{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BQG7I56QPBNH5YPULSNI2WS3BR","short_pith_number":"pith:BQG7I56Q","canonical_record":{"source":{"id":"1303.0528","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-03T16:52:45Z","cross_cats_sorted":["math.DS","math.NT"],"title_canon_sha256":"c9e8b2152588f53e4dbf4925e68755dc66a498f6ee7ab38e95d22c30f7b3622e","abstract_canon_sha256":"bcfa05acb5e91e27a6aa8f6782555687a22fe1341f0376b0981bd0da91ab9956"},"schema_version":"1.0"},"canonical_sha256":"0c0df477d0785a7ee1f45c9a8d5a5b0c5569522deb36854f92d2f9bf7c0a35bd","source":{"kind":"arxiv","id":"1303.0528","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0528","created_at":"2026-05-18T01:23:40Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0528v3","created_at":"2026-05-18T01:23:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0528","created_at":"2026-05-18T01:23:40Z"},{"alias_kind":"pith_short_12","alias_value":"BQG7I56QPBNH","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BQG7I56QPBNH5YPU","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BQG7I56Q","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BQG7I56QPBNH5YPULSNI2WS3BR","target":"record","payload":{"canonical_record":{"source":{"id":"1303.0528","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-03T16:52:45Z","cross_cats_sorted":["math.DS","math.NT"],"title_canon_sha256":"c9e8b2152588f53e4dbf4925e68755dc66a498f6ee7ab38e95d22c30f7b3622e","abstract_canon_sha256":"bcfa05acb5e91e27a6aa8f6782555687a22fe1341f0376b0981bd0da91ab9956"},"schema_version":"1.0"},"canonical_sha256":"0c0df477d0785a7ee1f45c9a8d5a5b0c5569522deb36854f92d2f9bf7c0a35bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:40.428662Z","signature_b64":"VqKIShV6MHudsBf0ZdMao6ePpeknY8gcyPLnsA+3jJQAoQK6m29Zyh6ttywn+bbehApX5ww+8mI75Uf8ZvMTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0c0df477d0785a7ee1f45c9a8d5a5b0c5569522deb36854f92d2f9bf7c0a35bd","last_reissued_at":"2026-05-18T01:23:40.428105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:40.428105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.0528","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f1bjbJO2Cg5H1H6gvutatHJqCj1m3Ns/PYJYGnq4uByUvt8VUNQxddbbi4SQTJCkOYqakfyXCd9/ZiCfYTIqBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T17:33:54.765126Z"},"content_sha256":"c401fd5cbed23477254daca1964efe2cd001d8817ef20799bffc7397b68a3aa6","schema_version":"1.0","event_id":"sha256:c401fd5cbed23477254daca1964efe2cd001d8817ef20799bffc7397b68a3aa6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BQG7I56QPBNH5YPULSNI2WS3BR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Odd and even Maass cusp forms for Hecke triangle groups, and the billiard flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.NT"],"primary_cat":"math.SP","authors_text":"Anke D. Pohl","submitted_at":"2013-03-03T16:52:45Z","abstract_excerpt":"By a transfer operator approach to Maass cusp forms and the Selberg zeta function for cofinite Hecke triangle groups, M. M\\\"oller and the author found a factorization of the Selberg zeta function into a product of Fredholm determinants of transfer-operator-like families: $Z(s) = \\det(1-\\mc L_s^+)\\det(1-\\mc L_s^-)$. In this article we show that the operator families $\\mc L_s^\\pm$ arise as families of transfer operators for the triangle groups underlying the Hecke triangle groups, and that for $s\\in\\C$, $\\Rea s=\\tfrac12$, the operator $\\mc L_s^+$ (resp. $\\mc L_s^-$) has a 1-eigenfunction if and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0528","kind":"arxiv","version":3},"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":"2026-05-18T01:23:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GLDkhL6KHso49PRlcNSKXT9FXXOp5H5H2TfQcWWP9GweUY0anr25jZrvCWOKGdgf9e1UlpZ2hRlQQLCRr4C7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T17:33:54.765483Z"},"content_sha256":"461453ffc24f8f98383deeddb4940cabf4b7b853bc12dc3507a4877fc5b94ff4","schema_version":"1.0","event_id":"sha256:461453ffc24f8f98383deeddb4940cabf4b7b853bc12dc3507a4877fc5b94ff4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BQG7I56QPBNH5YPULSNI2WS3BR/bundle.json","state_url":"https://pith.science/pith/BQG7I56QPBNH5YPULSNI2WS3BR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BQG7I56QPBNH5YPULSNI2WS3BR/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":"2026-06-21T17:33:54Z","links":{"resolver":"https://pith.science/pith/BQG7I56QPBNH5YPULSNI2WS3BR","bundle":"https://pith.science/pith/BQG7I56QPBNH5YPULSNI2WS3BR/bundle.json","state":"https://pith.science/pith/BQG7I56QPBNH5YPULSNI2WS3BR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BQG7I56QPBNH5YPULSNI2WS3BR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BQG7I56QPBNH5YPULSNI2WS3BR","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":"bcfa05acb5e91e27a6aa8f6782555687a22fe1341f0376b0981bd0da91ab9956","cross_cats_sorted":["math.DS","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-03T16:52:45Z","title_canon_sha256":"c9e8b2152588f53e4dbf4925e68755dc66a498f6ee7ab38e95d22c30f7b3622e"},"schema_version":"1.0","source":{"id":"1303.0528","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.0528","created_at":"2026-05-18T01:23:40Z"},{"alias_kind":"arxiv_version","alias_value":"1303.0528v3","created_at":"2026-05-18T01:23:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.0528","created_at":"2026-05-18T01:23:40Z"},{"alias_kind":"pith_short_12","alias_value":"BQG7I56QPBNH","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"BQG7I56QPBNH5YPU","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"BQG7I56Q","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:461453ffc24f8f98383deeddb4940cabf4b7b853bc12dc3507a4877fc5b94ff4","target":"graph","created_at":"2026-05-18T01:23:40Z","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":"By a transfer operator approach to Maass cusp forms and the Selberg zeta function for cofinite Hecke triangle groups, M. M\\\"oller and the author found a factorization of the Selberg zeta function into a product of Fredholm determinants of transfer-operator-like families: $Z(s) = \\det(1-\\mc L_s^+)\\det(1-\\mc L_s^-)$. In this article we show that the operator families $\\mc L_s^\\pm$ arise as families of transfer operators for the triangle groups underlying the Hecke triangle groups, and that for $s\\in\\C$, $\\Rea s=\\tfrac12$, the operator $\\mc L_s^+$ (resp. $\\mc L_s^-$) has a 1-eigenfunction if and ","authors_text":"Anke D. Pohl","cross_cats":["math.DS","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-03T16:52:45Z","title":"Odd and even Maass cusp forms for Hecke triangle groups, and the billiard flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.0528","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:c401fd5cbed23477254daca1964efe2cd001d8817ef20799bffc7397b68a3aa6","target":"record","created_at":"2026-05-18T01:23:40Z","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":"bcfa05acb5e91e27a6aa8f6782555687a22fe1341f0376b0981bd0da91ab9956","cross_cats_sorted":["math.DS","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-03T16:52:45Z","title_canon_sha256":"c9e8b2152588f53e4dbf4925e68755dc66a498f6ee7ab38e95d22c30f7b3622e"},"schema_version":"1.0","source":{"id":"1303.0528","kind":"arxiv","version":3}},"canonical_sha256":"0c0df477d0785a7ee1f45c9a8d5a5b0c5569522deb36854f92d2f9bf7c0a35bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0c0df477d0785a7ee1f45c9a8d5a5b0c5569522deb36854f92d2f9bf7c0a35bd","first_computed_at":"2026-05-18T01:23:40.428105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:40.428105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VqKIShV6MHudsBf0ZdMao6ePpeknY8gcyPLnsA+3jJQAoQK6m29Zyh6ttywn+bbehApX5ww+8mI75Uf8ZvMTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:40.428662Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.0528","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c401fd5cbed23477254daca1964efe2cd001d8817ef20799bffc7397b68a3aa6","sha256:461453ffc24f8f98383deeddb4940cabf4b7b853bc12dc3507a4877fc5b94ff4"],"state_sha256":"bd04bd841dde5d696dc3197961bd8624801ea23cf4da8cbbdfc4340f1f44d08c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9sgNJa/zcXvAJgwN6DmpSjk6ePTgEDIVh5mP18em8e7ywu7DlUDws/glU24dhgnr5d4RW/gxrl7ab/4upf3bBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T17:33:54.767697Z","bundle_sha256":"de2a5a5b405c93c344dcb2474463c12da62551abee923596f3d42b4269c44707"}}