11aaf3b3e42cbd6e11","target":"record","created_at":"2026-05-18T01:05:07Z","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":"978ce26fe0523e69eb3c31f151aac23532257e39dbe27899b8867c4988d15fe2","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1997-10-21T07:48:59Z","title_canon_sha256":"e53c3cd7718f122a639939b9fe144b9954de491f3a29f1c2a431cc9247554e1f"},"schema_version":"1.0","source":{"id":"q-alg/9710025","kind":"arxiv","version":1}},"canonical_sha256":"676e2f7b17318980ace8c3ee1f06929a8238907e8da703a66fefca232b3458dc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"676e2f7b17318980ace8c3ee1f06929a8238907e8da703a66fefca232b3458dc","first_computed_at":"2026-05-18T01:05:07.220260Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:07.220260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HFxoXYOcGnal5iFFb7/uIUhL+EVWc2vUzi7Zuk5ShwUfcCIP+gRL8VIbbq2/dr1uVEwvKZBq4aRXJ8tnxrFCCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:07.220960Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-alg/9710025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dbc643990892cd769ff6bcf2fd0f7f0c41251e435e47bc11aaf3b3e42cbd6e11","sha256:5c3cde73cd22682ffdc00b9378f056feb7181e0e0230b7570fe7db333c41fe59"],"state_sha256":"0bd4d152a5309bcca92cdb94157bc66a0c6517e0bf918db75521fc5f7e64a23b"}