{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:NJHDUMFKKQ2ZGBVDN7WCC7IBQL","short_pith_number":"pith:NJHDUMFK","canonical_record":{"source":{"id":"1301.1574","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-08T16:05:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f70e3ba229501c09fdb68aa924e55444021f3efde42fcb496067dc3140caf50e","abstract_canon_sha256":"6cd64f08dafc138aa4df7c6bf7ff09e4670e0a493143f771b6f08452e9fa4ac3"},"schema_version":"1.0"},"canonical_sha256":"6a4e3a30aa54359306a36fec217d0182f02fac4a57f6f9cd0c5d8081754a059d","source":{"kind":"arxiv","id":"1301.1574","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1574","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1574v2","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1574","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"NJHDUMFKKQ2Z","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NJHDUMFKKQ2ZGBVD","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NJHDUMFK","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:NJHDUMFKKQ2ZGBVDN7WCC7IBQL","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1574","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-08T16:05:26Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f70e3ba229501c09fdb68aa924e55444021f3efde42fcb496067dc3140caf50e","abstract_canon_sha256":"6cd64f08dafc138aa4df7c6bf7ff09e4670e0a493143f771b6f08452e9fa4ac3"},"schema_version":"1.0"},"canonical_sha256":"6a4e3a30aa54359306a36fec217d0182f02fac4a57f6f9cd0c5d8081754a059d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:35.473826Z","signature_b64":"NH1hd2RdlhSFdQdgU47crc2H8yroaC6fFlUHr7ihaC9vAi7ZtheW01EdqxYX1M8hJE5dLMiVC8Do0BzVUoI6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a4e3a30aa54359306a36fec217d0182f02fac4a57f6f9cd0c5d8081754a059d","last_reissued_at":"2026-05-18T00:45:35.472202Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:35.472202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1574","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":"2026-05-18T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PMAmoDpxe1BZl2+ukHpCgsH7yLFsYXALwV9gLZYip2uObZUw3TqxljsX5CpQrfGIgEYZOw5T6VHaclVJ/4wEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:19:46.521411Z"},"content_sha256":"88c33cdb8b254645230e21cfb8782db6cf75864504169db45c1b5927ea30206a","schema_version":"1.0","event_id":"sha256:88c33cdb8b254645230e21cfb8782db6cf75864504169db45c1b5927ea30206a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:NJHDUMFKKQ2ZGBVDN7WCC7IBQL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the distribution of eigenvalues of Maass forms on certain moonshine groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.NT","authors_text":"Holger Then, Jay Jorgenson, Lejla Smajlovi\\'c","submitted_at":"2013-01-08T16:05:26Z","abstract_excerpt":"In this paper we study, both analytically and numerically, questions involving the distribution of eigenvalues of Maass forms on the moonshine groups $\\Gamma_0(N)^+$, where $N>1$ is a square-free integer. After we prove that $\\Gamma_0(N)^+$ has one cusp, we compute the constant term of the associated non-holomorphic Eisenstein series. We then derive an \"average\" Weyl's law for the distribution of eigenvalues of Maass forms, from which we prove the \"classical\" Weyl's law as a special case. The groups corresponding to $N=5$ and $N=6$ have the same signature; however, our analysis shows that, asy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1574","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":"2026-05-18T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bfHatXgnZq1wRII6FV6py7nlKbe/5H2zosyHKwHJ1J54PaLaLq+aOex4ZxQ3GVesF34LQJobs6ui/1HNahKiCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:19:46.522134Z"},"content_sha256":"51925bc2720d674dbe4be1f26f462ae64291262fdcafe0fef0bd04c41288b268","schema_version":"1.0","event_id":"sha256:51925bc2720d674dbe4be1f26f462ae64291262fdcafe0fef0bd04c41288b268"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NJHDUMFKKQ2ZGBVDN7WCC7IBQL/bundle.json","state_url":"https://pith.science/pith/NJHDUMFKKQ2ZGBVDN7WCC7IBQL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NJHDUMFKKQ2ZGBVDN7WCC7IBQL/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":"2026-06-09T02:19:46Z","links":{"resolver":"https://pith.science/pith/NJHDUMFKKQ2ZGBVDN7WCC7IBQL","bundle":"https://pith.science/pith/NJHDUMFKKQ2ZGBVDN7WCC7IBQL/bundle.json","state":"https://pith.science/pith/NJHDUMFKKQ2ZGBVDN7WCC7IBQL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NJHDUMFKKQ2ZGBVDN7WCC7IBQL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NJHDUMFKKQ2ZGBVDN7WCC7IBQL","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":"6cd64f08dafc138aa4df7c6bf7ff09e4670e0a493143f771b6f08452e9fa4ac3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-08T16:05:26Z","title_canon_sha256":"f70e3ba229501c09fdb68aa924e55444021f3efde42fcb496067dc3140caf50e"},"schema_version":"1.0","source":{"id":"1301.1574","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1574","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1574v2","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1574","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"NJHDUMFKKQ2Z","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NJHDUMFKKQ2ZGBVD","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NJHDUMFK","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:51925bc2720d674dbe4be1f26f462ae64291262fdcafe0fef0bd04c41288b268","target":"graph","created_at":"2026-05-18T00:45:35Z","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 study, both analytically and numerically, questions involving the distribution of eigenvalues of Maass forms on the moonshine groups $\\Gamma_0(N)^+$, where $N>1$ is a square-free integer. After we prove that $\\Gamma_0(N)^+$ has one cusp, we compute the constant term of the associated non-holomorphic Eisenstein series. We then derive an \"average\" Weyl's law for the distribution of eigenvalues of Maass forms, from which we prove the \"classical\" Weyl's law as a special case. The groups corresponding to $N=5$ and $N=6$ have the same signature; however, our analysis shows that, asy","authors_text":"Holger Then, Jay Jorgenson, Lejla Smajlovi\\'c","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-08T16:05:26Z","title":"On the distribution of eigenvalues of Maass forms on certain moonshine groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1574","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":"sha256:88c33cdb8b254645230e21cfb8782db6cf75864504169db45c1b5927ea30206a","target":"record","created_at":"2026-05-18T00:45:35Z","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":"6cd64f08dafc138aa4df7c6bf7ff09e4670e0a493143f771b6f08452e9fa4ac3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-01-08T16:05:26Z","title_canon_sha256":"f70e3ba229501c09fdb68aa924e55444021f3efde42fcb496067dc3140caf50e"},"schema_version":"1.0","source":{"id":"1301.1574","kind":"arxiv","version":2}},"canonical_sha256":"6a4e3a30aa54359306a36fec217d0182f02fac4a57f6f9cd0c5d8081754a059d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a4e3a30aa54359306a36fec217d0182f02fac4a57f6f9cd0c5d8081754a059d","first_computed_at":"2026-05-18T00:45:35.472202Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:35.472202Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NH1hd2RdlhSFdQdgU47crc2H8yroaC6fFlUHr7ihaC9vAi7ZtheW01EdqxYX1M8hJE5dLMiVC8Do0BzVUoI6CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:35.473826Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1574","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88c33cdb8b254645230e21cfb8782db6cf75864504169db45c1b5927ea30206a","sha256:51925bc2720d674dbe4be1f26f462ae64291262fdcafe0fef0bd04c41288b268"],"state_sha256":"9aade9661d2bec7532ed8a6e570ac5a276fcd0e25bedfd1dc9c281574fefc5c9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HzQ2gtvixkVgNf6x4pDXnDHB0t0cCMDGRWl15Z1nA5SGqJxitUWb/hD7/MQU+UnafBs6S/EjNwO9/dUnbl3QBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:19:46.526134Z","bundle_sha256":"205a6df8901fd29a6128f31fd7bffe660c22f468dc23448a8bc760edf230cb05"}}