{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SSFBQQVD2TTUVVN3X3VDWPJIBM","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":"01e2520c18a575e7cafc2cb5636a4f22486b6ec366c7b897b91072b325264446","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-20T21:08:13Z","title_canon_sha256":"4a5d3450a5eeb7b4eee06ccf2561ea18fad12929a1efed0d3fa1b99659d77150"},"schema_version":"1.0","source":{"id":"1612.06877","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.06877","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1612.06877v1","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.06877","created_at":"2026-05-18T00:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"SSFBQQVD2TTU","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SSFBQQVD2TTUVVN3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SSFBQQVD","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:31bf97e33611579ec41d9ed74f1cdbec2a116d966e589c3c3c6b9597229b30ad","target":"graph","created_at":"2026-05-18T00:54:15Z","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":"These notes discuss an infinite translation surface, introduced by Chamanara. We review his proof that the Veech group is a non-elementary Fuchsian group of the second kind which is generated by two parabolic elements.","authors_text":"Anja Randecker, Frank Herrlich","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-20T21:08:13Z","title":"Notes on the Veech group of the Chamanara surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06877","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":"sha256:5ad61dea982790828982eb58c20cb0f9fc1e974dcd2c7225a12f3fd6a5b63af4","target":"record","created_at":"2026-05-18T00:54:15Z","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":"01e2520c18a575e7cafc2cb5636a4f22486b6ec366c7b897b91072b325264446","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2016-12-20T21:08:13Z","title_canon_sha256":"4a5d3450a5eeb7b4eee06ccf2561ea18fad12929a1efed0d3fa1b99659d77150"},"schema_version":"1.0","source":{"id":"1612.06877","kind":"arxiv","version":1}},"canonical_sha256":"948a1842a3d4e74ad5bbbeea3b3d280b021734d21c8df79c13a11bc4c23aebb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"948a1842a3d4e74ad5bbbeea3b3d280b021734d21c8df79c13a11bc4c23aebb7","first_computed_at":"2026-05-18T00:54:15.138504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:15.138504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UMShFZ3VY6XYJEqvCGFICL1g06zCdi7Xd+SVOC5HFrA/sLBZQOKdnVp+DEDnwcTeJ4zDCjSPBz5t8spgscf+AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:15.138950Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.06877","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5ad61dea982790828982eb58c20cb0f9fc1e974dcd2c7225a12f3fd6a5b63af4","sha256:31bf97e33611579ec41d9ed74f1cdbec2a116d966e589c3c3c6b9597229b30ad"],"state_sha256":"048e2cac6e4c1560dce7de048f6c25bb5b0258c0e9b32355d452a9c9d826afb5"}