{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PXWRRT2WANT3EY7WXJBNUIELWH","short_pith_number":"pith:PXWRRT2W","canonical_record":{"source":{"id":"1103.2076","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-10T16:44:13Z","cross_cats_sorted":[],"title_canon_sha256":"e9e39fcaa91b5207adc9d703fad8e8ab55d0ebbe0f8093c0e673fad9bd4aff35","abstract_canon_sha256":"31607574f3e977745152e6266184d0aac8096c72d51cbd4302581b20b7a5c0d9"},"schema_version":"1.0"},"canonical_sha256":"7ded18cf560367b263f6ba42da208bb1f88a2e5f96589056a57ace884712693e","source":{"kind":"arxiv","id":"1103.2076","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2076","created_at":"2026-05-18T04:27:03Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2076v1","created_at":"2026-05-18T04:27:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2076","created_at":"2026-05-18T04:27:03Z"},{"alias_kind":"pith_short_12","alias_value":"PXWRRT2WANT3","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PXWRRT2WANT3EY7W","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PXWRRT2W","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PXWRRT2WANT3EY7WXJBNUIELWH","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2076","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-10T16:44:13Z","cross_cats_sorted":[],"title_canon_sha256":"e9e39fcaa91b5207adc9d703fad8e8ab55d0ebbe0f8093c0e673fad9bd4aff35","abstract_canon_sha256":"31607574f3e977745152e6266184d0aac8096c72d51cbd4302581b20b7a5c0d9"},"schema_version":"1.0"},"canonical_sha256":"7ded18cf560367b263f6ba42da208bb1f88a2e5f96589056a57ace884712693e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:03.052292Z","signature_b64":"Kitm8yCo2Q3IkuWE3PIjDfqYqHO5Q4VnDrVMRkvSweHSN9WDquNnUSDFIKFfxl8UCxaV999aG+e3ercFHhvyAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ded18cf560367b263f6ba42da208bb1f88a2e5f96589056a57ace884712693e","last_reissued_at":"2026-05-18T04:27:03.051527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:03.051527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2076","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:27:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GkSP2lLJ26Wy+zco8XFDsolB1G0pQRYqVHO4xn0I+1ZCfwl129ydrSgPSGllpuuIJNMyUF6C3hqJ477HUZ4hAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:58:31.087918Z"},"content_sha256":"6a29f60397c83bf279939fa55b9275b25156c44dc25c00734b9d93363708e757","schema_version":"1.0","event_id":"sha256:6a29f60397c83bf279939fa55b9275b25156c44dc25c00734b9d93363708e757"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PXWRRT2WANT3EY7WXJBNUIELWH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Continued fractions for a class of triangle groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kariane Calta, Thomas Schmidt","submitted_at":"2011-03-10T16:44:13Z","abstract_excerpt":"We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval map that is piecewise linear fractional, given in terms of group elements. Using natural extensions, we find an ergodic invariant measure for the interval map. We also study diophantine properties of approximation in terms of the continued fractions; and furthermore show that these continued fractions are appropriate to obtain transcendence results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2076","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":""},"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":"2026-05-18T04:27:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gLHS2x9aSqPRuFJD5DkT/5YFFF7ytFq3l3M4CBLWCBQSxxT0/a7OjI1XV4cFE/VCRMBZdKLXJs583t0ncszyAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:58:31.088639Z"},"content_sha256":"5982393c6b465f0ae8b3c48794c7b33e4fc476f037444bb36a583e7040393395","schema_version":"1.0","event_id":"sha256:5982393c6b465f0ae8b3c48794c7b33e4fc476f037444bb36a583e7040393395"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PXWRRT2WANT3EY7WXJBNUIELWH/bundle.json","state_url":"https://pith.science/pith/PXWRRT2WANT3EY7WXJBNUIELWH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PXWRRT2WANT3EY7WXJBNUIELWH/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":"2026-05-27T12:58:31Z","links":{"resolver":"https://pith.science/pith/PXWRRT2WANT3EY7WXJBNUIELWH","bundle":"https://pith.science/pith/PXWRRT2WANT3EY7WXJBNUIELWH/bundle.json","state":"https://pith.science/pith/PXWRRT2WANT3EY7WXJBNUIELWH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PXWRRT2WANT3EY7WXJBNUIELWH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PXWRRT2WANT3EY7WXJBNUIELWH","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":"31607574f3e977745152e6266184d0aac8096c72d51cbd4302581b20b7a5c0d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-10T16:44:13Z","title_canon_sha256":"e9e39fcaa91b5207adc9d703fad8e8ab55d0ebbe0f8093c0e673fad9bd4aff35"},"schema_version":"1.0","source":{"id":"1103.2076","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2076","created_at":"2026-05-18T04:27:03Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2076v1","created_at":"2026-05-18T04:27:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2076","created_at":"2026-05-18T04:27:03Z"},{"alias_kind":"pith_short_12","alias_value":"PXWRRT2WANT3","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PXWRRT2WANT3EY7W","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PXWRRT2W","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:5982393c6b465f0ae8b3c48794c7b33e4fc476f037444bb36a583e7040393395","target":"graph","created_at":"2026-05-18T04:27:03Z","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":"We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval map that is piecewise linear fractional, given in terms of group elements. Using natural extensions, we find an ergodic invariant measure for the interval map. We also study diophantine properties of approximation in terms of the continued fractions; and furthermore show that these continued fractions are appropriate to obtain transcendence results.","authors_text":"Kariane Calta, Thomas Schmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-10T16:44:13Z","title":"Continued fractions for a class of triangle groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2076","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":"sha256:6a29f60397c83bf279939fa55b9275b25156c44dc25c00734b9d93363708e757","target":"record","created_at":"2026-05-18T04:27:03Z","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":"31607574f3e977745152e6266184d0aac8096c72d51cbd4302581b20b7a5c0d9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-03-10T16:44:13Z","title_canon_sha256":"e9e39fcaa91b5207adc9d703fad8e8ab55d0ebbe0f8093c0e673fad9bd4aff35"},"schema_version":"1.0","source":{"id":"1103.2076","kind":"arxiv","version":1}},"canonical_sha256":"7ded18cf560367b263f6ba42da208bb1f88a2e5f96589056a57ace884712693e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ded18cf560367b263f6ba42da208bb1f88a2e5f96589056a57ace884712693e","first_computed_at":"2026-05-18T04:27:03.051527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:03.051527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kitm8yCo2Q3IkuWE3PIjDfqYqHO5Q4VnDrVMRkvSweHSN9WDquNnUSDFIKFfxl8UCxaV999aG+e3ercFHhvyAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:03.052292Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2076","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a29f60397c83bf279939fa55b9275b25156c44dc25c00734b9d93363708e757","sha256:5982393c6b465f0ae8b3c48794c7b33e4fc476f037444bb36a583e7040393395"],"state_sha256":"fc7b6626157ad986fa158d3c83c412ebb8367fd45424242a5a0422988279c3f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3wiFYplWCn6hF3fp4HHXgRxARJg8tP43jvnsDb6Rq+7US+E7HXYwhaLMsoeeeWoGMm67tbiXZuPC8KDT+RPjDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:58:31.091645Z","bundle_sha256":"3af5928a2198801b104933ee3409a82c84a43d296f18fcce235b44a774f3b8e8"}}