{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TCC3JQNRHB34T423V4SD7BYYEB","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":"97571b5c717c087099d665fcfaa5cf59429785b0471e80b8b96cf516b458a4e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-28T15:09:01Z","title_canon_sha256":"25f9cf784d9ccc55665b51adee55d5371e8b3efc227509e0f1aa308e21be2190"},"schema_version":"1.0","source":{"id":"1903.12036","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.12036","created_at":"2026-05-17T23:49:58Z"},{"alias_kind":"arxiv_version","alias_value":"1903.12036v1","created_at":"2026-05-17T23:49:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12036","created_at":"2026-05-17T23:49:58Z"},{"alias_kind":"pith_short_12","alias_value":"TCC3JQNRHB34","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"TCC3JQNRHB34T423","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"TCC3JQNR","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:26646c8aad9e87ef7c95c2156d9cefadf35b1c5d32c445d56145fe28237077fe","target":"graph","created_at":"2026-05-17T23:49:58Z","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":"We determine the structure over $\\mathbb{Z}$ of the ring of symmetric Hermitian modular forms with respect to $\\mathbb{Q}(\\sqrt{-1})$ of degree $2$ (with a character), whose Fourier coefficients are integers. Namely, we give a set of generators consisting of $24$ modular forms. As an application of our structure theorem, we give the Sturm bounds of such the modular forms of weight $k$ with $4\\mid k$, in the case $p=2$, $3$. We remark that the bounds for $p\\ge 5$ are already known.","authors_text":"Toshiyuki Kikuta","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-28T15:09:01Z","title":"A ring of symmetric Hermitian modular forms of degree $2$ with integral Fourier coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12036","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":"sha256:339e61c7a25e65e7a8902ecad3dfc45f89c2c7aac5803ee48e9386a5c5f20fee","target":"record","created_at":"2026-05-17T23:49:58Z","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":"97571b5c717c087099d665fcfaa5cf59429785b0471e80b8b96cf516b458a4e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2019-03-28T15:09:01Z","title_canon_sha256":"25f9cf784d9ccc55665b51adee55d5371e8b3efc227509e0f1aa308e21be2190"},"schema_version":"1.0","source":{"id":"1903.12036","kind":"arxiv","version":1}},"canonical_sha256":"9885b4c1b13877c9f35baf243f871820739f0abf4e5b95eec6956f2122ed83c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9885b4c1b13877c9f35baf243f871820739f0abf4e5b95eec6956f2122ed83c5","first_computed_at":"2026-05-17T23:49:58.287851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:58.287851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8vRXhd7El3RpVpP66AcGMZuEGcGVLucpqDkG7AD/i71fBW43rVXm5QNpLpB6niy+fQIjPpS6UjrrP5ZM/ON3Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:58.288439Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.12036","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:339e61c7a25e65e7a8902ecad3dfc45f89c2c7aac5803ee48e9386a5c5f20fee","sha256:26646c8aad9e87ef7c95c2156d9cefadf35b1c5d32c445d56145fe28237077fe"],"state_sha256":"fcb626324403f6cae2bbf349bdf3a9586f79bf5a90fc992b7ee4d2bb2942c981"}