{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:A7WGKIPXHB6BAJ5EIT5KG5Q27V","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":"a3f2873f28c58cf0bd739f3bf746dc6c1bf0b1583c02ccf6cd983cdde0655420","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-04T03:27:13Z","title_canon_sha256":"ae4d03e752abf954fb3a78ce060f1f7fa701d9a1b0319083a7f6966585b13ece"},"schema_version":"1.0","source":{"id":"0909.0804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.0804","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"arxiv_version","alias_value":"0909.0804v1","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.0804","created_at":"2026-05-18T01:03:12Z"},{"alias_kind":"pith_short_12","alias_value":"A7WGKIPXHB6B","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"A7WGKIPXHB6BAJ5E","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"A7WGKIPX","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:c33748990242d119d5564e5f0c918fee658ca896b2eed7f971181b80af8e691d","target":"graph","created_at":"2026-05-18T01:03:12Z","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 K be a function field with constant field k and let \"infinity\" be a fixed place of K. Let C be the Dedekind domain consisting of all those elements of K which are integral outside \"infinity\". The group G=GL_2(C) is important for a number of reasons. For example, when k is finite, it plays a central role in the theory of Drinfeld modular curves. Many properties follow from the action of G on its associated Bruhat-Tits tree, T. Classical Bass-Serre theory shows how a presentation for G can be derived from the structure of the quotient graph (or fundamental domain) G\\T. The shape of this quot","authors_text":"Andreas Schweizer, A. W. Mason","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-04T03:27:13Z","title":"Nonrational genus zero function fields and the Bruhat-Tits tree"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.0804","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":"sha256:34c307c24cd98aa62ade4783ed3194ee080eb075dc05a8589ef9f65dc1a566fe","target":"record","created_at":"2026-05-18T01:03:12Z","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":"a3f2873f28c58cf0bd739f3bf746dc6c1bf0b1583c02ccf6cd983cdde0655420","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2009-09-04T03:27:13Z","title_canon_sha256":"ae4d03e752abf954fb3a78ce060f1f7fa701d9a1b0319083a7f6966585b13ece"},"schema_version":"1.0","source":{"id":"0909.0804","kind":"arxiv","version":1}},"canonical_sha256":"07ec6521f7387c1027a444faa3761afd44b9b948d524582b24e003721635ca86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07ec6521f7387c1027a444faa3761afd44b9b948d524582b24e003721635ca86","first_computed_at":"2026-05-18T01:03:12.288509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:12.288509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qm6UtvXSTjNRpTzpO4pEyZIGMYcMLeptnEcV0TBvjT51+KxSrmNgAxDb26Rva5OvGLYtC45rCDhDTAYC2bsIBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:12.289161Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.0804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34c307c24cd98aa62ade4783ed3194ee080eb075dc05a8589ef9f65dc1a566fe","sha256:c33748990242d119d5564e5f0c918fee658ca896b2eed7f971181b80af8e691d"],"state_sha256":"ea735e1b3354717ef13f2c50e0d9bf35c233d00cfe9604e70afc1d83a2fb9c0e"}