{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KFJEFXGGU4VAL7JLXCYBFHS7ZI","short_pith_number":"pith:KFJEFXGG","canonical_record":{"source":{"id":"1212.6695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-30T08:23:44Z","cross_cats_sorted":[],"title_canon_sha256":"15e4c74bb773f0de6751c2f6b61b667f896e9208a57d61dbc0f67ae452c516a9","abstract_canon_sha256":"cabe4044f53f425bee211cd6a50bca628f0c01f29d1de7ad09d6afe1b026c3c0"},"schema_version":"1.0"},"canonical_sha256":"515242dcc6a72a05fd2bb8b0129e5fca0f95950f292e3b33c5b0a73cec93c6de","source":{"kind":"arxiv","id":"1212.6695","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6695","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6695v1","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6695","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"pith_short_12","alias_value":"KFJEFXGGU4VA","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KFJEFXGGU4VAL7JL","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KFJEFXGG","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KFJEFXGGU4VAL7JLXCYBFHS7ZI","target":"record","payload":{"canonical_record":{"source":{"id":"1212.6695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-30T08:23:44Z","cross_cats_sorted":[],"title_canon_sha256":"15e4c74bb773f0de6751c2f6b61b667f896e9208a57d61dbc0f67ae452c516a9","abstract_canon_sha256":"cabe4044f53f425bee211cd6a50bca628f0c01f29d1de7ad09d6afe1b026c3c0"},"schema_version":"1.0"},"canonical_sha256":"515242dcc6a72a05fd2bb8b0129e5fca0f95950f292e3b33c5b0a73cec93c6de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:31.168562Z","signature_b64":"D0AlPPsPScMABWrZCwNDqF80cbopTNwaagE0CeSijLjJijNcFxlRX0Pxu0dLeEJ+iLBB3FYxj+v8CAinGjLNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"515242dcc6a72a05fd2bb8b0129e5fca0f95950f292e3b33c5b0a73cec93c6de","last_reissued_at":"2026-05-18T03:37:31.167850Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:31.167850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.6695","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":"2026-05-18T03:37:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m7HnFYSlmGINzbEarqESNsp5V616ib3UUMZTW3DU10FS35GC64IbCt8BmjujCtVFFVB3Hb+s4pWkKXAslmhoAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:42:34.861584Z"},"content_sha256":"a570e05f2b4d7d9035daddcc32dea790be12eb8da199c32cd1e98ac39d9cac05","schema_version":"1.0","event_id":"sha256:a570e05f2b4d7d9035daddcc32dea790be12eb8da199c32cd1e98ac39d9cac05"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KFJEFXGGU4VAL7JLXCYBFHS7ZI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cycle integrals of a sesqui-harmonic Maass form of weight zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Chang Heon Kim, Daeyeol Jeon, Soon-Yi Kang","submitted_at":"2012-12-30T08:23:44Z","abstract_excerpt":"Borcherds-Zagier bases of the spaces of weakly holomorphic modular forms of weights 1/2 and 3/2 share the Fourier coefficients which are traces of singular moduli. Recently, Duke, Imamo\\={g}lu, and T\\'{o}th have constructed a basis of the space of weight 1/2 mock modular forms, each member in which has Zagier's generating series of traces of singular moduli as its shadow. They also showed that Fourier coefficients of their mock modular forms are sums of cycle integrals of the $j$-function which are real quadratic analogues of singular moduli. In this paper, we prove the Fourier coefficients of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6695","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":"2026-05-18T03:37:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QlVH4Bwjrfcbcd/mQQOf63vu7MEOPe1m8ivwy4nU3u5SZ0nxdRpSt2ZwASCoDPIG0mkobaP8YrwNhLWaGllXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:42:34.861936Z"},"content_sha256":"69b51a25c32374117b31de605223568c3dfc5363ccd6cc218f2cc65aeab62a09","schema_version":"1.0","event_id":"sha256:69b51a25c32374117b31de605223568c3dfc5363ccd6cc218f2cc65aeab62a09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KFJEFXGGU4VAL7JLXCYBFHS7ZI/bundle.json","state_url":"https://pith.science/pith/KFJEFXGGU4VAL7JLXCYBFHS7ZI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KFJEFXGGU4VAL7JLXCYBFHS7ZI/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":"2026-06-21T08:42:34Z","links":{"resolver":"https://pith.science/pith/KFJEFXGGU4VAL7JLXCYBFHS7ZI","bundle":"https://pith.science/pith/KFJEFXGGU4VAL7JLXCYBFHS7ZI/bundle.json","state":"https://pith.science/pith/KFJEFXGGU4VAL7JLXCYBFHS7ZI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KFJEFXGGU4VAL7JLXCYBFHS7ZI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KFJEFXGGU4VAL7JLXCYBFHS7ZI","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":"cabe4044f53f425bee211cd6a50bca628f0c01f29d1de7ad09d6afe1b026c3c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-30T08:23:44Z","title_canon_sha256":"15e4c74bb773f0de6751c2f6b61b667f896e9208a57d61dbc0f67ae452c516a9"},"schema_version":"1.0","source":{"id":"1212.6695","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6695","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6695v1","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6695","created_at":"2026-05-18T03:37:31Z"},{"alias_kind":"pith_short_12","alias_value":"KFJEFXGGU4VA","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KFJEFXGGU4VAL7JL","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KFJEFXGG","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:69b51a25c32374117b31de605223568c3dfc5363ccd6cc218f2cc65aeab62a09","target":"graph","created_at":"2026-05-18T03:37:31Z","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":"Borcherds-Zagier bases of the spaces of weakly holomorphic modular forms of weights 1/2 and 3/2 share the Fourier coefficients which are traces of singular moduli. Recently, Duke, Imamo\\={g}lu, and T\\'{o}th have constructed a basis of the space of weight 1/2 mock modular forms, each member in which has Zagier's generating series of traces of singular moduli as its shadow. They also showed that Fourier coefficients of their mock modular forms are sums of cycle integrals of the $j$-function which are real quadratic analogues of singular moduli. In this paper, we prove the Fourier coefficients of","authors_text":"Chang Heon Kim, Daeyeol Jeon, Soon-Yi Kang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-30T08:23:44Z","title":"Cycle integrals of a sesqui-harmonic Maass form of weight zero"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6695","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:a570e05f2b4d7d9035daddcc32dea790be12eb8da199c32cd1e98ac39d9cac05","target":"record","created_at":"2026-05-18T03:37:31Z","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":"cabe4044f53f425bee211cd6a50bca628f0c01f29d1de7ad09d6afe1b026c3c0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-12-30T08:23:44Z","title_canon_sha256":"15e4c74bb773f0de6751c2f6b61b667f896e9208a57d61dbc0f67ae452c516a9"},"schema_version":"1.0","source":{"id":"1212.6695","kind":"arxiv","version":1}},"canonical_sha256":"515242dcc6a72a05fd2bb8b0129e5fca0f95950f292e3b33c5b0a73cec93c6de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"515242dcc6a72a05fd2bb8b0129e5fca0f95950f292e3b33c5b0a73cec93c6de","first_computed_at":"2026-05-18T03:37:31.167850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:31.167850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D0AlPPsPScMABWrZCwNDqF80cbopTNwaagE0CeSijLjJijNcFxlRX0Pxu0dLeEJ+iLBB3FYxj+v8CAinGjLNDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:31.168562Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6695","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a570e05f2b4d7d9035daddcc32dea790be12eb8da199c32cd1e98ac39d9cac05","sha256:69b51a25c32374117b31de605223568c3dfc5363ccd6cc218f2cc65aeab62a09"],"state_sha256":"1bfab12d656fd861451bd77febd223aa33ac92c4b22d804be978373a7e165203"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XHd9EpcqrU3eE5tF5dHD4o91Kckp4JbJg5DP88zdQb8EBJtyiP6xPVz6+bZRZ4yBMq8dOFOTZiSRntiVtzQMDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T08:42:34.863970Z","bundle_sha256":"d7d9043ec9c0de2984511914229b1312f6956b9077ba1786b92a6445871563ce"}}