{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:FCSCLTNS74RRUH7Y3FWSEWQP4P","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":"cb969f88c2b068a24fb1d36b23e774b9c5d655d0352ad2a9abaf0d31e128bd22","cross_cats_sorted":["hep-ph","math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-06T19:43:56Z","title_canon_sha256":"2b51a05a1dc32fb49adc4a094b0e567f0736f9b1e82c804171343d60be74c7fa"},"schema_version":"1.0","source":{"id":"2508.04844","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2508.04844","created_at":"2026-07-05T11:55:21Z"},{"alias_kind":"arxiv_version","alias_value":"2508.04844v2","created_at":"2026-07-05T11:55:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.04844","created_at":"2026-07-05T11:55:21Z"},{"alias_kind":"pith_short_12","alias_value":"FCSCLTNS74RR","created_at":"2026-07-05T11:55:21Z"},{"alias_kind":"pith_short_16","alias_value":"FCSCLTNS74RRUH7Y","created_at":"2026-07-05T11:55:21Z"},{"alias_kind":"pith_short_8","alias_value":"FCSCLTNS","created_at":"2026-07-05T11:55:21Z"}],"graph_snapshots":[{"event_id":"sha256:0fc56ad0361f6b2c9a758de1f6e4b41f375ca957097dfd896749e70dc0aa0612","target":"graph","created_at":"2026-07-05T11:55:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2508.04844/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Francis Brown, Tiago J. Fonseca","cross_cats":["hep-ph","math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-06T19:43:56Z","title":"Single-valued periods of meromorphic modular forms and a motivic interpretation of the Gross-Zagier conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.04844","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":"sha256:100d77dd6b8fe22d30fdf1c7160dc8453068dee8aa3f9f9a987d03566c7df89a","target":"record","created_at":"2026-07-05T11:55:21Z","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":"cb969f88c2b068a24fb1d36b23e774b9c5d655d0352ad2a9abaf0d31e128bd22","cross_cats_sorted":["hep-ph","math.AG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-08-06T19:43:56Z","title_canon_sha256":"2b51a05a1dc32fb49adc4a094b0e567f0736f9b1e82c804171343d60be74c7fa"},"schema_version":"1.0","source":{"id":"2508.04844","kind":"arxiv","version":2}},"canonical_sha256":"28a425cdb2ff231a1ff8d96d225a0fe3ff90eceed5519095ff474f4ca9ca7771","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28a425cdb2ff231a1ff8d96d225a0fe3ff90eceed5519095ff474f4ca9ca7771","first_computed_at":"2026-07-05T11:55:21.042946Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:55:21.042946Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ovyWx2HAPipZtH4O86/rQ+FIwojvxtuyZD+tbZQpIIfZMw0C1E/iVAKLMmaJS5y7Y5j2eCvlaWEQUKd/oTYCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:55:21.043370Z","signed_message":"canonical_sha256_bytes"},"source_id":"2508.04844","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:100d77dd6b8fe22d30fdf1c7160dc8453068dee8aa3f9f9a987d03566c7df89a","sha256:0fc56ad0361f6b2c9a758de1f6e4b41f375ca957097dfd896749e70dc0aa0612"],"state_sha256":"82cc0ed45789a1d82c5c200592f88068274fc608e0c17778ac63e4f0bc688d40"}