{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:I3YMJWIPD7I44D3M2GJACHKXNW","short_pith_number":"pith:I3YMJWIP","canonical_record":{"source":{"id":"1404.6402","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-25T11:41:43Z","cross_cats_sorted":[],"title_canon_sha256":"d3929e237fd9d352d7d2e85c3447039a3b57e53f25deb245733d82ac20ec6cd7","abstract_canon_sha256":"f7e7bb6daa4014f6d0d34ba790f0fdd17623a0d1afd644be9c050e9a04184b9f"},"schema_version":"1.0"},"canonical_sha256":"46f0c4d90f1fd1ce0f6cd192011d576dbf2f1b29f9304ee65e62e40c78bb4163","source":{"kind":"arxiv","id":"1404.6402","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6402","created_at":"2026-05-18T02:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6402v2","created_at":"2026-05-18T02:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6402","created_at":"2026-05-18T02:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"I3YMJWIPD7I4","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I3YMJWIPD7I44D3M","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I3YMJWIP","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:I3YMJWIPD7I44D3M2GJACHKXNW","target":"record","payload":{"canonical_record":{"source":{"id":"1404.6402","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-25T11:41:43Z","cross_cats_sorted":[],"title_canon_sha256":"d3929e237fd9d352d7d2e85c3447039a3b57e53f25deb245733d82ac20ec6cd7","abstract_canon_sha256":"f7e7bb6daa4014f6d0d34ba790f0fdd17623a0d1afd644be9c050e9a04184b9f"},"schema_version":"1.0"},"canonical_sha256":"46f0c4d90f1fd1ce0f6cd192011d576dbf2f1b29f9304ee65e62e40c78bb4163","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:58.309374Z","signature_b64":"uka9N9ofBxqOC3DHq1buD4GpLGMmB1MHgaoy3GhbIUhjdR+GbyOfnPZZRtVmQHOdDEwaKwdNGxSnS4ZDNjmGBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46f0c4d90f1fd1ce0f6cd192011d576dbf2f1b29f9304ee65e62e40c78bb4163","last_reissued_at":"2026-05-18T02:51:58.308995Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:58.308995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.6402","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":"2026-05-18T02:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1q+g8V5dAGMPGabl/u12HqbHisAeuM1hm+8o39wQwdxEoEOEosHoudTqsHDGS/sycn+9VJdrdMABGpi0mYqyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:05:32.823804Z"},"content_sha256":"e37152aa6f21c1097adea36fb6b5a8b928adfa9c08c9b2120b955601e896ce98","schema_version":"1.0","event_id":"sha256:e37152aa6f21c1097adea36fb6b5a8b928adfa9c08c9b2120b955601e896ce98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:I3YMJWIPD7I44D3M2GJACHKXNW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weakly holomorphic modular forms for some moonshine groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Martina Lahr, Rainer Schulze-Pillot","submitted_at":"2014-04-25T11:41:43Z","abstract_excerpt":"In an article in the Pure and Applied Mathematics Quarterly in 2008, Duke and Jenkins investigated a certain natural basis of the space of weakly holomorphic modular forms for the full modular group $SL_2({\\bf Z})$. We show here that their results can be generalized to certain moonshine groups, also allowing characters that are real on the underlying subgroup $\\Gamma_0(N)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6402","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":"2026-05-18T02:51:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mLOLW7HwdXj8KiFLv6d88Jy61Z6NH2FVruHZwIDAmivoKw2irjVUS4qz+A1TUDlvPgvkQb9MRiH7ShTpk9yRDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T19:05:32.824448Z"},"content_sha256":"05e6cb8026c7d3b807ceeb871eb461b5f1a69f34ef922a41def9d06792bb93cb","schema_version":"1.0","event_id":"sha256:05e6cb8026c7d3b807ceeb871eb461b5f1a69f34ef922a41def9d06792bb93cb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I3YMJWIPD7I44D3M2GJACHKXNW/bundle.json","state_url":"https://pith.science/pith/I3YMJWIPD7I44D3M2GJACHKXNW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I3YMJWIPD7I44D3M2GJACHKXNW/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":"2026-06-05T19:05:32Z","links":{"resolver":"https://pith.science/pith/I3YMJWIPD7I44D3M2GJACHKXNW","bundle":"https://pith.science/pith/I3YMJWIPD7I44D3M2GJACHKXNW/bundle.json","state":"https://pith.science/pith/I3YMJWIPD7I44D3M2GJACHKXNW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I3YMJWIPD7I44D3M2GJACHKXNW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:I3YMJWIPD7I44D3M2GJACHKXNW","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":"f7e7bb6daa4014f6d0d34ba790f0fdd17623a0d1afd644be9c050e9a04184b9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-25T11:41:43Z","title_canon_sha256":"d3929e237fd9d352d7d2e85c3447039a3b57e53f25deb245733d82ac20ec6cd7"},"schema_version":"1.0","source":{"id":"1404.6402","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.6402","created_at":"2026-05-18T02:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1404.6402v2","created_at":"2026-05-18T02:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.6402","created_at":"2026-05-18T02:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"I3YMJWIPD7I4","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"I3YMJWIPD7I44D3M","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"I3YMJWIP","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:05e6cb8026c7d3b807ceeb871eb461b5f1a69f34ef922a41def9d06792bb93cb","target":"graph","created_at":"2026-05-18T02:51:58Z","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 an article in the Pure and Applied Mathematics Quarterly in 2008, Duke and Jenkins investigated a certain natural basis of the space of weakly holomorphic modular forms for the full modular group $SL_2({\\bf Z})$. We show here that their results can be generalized to certain moonshine groups, also allowing characters that are real on the underlying subgroup $\\Gamma_0(N)$.","authors_text":"Martina Lahr, Rainer Schulze-Pillot","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-25T11:41:43Z","title":"Weakly holomorphic modular forms for some moonshine groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6402","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:e37152aa6f21c1097adea36fb6b5a8b928adfa9c08c9b2120b955601e896ce98","target":"record","created_at":"2026-05-18T02:51:58Z","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":"f7e7bb6daa4014f6d0d34ba790f0fdd17623a0d1afd644be9c050e9a04184b9f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-04-25T11:41:43Z","title_canon_sha256":"d3929e237fd9d352d7d2e85c3447039a3b57e53f25deb245733d82ac20ec6cd7"},"schema_version":"1.0","source":{"id":"1404.6402","kind":"arxiv","version":2}},"canonical_sha256":"46f0c4d90f1fd1ce0f6cd192011d576dbf2f1b29f9304ee65e62e40c78bb4163","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46f0c4d90f1fd1ce0f6cd192011d576dbf2f1b29f9304ee65e62e40c78bb4163","first_computed_at":"2026-05-18T02:51:58.308995Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:58.308995Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uka9N9ofBxqOC3DHq1buD4GpLGMmB1MHgaoy3GhbIUhjdR+GbyOfnPZZRtVmQHOdDEwaKwdNGxSnS4ZDNjmGBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:58.309374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.6402","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e37152aa6f21c1097adea36fb6b5a8b928adfa9c08c9b2120b955601e896ce98","sha256:05e6cb8026c7d3b807ceeb871eb461b5f1a69f34ef922a41def9d06792bb93cb"],"state_sha256":"95b0d364067c64c30e71c4fb6701e8a9b21d14d305632f905bb2021c0d2de18b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"izEJ5KLOKOBYZqzs2S7J18deM0r2baFUmvtdKnBeMt/Jc/0SrQpQocO3nEQ1aJ3/D7kUyAlO24ub97hm1iABDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T19:05:32.827463Z","bundle_sha256":"d03ef0de7fad6d7e61956abc5a30a85049646689692cb56a7bbad75162397f36"}}