{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:2AIMOYAOGXYAPOA3W5G5V6XIV5","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":"eda54a6e8da7471e86c691bb792e5f0a7b34c9fe74252c5b34098e83c879075e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-14T19:27:31Z","title_canon_sha256":"94c8f59a0740497129b70b871ec1e183732307aa78e4784ebb3c6164792cfb2c"},"schema_version":"1.0","source":{"id":"1612.04778","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04778","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04778v1","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04778","created_at":"2026-05-18T00:54:58Z"},{"alias_kind":"pith_short_12","alias_value":"2AIMOYAOGXYA","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"2AIMOYAOGXYAPOA3","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"2AIMOYAO","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:93cfd33cca250835907f8c4975104463e0d32b2b7fbb4639ede096b77878fd47","target":"graph","created_at":"2026-05-18T00:54:58Z","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":"Let $F$ be a nearly holomorphic vector-valued Siegel modular form of weight $\\rho$ with respect to some congruence subgroup of $\\mathrm{Sp}_{2n}(\\mathbb Q)$. In this note, we prove that the function on $\\mathrm{Sp}_{2n}(\\mathbb R)$ obtained by lifting $F$ has the moderate growth (or \"slowly increasing\") property. This is a consequence of the following bound that we prove: $\\|\\rho(Y^{1/2})F(Z) \\| \\ll \\prod_{i=1}^n (\\mu_i(Y)^{\\lambda_1/2} + \\mu_i(Y)^{-\\lambda_1/2})$ where $ \\lambda_1 \\ge \\ldots \\ge \\lambda_n$ is the highest weight of $\\rho$ and $\\mu_i(Y)$ are the eigenvalues of the matrix $Y$.","authors_text":"Abhishek Saha, Ameya Pitale, Ralf Schmidt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-14T19:27:31Z","title":"A note on the growth of nearly holomorphic vector-valued Siegel modular forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04778","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":"sha256:5660d125a966958974b1d62c55cd6f15d74787b63a97a893244184f155b307ca","target":"record","created_at":"2026-05-18T00:54:58Z","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":"eda54a6e8da7471e86c691bb792e5f0a7b34c9fe74252c5b34098e83c879075e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-14T19:27:31Z","title_canon_sha256":"94c8f59a0740497129b70b871ec1e183732307aa78e4784ebb3c6164792cfb2c"},"schema_version":"1.0","source":{"id":"1612.04778","kind":"arxiv","version":1}},"canonical_sha256":"d010c7600e35f007b81bb74ddafae8af675e172f07c9aec2e0ebc49678f0a577","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d010c7600e35f007b81bb74ddafae8af675e172f07c9aec2e0ebc49678f0a577","first_computed_at":"2026-05-18T00:54:58.638606Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:58.638606Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KL+aFJTcnKuepz4ZLKYA+X1rsEVlE8tUNBbvWBBzpn4n9IC9GVWydvjNWYHAgFKLkyrALP5TX1vO+ww4D60uDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:58.639215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04778","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5660d125a966958974b1d62c55cd6f15d74787b63a97a893244184f155b307ca","sha256:93cfd33cca250835907f8c4975104463e0d32b2b7fbb4639ede096b77878fd47"],"state_sha256":"35b4e23184c29f394fd61d437d21e8276a6ae8c8601c1794cd4af124e5cb2de0"}