{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:SPSVQQTDO7HAJTCAU527NARQIX","short_pith_number":"pith:SPSVQQTD","canonical_record":{"source":{"id":"0912.2236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-12-11T14:16:46Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"d39300d30b3e22a2a2fa1bca12ac95f6e359a3779499946ec068a36b70bf3083","abstract_canon_sha256":"9afcd8bd5b3bb708b8212e02e70d946702687facc3a07f2fe15d2dce03f62236"},"schema_version":"1.0"},"canonical_sha256":"93e558426377ce04cc40a775f6823045e42034e0f741169abe2f4420e8560b15","source":{"kind":"arxiv","id":"0912.2236","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2236","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2236v2","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2236","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"pith_short_12","alias_value":"SPSVQQTDO7HA","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SPSVQQTDO7HAJTCA","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SPSVQQTD","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:SPSVQQTDO7HAJTCAU527NARQIX","target":"record","payload":{"canonical_record":{"source":{"id":"0912.2236","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-12-11T14:16:46Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"d39300d30b3e22a2a2fa1bca12ac95f6e359a3779499946ec068a36b70bf3083","abstract_canon_sha256":"9afcd8bd5b3bb708b8212e02e70d946702687facc3a07f2fe15d2dce03f62236"},"schema_version":"1.0"},"canonical_sha256":"93e558426377ce04cc40a775f6823045e42034e0f741169abe2f4420e8560b15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:03.000608Z","signature_b64":"XMjT4DiwHNbemXzZ/UOLlExWqWq05T9o5L51s4o4B8/5IN/NvgaN+quBoZXawl30P4HJhHyNvE1fBGeXEUltBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93e558426377ce04cc40a775f6823045e42034e0f741169abe2f4420e8560b15","last_reissued_at":"2026-05-18T03:44:03.000035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:03.000035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0912.2236","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:44:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"olJSEmLtjFcx0ftFf8RGk278lJOuaTae6z8+/ncdMMOChjV0gEYWBfwn6Bq5o9R6fOcwbCIfDlh67FSwC5CLCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:12:18.572954Z"},"content_sha256":"6ca28712cde37897363b71ab42a1eb1bce225d2da2b0e822c2961c6c6c1e2d37","schema_version":"1.0","event_id":"sha256:6ca28712cde37897363b71ab42a1eb1bce225d2da2b0e822c2961c6c6c1e2d37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:SPSVQQTDO7HAJTCAU527NARQIX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The transfer operator for the Hecke triangle groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Dieter Mayer, Fredrik Str\\\"omberg, Tobias M\\\"uhlenbruch","submitted_at":"2009-12-11T14:16:46Z","abstract_excerpt":"In this paper we extend the transfer operator approach to Selberg's zeta function for cofinite Fuchsian groups to the Hecke triangle groups G_q, q=3,4,..., which are non-arithmetic for q \\not= 3,4,6. For this we make use of a Poincare map for the geodesic flow on the corresponding Hecke surfaces which has been constructed in arXiv:0801.3951 and which is closely related to the natural extension of the generating map for the so called Hurwitz-Nakada continued fractions. We derive simple functional equations for the eigenfunctions of the transfer operator which for eigenvalues rho =1 are expected"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2236","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:44:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OhCkDXJ5vySQGyzbSvkZXvgDoCa3u8bSY1AeZ0U23MBh96o5uxZ+e4+WLDiYigotkv537cXNJ4TOStywDjr6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T06:12:18.573546Z"},"content_sha256":"42e37bb78b228513d0d7d55ff1a937b190e47c6f87a23f49a7b006ac41051ac8","schema_version":"1.0","event_id":"sha256:42e37bb78b228513d0d7d55ff1a937b190e47c6f87a23f49a7b006ac41051ac8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SPSVQQTDO7HAJTCAU527NARQIX/bundle.json","state_url":"https://pith.science/pith/SPSVQQTDO7HAJTCAU527NARQIX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SPSVQQTDO7HAJTCAU527NARQIX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T06:12:18Z","links":{"resolver":"https://pith.science/pith/SPSVQQTDO7HAJTCAU527NARQIX","bundle":"https://pith.science/pith/SPSVQQTDO7HAJTCAU527NARQIX/bundle.json","state":"https://pith.science/pith/SPSVQQTDO7HAJTCAU527NARQIX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SPSVQQTDO7HAJTCAU527NARQIX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:SPSVQQTDO7HAJTCAU527NARQIX","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":"9afcd8bd5b3bb708b8212e02e70d946702687facc3a07f2fe15d2dce03f62236","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-12-11T14:16:46Z","title_canon_sha256":"d39300d30b3e22a2a2fa1bca12ac95f6e359a3779499946ec068a36b70bf3083"},"schema_version":"1.0","source":{"id":"0912.2236","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0912.2236","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"arxiv_version","alias_value":"0912.2236v2","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0912.2236","created_at":"2026-05-18T03:44:03Z"},{"alias_kind":"pith_short_12","alias_value":"SPSVQQTDO7HA","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"SPSVQQTDO7HAJTCA","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"SPSVQQTD","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:42e37bb78b228513d0d7d55ff1a937b190e47c6f87a23f49a7b006ac41051ac8","target":"graph","created_at":"2026-05-18T03:44:03Z","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":"In this paper we extend the transfer operator approach to Selberg's zeta function for cofinite Fuchsian groups to the Hecke triangle groups G_q, q=3,4,..., which are non-arithmetic for q \\not= 3,4,6. For this we make use of a Poincare map for the geodesic flow on the corresponding Hecke surfaces which has been constructed in arXiv:0801.3951 and which is closely related to the natural extension of the generating map for the so called Hurwitz-Nakada continued fractions. We derive simple functional equations for the eigenfunctions of the transfer operator which for eigenvalues rho =1 are expected","authors_text":"Dieter Mayer, Fredrik Str\\\"omberg, Tobias M\\\"uhlenbruch","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-12-11T14:16:46Z","title":"The transfer operator for the Hecke triangle groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.2236","kind":"arxiv","version":2},"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":"sha256:6ca28712cde37897363b71ab42a1eb1bce225d2da2b0e822c2961c6c6c1e2d37","target":"record","created_at":"2026-05-18T03:44:03Z","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":"9afcd8bd5b3bb708b8212e02e70d946702687facc3a07f2fe15d2dce03f62236","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-12-11T14:16:46Z","title_canon_sha256":"d39300d30b3e22a2a2fa1bca12ac95f6e359a3779499946ec068a36b70bf3083"},"schema_version":"1.0","source":{"id":"0912.2236","kind":"arxiv","version":2}},"canonical_sha256":"93e558426377ce04cc40a775f6823045e42034e0f741169abe2f4420e8560b15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93e558426377ce04cc40a775f6823045e42034e0f741169abe2f4420e8560b15","first_computed_at":"2026-05-18T03:44:03.000035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:44:03.000035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XMjT4DiwHNbemXzZ/UOLlExWqWq05T9o5L51s4o4B8/5IN/NvgaN+quBoZXawl30P4HJhHyNvE1fBGeXEUltBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:44:03.000608Z","signed_message":"canonical_sha256_bytes"},"source_id":"0912.2236","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ca28712cde37897363b71ab42a1eb1bce225d2da2b0e822c2961c6c6c1e2d37","sha256:42e37bb78b228513d0d7d55ff1a937b190e47c6f87a23f49a7b006ac41051ac8"],"state_sha256":"18f117d486099808a5f061b5246c9ed96e087fc11cc130880fdf4d3f1cfae1da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WGA2qK7j4qSnkQpG6tkcq50fIYUGkmwF1swMTQKGWrbddx/kJkcx8wzC2X6BqI73k+bx40Lnck2uo+eibAkOAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T06:12:18.576558Z","bundle_sha256":"a477c64113830c0e84b8239bb2cd7a3aef7bcc481399d8467827e8ce4b289f39"}}