{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:LFVDBFITYD3TMAY76W66IG4U32","short_pith_number":"pith:LFVDBFIT","canonical_record":{"source":{"id":"1005.1234","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-07T15:39:12Z","cross_cats_sorted":[],"title_canon_sha256":"ea3889bd5302dc5c1be8b8b7cb6ec2ce8bae4e71f40059ac73eb96f7a104a1af","abstract_canon_sha256":"7c48dc017276d919ca4575bbabace5d2182b6c16b1e21f16071bcc06a6a335c4"},"schema_version":"1.0"},"canonical_sha256":"596a309513c0f736031ff5bde41b94de9b8455b9f162f6df153e8b428698ca1e","source":{"kind":"arxiv","id":"1005.1234","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1234","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1234v2","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1234","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"LFVDBFITYD3T","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LFVDBFITYD3TMAY7","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LFVDBFIT","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:LFVDBFITYD3TMAY76W66IG4U32","target":"record","payload":{"canonical_record":{"source":{"id":"1005.1234","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-07T15:39:12Z","cross_cats_sorted":[],"title_canon_sha256":"ea3889bd5302dc5c1be8b8b7cb6ec2ce8bae4e71f40059ac73eb96f7a104a1af","abstract_canon_sha256":"7c48dc017276d919ca4575bbabace5d2182b6c16b1e21f16071bcc06a6a335c4"},"schema_version":"1.0"},"canonical_sha256":"596a309513c0f736031ff5bde41b94de9b8455b9f162f6df153e8b428698ca1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:31:13.083011Z","signature_b64":"MMinXRMEpYkQ2WAlgWwZj9d7IS/IfyOrc/o3uXFUJnGw6lhUJY//vBUpT4aUUMF+Q9OsjvG9zZeOCg1fX0SaCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"596a309513c0f736031ff5bde41b94de9b8455b9f162f6df153e8b428698ca1e","last_reissued_at":"2026-05-18T04:31:13.082445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:31:13.082445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.1234","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fxSWxuogdoCd+wztjJ6jgfg6nIS3hcFkrIV3GcQJxNHBg22q9HLj+SNCmNZTyoOrSbey4wvGZ73QhfjJVv87AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:16:13.181428Z"},"content_sha256":"24546c746b3793e42f4c6038d3cf64f0132c9c39527bd9e42cff4dd4ce78f6ad","schema_version":"1.0","event_id":"sha256:24546c746b3793e42f4c6038d3cf64f0132c9c39527bd9e42cff4dd4ce78f6ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:LFVDBFITYD3TMAY76W66IG4U32","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evaluating Igusa functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Kristin Lauter, Reinier Broker","submitted_at":"2010-05-07T15:39:12Z","abstract_excerpt":"The moduli space of principally polarized abelian surfaces is parametrized by three Igusa functions. In this article we investigate a new way to evaluate these functions by using Siegel Eisenstein series. We explain how to compute the Fourier coefficients of certain Siegel modular forms using classical modular forms of half-integral weight. One of the results in this paper is an explicit algorithm to evaluate the Igusa functions to a prescribed precision."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1234","kind":"arxiv","version":2},"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":"2026-05-18T04:31:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DzYvZa8RRsc5IXTyBrIq4UB/QQ3G2nxZoWwIxv++IYjSXAi9nJNL2iyzrDro6WuBXJQWwfSrgoM+XkUyTlgqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:16:13.181772Z"},"content_sha256":"5a0883d6413944305153ffc3900a3cd93cd788ac7ac83b2bad233baf287eda66","schema_version":"1.0","event_id":"sha256:5a0883d6413944305153ffc3900a3cd93cd788ac7ac83b2bad233baf287eda66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LFVDBFITYD3TMAY76W66IG4U32/bundle.json","state_url":"https://pith.science/pith/LFVDBFITYD3TMAY76W66IG4U32/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LFVDBFITYD3TMAY76W66IG4U32/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":"2026-06-03T02:16:13Z","links":{"resolver":"https://pith.science/pith/LFVDBFITYD3TMAY76W66IG4U32","bundle":"https://pith.science/pith/LFVDBFITYD3TMAY76W66IG4U32/bundle.json","state":"https://pith.science/pith/LFVDBFITYD3TMAY76W66IG4U32/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LFVDBFITYD3TMAY76W66IG4U32/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:LFVDBFITYD3TMAY76W66IG4U32","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":"7c48dc017276d919ca4575bbabace5d2182b6c16b1e21f16071bcc06a6a335c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-07T15:39:12Z","title_canon_sha256":"ea3889bd5302dc5c1be8b8b7cb6ec2ce8bae4e71f40059ac73eb96f7a104a1af"},"schema_version":"1.0","source":{"id":"1005.1234","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1234","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1234v2","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1234","created_at":"2026-05-18T04:31:13Z"},{"alias_kind":"pith_short_12","alias_value":"LFVDBFITYD3T","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"LFVDBFITYD3TMAY7","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"LFVDBFIT","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:5a0883d6413944305153ffc3900a3cd93cd788ac7ac83b2bad233baf287eda66","target":"graph","created_at":"2026-05-18T04:31:13Z","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 moduli space of principally polarized abelian surfaces is parametrized by three Igusa functions. In this article we investigate a new way to evaluate these functions by using Siegel Eisenstein series. We explain how to compute the Fourier coefficients of certain Siegel modular forms using classical modular forms of half-integral weight. One of the results in this paper is an explicit algorithm to evaluate the Igusa functions to a prescribed precision.","authors_text":"Kristin Lauter, Reinier Broker","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-07T15:39:12Z","title":"Evaluating Igusa functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1234","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":"sha256:24546c746b3793e42f4c6038d3cf64f0132c9c39527bd9e42cff4dd4ce78f6ad","target":"record","created_at":"2026-05-18T04:31:13Z","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":"7c48dc017276d919ca4575bbabace5d2182b6c16b1e21f16071bcc06a6a335c4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-05-07T15:39:12Z","title_canon_sha256":"ea3889bd5302dc5c1be8b8b7cb6ec2ce8bae4e71f40059ac73eb96f7a104a1af"},"schema_version":"1.0","source":{"id":"1005.1234","kind":"arxiv","version":2}},"canonical_sha256":"596a309513c0f736031ff5bde41b94de9b8455b9f162f6df153e8b428698ca1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"596a309513c0f736031ff5bde41b94de9b8455b9f162f6df153e8b428698ca1e","first_computed_at":"2026-05-18T04:31:13.082445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:13.082445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MMinXRMEpYkQ2WAlgWwZj9d7IS/IfyOrc/o3uXFUJnGw6lhUJY//vBUpT4aUUMF+Q9OsjvG9zZeOCg1fX0SaCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:13.083011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.1234","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:24546c746b3793e42f4c6038d3cf64f0132c9c39527bd9e42cff4dd4ce78f6ad","sha256:5a0883d6413944305153ffc3900a3cd93cd788ac7ac83b2bad233baf287eda66"],"state_sha256":"5b0c4b733562dcdbf6f86dbf0088a927d564c770c7e183a15787901bb82d251b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6js9qWsI9BBhnZN8kFllr9wZKia9xKq/ycXSnqH8YV1FaTnmrDW/E3gqkqLSmYuUW1Vw2vTqoWq9NNOQRJ4eCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:16:13.183686Z","bundle_sha256":"0d79bb2bd3680207d153e5b76ad148f9af7897f541ebb0bd12514e74226dd480"}}