{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:FCSCLTNS74RRUH7Y3FWSEWQP4P","short_pith_number":"pith:FCSCLTNS","schema_version":"1.0","canonical_sha256":"28a425cdb2ff231a1ff8d96d225a0fe3ff90eceed5519095ff474f4ca9ca7771","source":{"kind":"arxiv","id":"2508.04844","version":2},"attestation_state":"computed","paper":{"title":"Single-valued periods of meromorphic modular forms and a motivic interpretation of the Gross-Zagier conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","math.AG"],"primary_cat":"math.NT","authors_text":"Francis Brown, Tiago J. Fonseca","submitted_at":"2025-08-06T19:43:56Z","abstract_excerpt":"A well-known conjecture of Gross and Zagier states that the values of the higher automorphic Green's function at pairs of points with complex multiplication in the upper half-plane are proportional to the logarithm of an algebraic number. It was recently settled in the case of congruence subgroups of the form $\\Gamma_0(N)$ by analytic methods. In this paper we provide a geometric and motivic interpretation of the general conjecture, and show that it is a consequence of a standard conjecture in the theory of motives. In addition, we define a new class of matrix-valued higher Green's functions f"},"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":"2508.04844","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-06T19:43:56Z","cross_cats_sorted":["hep-ph","math.AG"],"title_canon_sha256":"2b51a05a1dc32fb49adc4a094b0e567f0736f9b1e82c804171343d60be74c7fa","abstract_canon_sha256":"cb969f88c2b068a24fb1d36b23e774b9c5d655d0352ad2a9abaf0d31e128bd22"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:55:21.043370Z","signature_b64":"8ovyWx2HAPipZtH4O86/rQ+FIwojvxtuyZD+tbZQpIIfZMw0C1E/iVAKLMmaJS5y7Y5j2eCvlaWEQUKd/oTYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28a425cdb2ff231a1ff8d96d225a0fe3ff90eceed5519095ff474f4ca9ca7771","last_reissued_at":"2026-07-05T11:55:21.042946Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:55:21.042946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Single-valued periods of meromorphic modular forms and a motivic interpretation of the Gross-Zagier conjecture","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["hep-ph","math.AG"],"primary_cat":"math.NT","authors_text":"Francis Brown, Tiago J. Fonseca","submitted_at":"2025-08-06T19:43:56Z","abstract_excerpt":"A well-known conjecture of Gross and Zagier states that the values of the higher automorphic Green's function at pairs of points with complex multiplication in the upper half-plane are proportional to the logarithm of an algebraic number. It was recently settled in the case of congruence subgroups of the form $\\Gamma_0(N)$ by analytic methods. In this paper we provide a geometric and motivic interpretation of the general conjecture, and show that it is a consequence of a standard conjecture in the theory of motives. In addition, we define a new class of matrix-valued higher Green's functions f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.04844","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/2508.04844/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":"2508.04844","created_at":"2026-07-05T11:55:21.043002+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.04844v2","created_at":"2026-07-05T11:55:21.043002+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.04844","created_at":"2026-07-05T11:55:21.043002+00:00"},{"alias_kind":"pith_short_12","alias_value":"FCSCLTNS74RR","created_at":"2026-07-05T11:55:21.043002+00:00"},{"alias_kind":"pith_short_16","alias_value":"FCSCLTNS74RRUH7Y","created_at":"2026-07-05T11:55:21.043002+00:00"},{"alias_kind":"pith_short_8","alias_value":"FCSCLTNS","created_at":"2026-07-05T11:55:21.043002+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.02382","citing_title":"A note on higher Green's functions","ref_index":2,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FCSCLTNS74RRUH7Y3FWSEWQP4P","json":"https://pith.science/pith/FCSCLTNS74RRUH7Y3FWSEWQP4P.json","graph_json":"https://pith.science/api/pith-number/FCSCLTNS74RRUH7Y3FWSEWQP4P/graph.json","events_json":"https://pith.science/api/pith-number/FCSCLTNS74RRUH7Y3FWSEWQP4P/events.json","paper":"https://pith.science/paper/FCSCLTNS"},"agent_actions":{"view_html":"https://pith.science/pith/FCSCLTNS74RRUH7Y3FWSEWQP4P","download_json":"https://pith.science/pith/FCSCLTNS74RRUH7Y3FWSEWQP4P.json","view_paper":"https://pith.science/paper/FCSCLTNS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.04844&json=true","fetch_graph":"https://pith.science/api/pith-number/FCSCLTNS74RRUH7Y3FWSEWQP4P/graph.json","fetch_events":"https://pith.science/api/pith-number/FCSCLTNS74RRUH7Y3FWSEWQP4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FCSCLTNS74RRUH7Y3FWSEWQP4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FCSCLTNS74RRUH7Y3FWSEWQP4P/action/storage_attestation","attest_author":"https://pith.science/pith/FCSCLTNS74RRUH7Y3FWSEWQP4P/action/author_attestation","sign_citation":"https://pith.science/pith/FCSCLTNS74RRUH7Y3FWSEWQP4P/action/citation_signature","submit_replication":"https://pith.science/pith/FCSCLTNS74RRUH7Y3FWSEWQP4P/action/replication_record"}},"created_at":"2026-07-05T11:55:21.043002+00:00","updated_at":"2026-07-05T11:55:21.043002+00:00"}