{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PNYL7I4MVFCKBPD24WNG5IEWVO","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":"c29e4443f9398c9b26fd3fc71faef77c4ca6cb0b24d051ceb68ecde8b5368ba0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-28T09:50:24Z","title_canon_sha256":"f3bc93610fc4325258d3c9978cfea210d3f338159c8d8c8f2d8c30e050d92c21"},"schema_version":"1.0","source":{"id":"1301.6495","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6495","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6495v3","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6495","created_at":"2026-05-18T00:44:46Z"},{"alias_kind":"pith_short_12","alias_value":"PNYL7I4MVFCK","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PNYL7I4MVFCKBPD2","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PNYL7I4M","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:d33ca34fac48ca365c0d154db31c4a542cb419d7c0b63ed94c0ee28a6c0c478a","target":"graph","created_at":"2026-05-18T00:44:46Z","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 study the action of the Veech group of square-tiled surfaces of genus two on homology. This action defines the homology Veech group which is a subgroup of $\\textrm{SL}_2(\\mathcal{O}_D)$ where $\\mathcal{O}_D$ is a quadratic order of square discriminant. Extending a result of Weitze-Schmith\\\"usen we show that also the homology Veech group is a totally non-congruence subgroup with exceptions stemming only from the prime ideals lying above 2. While Weitze-Schmith\\\"usen's result for Veech groups is asymmetric with respect to the spin structure our use of the homology Veech group yields a complet","authors_text":"Christian Wei{\\ss}","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-28T09:50:24Z","title":"Non-congruence of homology Veech groups in genus two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6495","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":"sha256:55f3de10826d4141b0053f76eceb7bf4a13bb26c43eaed869ee648c5c3f22e5a","target":"record","created_at":"2026-05-18T00:44:46Z","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":"c29e4443f9398c9b26fd3fc71faef77c4ca6cb0b24d051ceb68ecde8b5368ba0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2013-01-28T09:50:24Z","title_canon_sha256":"f3bc93610fc4325258d3c9978cfea210d3f338159c8d8c8f2d8c30e050d92c21"},"schema_version":"1.0","source":{"id":"1301.6495","kind":"arxiv","version":3}},"canonical_sha256":"7b70bfa38ca944a0bc7ae59a6ea096abaeda6e02dd1cb45759e8e72cb49dc87e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b70bfa38ca944a0bc7ae59a6ea096abaeda6e02dd1cb45759e8e72cb49dc87e","first_computed_at":"2026-05-18T00:44:46.430038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:46.430038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DHJMVhxCVuBpJhAvIhvBf3Gftn9t3uglu5O7wqAXYAeBtRakyD8LCz7Ubna82qOXp+KzMj4iRQ59YdGnW6zVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:46.430458Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.6495","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55f3de10826d4141b0053f76eceb7bf4a13bb26c43eaed869ee648c5c3f22e5a","sha256:d33ca34fac48ca365c0d154db31c4a542cb419d7c0b63ed94c0ee28a6c0c478a"],"state_sha256":"e46e6989819bfcf1e11c7d644cef612bb0547d7f3ea8613399bbea472c27c65e"}