{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:HIG7YKQ72B73IDJZ3N4D35P3JS","short_pith_number":"pith:HIG7YKQ7","schema_version":"1.0","canonical_sha256":"3a0dfc2a1fd07fb40d39db783df5fb4ca796a5fc2bfb4bb63279067620eb5e8b","source":{"kind":"arxiv","id":"1210.7841","version":2},"attestation_state":"computed","paper":{"title":"An arithmetic intersection formula for denominators of Igusa class polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bianca Viray, Kristin Lauter","submitted_at":"2012-10-29T21:09:06Z","abstract_excerpt":"In this paper we prove an explicit formula for the arithmetic intersection number (CM(K).G1)_{\\ell} on the Siegel moduli space of abelian surfaces, generalizing the work of Bruinier-Yang and Yang. These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus 2 curves for use in cryptography.\n  Bruinier and Yang conjectured a formula for intersection numbers on an arithmetic Hilbert modular surface, and as a consequence obtained a conjectural formula for the intersection number (CM(K).G1)_{\\ell} under s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1210.7841","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-29T21:09:06Z","cross_cats_sorted":[],"title_canon_sha256":"1fac04eb46ba74c7897147117bfaf78a6718f9c1568f97905315426f127fb190","abstract_canon_sha256":"e6b1bd0232c78a32abb31fc076cf36df7a7d12040e8c5fef28a4303e05802e0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:21.199613Z","signature_b64":"lSaLokqvXBEveCLKPVOPYY7yZ9iKHwIDIxL0KGg046XNee7DH1iwproUV1GQ5DAKuk7ptZgk+G4WfHJb+9bgCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a0dfc2a1fd07fb40d39db783df5fb4ca796a5fc2bfb4bb63279067620eb5e8b","last_reissued_at":"2026-05-18T01:36:21.199122Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:21.199122Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An arithmetic intersection formula for denominators of Igusa class polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Bianca Viray, Kristin Lauter","submitted_at":"2012-10-29T21:09:06Z","abstract_excerpt":"In this paper we prove an explicit formula for the arithmetic intersection number (CM(K).G1)_{\\ell} on the Siegel moduli space of abelian surfaces, generalizing the work of Bruinier-Yang and Yang. These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus 2 curves for use in cryptography.\n  Bruinier and Yang conjectured a formula for intersection numbers on an arithmetic Hilbert modular surface, and as a consequence obtained a conjectural formula for the intersection number (CM(K).G1)_{\\ell} under s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.7841","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1210.7841","created_at":"2026-05-18T01:36:21.199204+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.7841v2","created_at":"2026-05-18T01:36:21.199204+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.7841","created_at":"2026-05-18T01:36:21.199204+00:00"},{"alias_kind":"pith_short_12","alias_value":"HIG7YKQ72B73","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"HIG7YKQ72B73IDJZ","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"HIG7YKQ7","created_at":"2026-05-18T12:27:09.501522+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/HIG7YKQ72B73IDJZ3N4D35P3JS","json":"https://pith.science/pith/HIG7YKQ72B73IDJZ3N4D35P3JS.json","graph_json":"https://pith.science/api/pith-number/HIG7YKQ72B73IDJZ3N4D35P3JS/graph.json","events_json":"https://pith.science/api/pith-number/HIG7YKQ72B73IDJZ3N4D35P3JS/events.json","paper":"https://pith.science/paper/HIG7YKQ7"},"agent_actions":{"view_html":"https://pith.science/pith/HIG7YKQ72B73IDJZ3N4D35P3JS","download_json":"https://pith.science/pith/HIG7YKQ72B73IDJZ3N4D35P3JS.json","view_paper":"https://pith.science/paper/HIG7YKQ7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.7841&json=true","fetch_graph":"https://pith.science/api/pith-number/HIG7YKQ72B73IDJZ3N4D35P3JS/graph.json","fetch_events":"https://pith.science/api/pith-number/HIG7YKQ72B73IDJZ3N4D35P3JS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HIG7YKQ72B73IDJZ3N4D35P3JS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HIG7YKQ72B73IDJZ3N4D35P3JS/action/storage_attestation","attest_author":"https://pith.science/pith/HIG7YKQ72B73IDJZ3N4D35P3JS/action/author_attestation","sign_citation":"https://pith.science/pith/HIG7YKQ72B73IDJZ3N4D35P3JS/action/citation_signature","submit_replication":"https://pith.science/pith/HIG7YKQ72B73IDJZ3N4D35P3JS/action/replication_record"}},"created_at":"2026-05-18T01:36:21.199204+00:00","updated_at":"2026-05-18T01:36:21.199204+00:00"}