{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VWWHELORDJHAXMMOTIWYSP5VNM","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":"74d6e11020bd64e6e50ba5af0c64f42458955d91e01067509e14a9f3ec9ab799","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-26T09:42:47Z","title_canon_sha256":"1b19ead7f4374c0262df1413375a7cbcbb84c79744334399f1384ac3a0876e8f"},"schema_version":"1.0","source":{"id":"1203.5611","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5611","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5611v2","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5611","created_at":"2026-05-18T03:54:05Z"},{"alias_kind":"pith_short_12","alias_value":"VWWHELORDJHA","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VWWHELORDJHAXMMO","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VWWHELOR","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:24c60b51097fad7620cab227e08fc029564321f45a9d948a9f5ba33a58ba1262","target":"graph","created_at":"2026-05-18T03:54:05Z","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 carry out some computations of vector valued Siegel modular forms of degree two, weight (k,2) and level one. Our approach is based on Satoh's description of the module of vector-valued Siegel modular forms of weight (k, 2) and an explicit description of the Hecke action on Fourier expansions. We highlight three experimental results: (1) we identify a rational eigenform in a three dimensional space of cusp forms, (2) we observe that non-cuspidal eigenforms of level one are not always rational and (3) we verify a number of cases of conjectures about congruences between classical modular forms","authors_text":"Alexandru Ghitza, David Sulon, Nathan C. Ryan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-26T09:42:47Z","title":"Computations of vector-valued Siegel modular forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5611","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":"sha256:5a9e92aba61f44b34f06aa5515a7f439a6b772f615d406bed2c5f27b9629b791","target":"record","created_at":"2026-05-18T03:54:05Z","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":"74d6e11020bd64e6e50ba5af0c64f42458955d91e01067509e14a9f3ec9ab799","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-03-26T09:42:47Z","title_canon_sha256":"1b19ead7f4374c0262df1413375a7cbcbb84c79744334399f1384ac3a0876e8f"},"schema_version":"1.0","source":{"id":"1203.5611","kind":"arxiv","version":2}},"canonical_sha256":"adac722dd11a4e0bb18e9a2d893fb56b025e0c12c0e5a239c079df681e0903d2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adac722dd11a4e0bb18e9a2d893fb56b025e0c12c0e5a239c079df681e0903d2","first_computed_at":"2026-05-18T03:54:05.699460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:54:05.699460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8JilR3HHdaCGjuMPJBey/xlFEDvn89vHSuvWmEF6NTqDNAJBU9ienk6lb/v4LrQHEMMtoeuHXE6XKriLAGPHBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:54:05.700047Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.5611","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a9e92aba61f44b34f06aa5515a7f439a6b772f615d406bed2c5f27b9629b791","sha256:24c60b51097fad7620cab227e08fc029564321f45a9d948a9f5ba33a58ba1262"],"state_sha256":"a17a7b7a20d7ccbd5d1b5762f3262027c20ef9b5e5a22901b31e7175fe6f4322"}