{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:W7MPRSPDPWERISDMVJKHJZMSXG","short_pith_number":"pith:W7MPRSPD","schema_version":"1.0","canonical_sha256":"b7d8f8c9e37d8914486caa5474e592b990776bedf7e17d9cf9c888a874c61e1a","source":{"kind":"arxiv","id":"2507.02522","version":2},"attestation_state":"computed","paper":{"title":"Cusp forms of weight 1/2 and pairs of quadratic forms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andr\\'as Bir\\'o","submitted_at":"2025-07-03T10:38:02Z","abstract_excerpt":"We prove a spectral summation formula for the product of four Fourier coefficients of half-integral weight cusp forms in Kohnen's subspace. The other side of the formula involves certain generalized class numbers of pairs of quadratic forms with integer coefficients."},"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":"2507.02522","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-07-03T10:38:02Z","cross_cats_sorted":[],"title_canon_sha256":"20a64f1a6c117e1b93ad2a258a043e041f0cd71dde898608d78fef4b11e91f82","abstract_canon_sha256":"63ad8d2626d4c11053375a452fa428efd856d97db953aa27ceb050cde07fb8bd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:41:26.268642Z","signature_b64":"5xCNgTWPPmKeORGEu4ByV59zgmg0+e+DhDNp2bfDmrd2HBkNj3dflgEf5w8fCMgNUe0LJRfYAnXpvw3OnaxYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7d8f8c9e37d8914486caa5474e592b990776bedf7e17d9cf9c888a874c61e1a","last_reissued_at":"2026-07-05T11:41:26.268098Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:41:26.268098Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cusp forms of weight 1/2 and pairs of quadratic forms","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Andr\\'as Bir\\'o","submitted_at":"2025-07-03T10:38:02Z","abstract_excerpt":"We prove a spectral summation formula for the product of four Fourier coefficients of half-integral weight cusp forms in Kohnen's subspace. The other side of the formula involves certain generalized class numbers of pairs of quadratic forms with integer coefficients."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.02522","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.02522/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2507.02522","created_at":"2026-07-05T11:41:26.268157+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.02522v2","created_at":"2026-07-05T11:41:26.268157+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.02522","created_at":"2026-07-05T11:41:26.268157+00:00"},{"alias_kind":"pith_short_12","alias_value":"W7MPRSPDPWER","created_at":"2026-07-05T11:41:26.268157+00:00"},{"alias_kind":"pith_short_16","alias_value":"W7MPRSPDPWERISDM","created_at":"2026-07-05T11:41:26.268157+00:00"},{"alias_kind":"pith_short_8","alias_value":"W7MPRSPD","created_at":"2026-07-05T11:41:26.268157+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/W7MPRSPDPWERISDMVJKHJZMSXG","json":"https://pith.science/pith/W7MPRSPDPWERISDMVJKHJZMSXG.json","graph_json":"https://pith.science/api/pith-number/W7MPRSPDPWERISDMVJKHJZMSXG/graph.json","events_json":"https://pith.science/api/pith-number/W7MPRSPDPWERISDMVJKHJZMSXG/events.json","paper":"https://pith.science/paper/W7MPRSPD"},"agent_actions":{"view_html":"https://pith.science/pith/W7MPRSPDPWERISDMVJKHJZMSXG","download_json":"https://pith.science/pith/W7MPRSPDPWERISDMVJKHJZMSXG.json","view_paper":"https://pith.science/paper/W7MPRSPD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.02522&json=true","fetch_graph":"https://pith.science/api/pith-number/W7MPRSPDPWERISDMVJKHJZMSXG/graph.json","fetch_events":"https://pith.science/api/pith-number/W7MPRSPDPWERISDMVJKHJZMSXG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W7MPRSPDPWERISDMVJKHJZMSXG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W7MPRSPDPWERISDMVJKHJZMSXG/action/storage_attestation","attest_author":"https://pith.science/pith/W7MPRSPDPWERISDMVJKHJZMSXG/action/author_attestation","sign_citation":"https://pith.science/pith/W7MPRSPDPWERISDMVJKHJZMSXG/action/citation_signature","submit_replication":"https://pith.science/pith/W7MPRSPDPWERISDMVJKHJZMSXG/action/replication_record"}},"created_at":"2026-07-05T11:41:26.268157+00:00","updated_at":"2026-07-05T11:41:26.268157+00:00"}