{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5Z6C2SCWYX5SDAHLPKG54BP563","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":"c0a216dd83a398eb88ab0753170b94f40d49af42ab12f11b9efc27271b5e05f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-15T10:05:07Z","title_canon_sha256":"2baac72248ef1ca473ead51518d7b94ec028214949188e923daf65741923d799"},"schema_version":"1.0","source":{"id":"1809.05690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.05690","created_at":"2026-05-18T00:05:40Z"},{"alias_kind":"arxiv_version","alias_value":"1809.05690v1","created_at":"2026-05-18T00:05:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.05690","created_at":"2026-05-18T00:05:40Z"},{"alias_kind":"pith_short_12","alias_value":"5Z6C2SCWYX5S","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5Z6C2SCWYX5SDAHL","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5Z6C2SCW","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:2aa328e13181fb9d9f1ee0516d299dde97fc59634df9e8ea9fe32b6e38504b2f","target":"graph","created_at":"2026-05-18T00:05:40Z","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":"The purpose of this article is to give a simple and explicit construction of mock modular forms whose shadows are Eisenstein series of arbitrary integral weight, level, and character. As application, we construct forms whose shadows are Hecke's Eisenstein series of weight one associated to imaginary quadratic fields, recovering some results by Kudla, Rapoport and Yang (1999), and Schofer (2009), and forms whose shadows equal $\\Theta^{2k}(z)$ for $k\\in \\{1,2,3,4\\}$, where $\\Theta(z)$ denotes Jacobi's theta function.","authors_text":"Anna-Maria von Pippich, Sebasti\\'an Herrero","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-15T10:05:07Z","title":"Mock modular forms whose shadows are Eisenstein series of integral weight"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.05690","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":"sha256:514c28dddd1f48980b28a8f547931dfe14e812331adf5c2017ab27f34f0878a2","target":"record","created_at":"2026-05-18T00:05:40Z","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":"c0a216dd83a398eb88ab0753170b94f40d49af42ab12f11b9efc27271b5e05f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-09-15T10:05:07Z","title_canon_sha256":"2baac72248ef1ca473ead51518d7b94ec028214949188e923daf65741923d799"},"schema_version":"1.0","source":{"id":"1809.05690","kind":"arxiv","version":1}},"canonical_sha256":"ee7c2d4856c5fb2180eb7a8dde05fdf6d2dc66067e622f2636a4097af61aee5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee7c2d4856c5fb2180eb7a8dde05fdf6d2dc66067e622f2636a4097af61aee5d","first_computed_at":"2026-05-18T00:05:40.255965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:40.255965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"olf4TcKZ0Rb7e5K9BGOCy/5bDBlTjLEUWEXMAixZg+GX5seien0SpWDhAUIW+iCZqsvOIdRjOD/9mgcqOmaxAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:40.256397Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.05690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:514c28dddd1f48980b28a8f547931dfe14e812331adf5c2017ab27f34f0878a2","sha256:2aa328e13181fb9d9f1ee0516d299dde97fc59634df9e8ea9fe32b6e38504b2f"],"state_sha256":"b760c82b2be07d639f857142427679bccc20ae175b1cbcf005f3c995bf5e3dc9"}