{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:TXH7UK7IMBHGT6UASXHN4MCVVU","short_pith_number":"pith:TXH7UK7I","schema_version":"1.0","canonical_sha256":"9dcffa2be8604e69fa8095cede3055ad1c97e1f9aa03dba318cee9de6a399771","source":{"kind":"arxiv","id":"2605.30064","version":1},"attestation_state":"computed","paper":{"title":"Hecke Triangle Groups and Special Hyperbolic Elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Karl Winsor","submitted_at":"2026-05-28T15:14:07Z","abstract_excerpt":"We study the action of the Hecke triangle groups $G_q$ on $\\lambda_q \\mathbb{Q}(\\lambda_q^2) \\cup \\{\\infty\\}$ with $\\lambda_q = 2 \\cos (\\pi / q)$. When $q = 18$, we show the existence of infinitely many distinct orbits of fixed points of special hyperbolic elements of $G_q$. We also find new orbits for several other values of $q$. These results provide new examples of special affine pseudo-Anosov homeomorphisms on the unfoldings of regular $q$-gons. In particular, on the unfolding of the regular $18$-gon, there are infinitely many distinct Veech group orbits of directions invariant under a spe"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2605.30064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-05-28T15:14:07Z","cross_cats_sorted":[],"title_canon_sha256":"3f36108ddb565d3d8f28e70d50ecceeeb224c825235bdaa97afb9f95f200e558","abstract_canon_sha256":"b84d379affa539a01f7350258f979ec7c950d776c60939c1765854f9e81af946"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-29T02:06:08.950010Z","signature_b64":"uB6JfUEtkFju7S6Y0MMGP0wTZUiGU52SH84LhNCz9fCpa5YyWXr7FdHHNThJw4Fk2Ca8aXObAT/T0V0HSue8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9dcffa2be8604e69fa8095cede3055ad1c97e1f9aa03dba318cee9de6a399771","last_reissued_at":"2026-05-29T02:06:08.949609Z","signature_status":"signed_v1","first_computed_at":"2026-05-29T02:06:08.949609Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hecke Triangle Groups and Special Hyperbolic Elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Karl Winsor","submitted_at":"2026-05-28T15:14:07Z","abstract_excerpt":"We study the action of the Hecke triangle groups $G_q$ on $\\lambda_q \\mathbb{Q}(\\lambda_q^2) \\cup \\{\\infty\\}$ with $\\lambda_q = 2 \\cos (\\pi / q)$. When $q = 18$, we show the existence of infinitely many distinct orbits of fixed points of special hyperbolic elements of $G_q$. We also find new orbits for several other values of $q$. These results provide new examples of special affine pseudo-Anosov homeomorphisms on the unfoldings of regular $q$-gons. In particular, on the unfolding of the regular $18$-gon, there are infinitely many distinct Veech group orbits of directions invariant under a spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.30064","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.30064/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2605.30064","created_at":"2026-05-29T02:06:08.949668+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.30064v1","created_at":"2026-05-29T02:06:08.949668+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.30064","created_at":"2026-05-29T02:06:08.949668+00:00"},{"alias_kind":"pith_short_12","alias_value":"TXH7UK7IMBHG","created_at":"2026-05-29T02:06:08.949668+00:00"},{"alias_kind":"pith_short_16","alias_value":"TXH7UK7IMBHGT6UA","created_at":"2026-05-29T02:06:08.949668+00:00"},{"alias_kind":"pith_short_8","alias_value":"TXH7UK7I","created_at":"2026-05-29T02:06:08.949668+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TXH7UK7IMBHGT6UASXHN4MCVVU","json":"https://pith.science/pith/TXH7UK7IMBHGT6UASXHN4MCVVU.json","graph_json":"https://pith.science/api/pith-number/TXH7UK7IMBHGT6UASXHN4MCVVU/graph.json","events_json":"https://pith.science/api/pith-number/TXH7UK7IMBHGT6UASXHN4MCVVU/events.json","paper":"https://pith.science/paper/TXH7UK7I"},"agent_actions":{"view_html":"https://pith.science/pith/TXH7UK7IMBHGT6UASXHN4MCVVU","download_json":"https://pith.science/pith/TXH7UK7IMBHGT6UASXHN4MCVVU.json","view_paper":"https://pith.science/paper/TXH7UK7I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.30064&json=true","fetch_graph":"https://pith.science/api/pith-number/TXH7UK7IMBHGT6UASXHN4MCVVU/graph.json","fetch_events":"https://pith.science/api/pith-number/TXH7UK7IMBHGT6UASXHN4MCVVU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TXH7UK7IMBHGT6UASXHN4MCVVU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TXH7UK7IMBHGT6UASXHN4MCVVU/action/storage_attestation","attest_author":"https://pith.science/pith/TXH7UK7IMBHGT6UASXHN4MCVVU/action/author_attestation","sign_citation":"https://pith.science/pith/TXH7UK7IMBHGT6UASXHN4MCVVU/action/citation_signature","submit_replication":"https://pith.science/pith/TXH7UK7IMBHGT6UASXHN4MCVVU/action/replication_record"}},"created_at":"2026-05-29T02:06:08.949668+00:00","updated_at":"2026-05-29T02:06:08.949668+00:00"}