{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:E5LFD2ZBVSUZ32WW24LLOAZTJZ","short_pith_number":"pith:E5LFD2ZB","schema_version":"1.0","canonical_sha256":"275651eb21aca99dead6d716b703334e5053fd241fc4cc3828daf9474f990c8e","source":{"kind":"arxiv","id":"2501.09867","version":1},"attestation_state":"computed","paper":{"title":"G-functions, motives, and unlikely intersections -- old and new","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Yves Andr\\'e","submitted_at":"2025-01-16T22:39:14Z","abstract_excerpt":"In this survey, we outline the role of G-functions in arithmetic geometry, notably their link with Picard-Fuchs differential equations and periods. We explain how polynomial relations between special values of G-functions arising from a pencil of algebraic varieties may occur at a parameter where the fiber has more ``motivic\" symmetries; and how Bombieri's principle of global relations can be used to control the height of such parameters (which was also one of the origins of the Andr\\'e-Oort conjecture). At the end, we sketch the recent revival of the G-function method in the context of unlike"},"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":"2501.09867","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-01-16T22:39:14Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"2f9ea77508f85ec5985fed8185aedecbbfcb17844d2efeb9ab649b4d309089bc","abstract_canon_sha256":"c6708cd024a10a6651b6e545a4316be5548bf95dc2219b9a48e650a4e547b4ce"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:02:12.548712Z","signature_b64":"qNGJlyy8oUc0RZ8LHK8Wk9GD301JT8csTIgpSlE6s2jKhnREPQLkba9IqOr1lgm810Eoil74rqe5VY/vhTMgDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"275651eb21aca99dead6d716b703334e5053fd241fc4cc3828daf9474f990c8e","last_reissued_at":"2026-07-05T10:02:12.548289Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:02:12.548289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"G-functions, motives, and unlikely intersections -- old and new","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Yves Andr\\'e","submitted_at":"2025-01-16T22:39:14Z","abstract_excerpt":"In this survey, we outline the role of G-functions in arithmetic geometry, notably their link with Picard-Fuchs differential equations and periods. We explain how polynomial relations between special values of G-functions arising from a pencil of algebraic varieties may occur at a parameter where the fiber has more ``motivic\" symmetries; and how Bombieri's principle of global relations can be used to control the height of such parameters (which was also one of the origins of the Andr\\'e-Oort conjecture). At the end, we sketch the recent revival of the G-function method in the context of unlike"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.09867","kind":"arxiv","version":1},"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/2501.09867/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":"2501.09867","created_at":"2026-07-05T10:02:12.548358+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.09867v1","created_at":"2026-07-05T10:02:12.548358+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.09867","created_at":"2026-07-05T10:02:12.548358+00:00"},{"alias_kind":"pith_short_12","alias_value":"E5LFD2ZBVSUZ","created_at":"2026-07-05T10:02:12.548358+00:00"},{"alias_kind":"pith_short_16","alias_value":"E5LFD2ZBVSUZ32WW","created_at":"2026-07-05T10:02:12.548358+00:00"},{"alias_kind":"pith_short_8","alias_value":"E5LFD2ZB","created_at":"2026-07-05T10:02:12.548358+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.02900","citing_title":"Unlikely intersections in Shimura varieties and beyond: a survey","ref_index":163,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/E5LFD2ZBVSUZ32WW24LLOAZTJZ","json":"https://pith.science/pith/E5LFD2ZBVSUZ32WW24LLOAZTJZ.json","graph_json":"https://pith.science/api/pith-number/E5LFD2ZBVSUZ32WW24LLOAZTJZ/graph.json","events_json":"https://pith.science/api/pith-number/E5LFD2ZBVSUZ32WW24LLOAZTJZ/events.json","paper":"https://pith.science/paper/E5LFD2ZB"},"agent_actions":{"view_html":"https://pith.science/pith/E5LFD2ZBVSUZ32WW24LLOAZTJZ","download_json":"https://pith.science/pith/E5LFD2ZBVSUZ32WW24LLOAZTJZ.json","view_paper":"https://pith.science/paper/E5LFD2ZB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.09867&json=true","fetch_graph":"https://pith.science/api/pith-number/E5LFD2ZBVSUZ32WW24LLOAZTJZ/graph.json","fetch_events":"https://pith.science/api/pith-number/E5LFD2ZBVSUZ32WW24LLOAZTJZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E5LFD2ZBVSUZ32WW24LLOAZTJZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E5LFD2ZBVSUZ32WW24LLOAZTJZ/action/storage_attestation","attest_author":"https://pith.science/pith/E5LFD2ZBVSUZ32WW24LLOAZTJZ/action/author_attestation","sign_citation":"https://pith.science/pith/E5LFD2ZBVSUZ32WW24LLOAZTJZ/action/citation_signature","submit_replication":"https://pith.science/pith/E5LFD2ZBVSUZ32WW24LLOAZTJZ/action/replication_record"}},"created_at":"2026-07-05T10:02:12.548358+00:00","updated_at":"2026-07-05T10:02:12.548358+00:00"}