{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:S72A4SIPG4JRWN2N3UPK5E4VQQ","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":"760366cdf09dc0426ec082d8893ae0546de471e24acf4e0851708aa67f1e0212","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-08-10T07:00:18Z","title_canon_sha256":"4885862e608518125ce15726e06f6181ae1c8518e01d4efb78b81b47d49e463a"},"schema_version":"1.0","source":{"id":"2208.05182","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2208.05182","created_at":"2026-07-05T07:21:09Z"},{"alias_kind":"arxiv_version","alias_value":"2208.05182v2","created_at":"2026-07-05T07:21:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.05182","created_at":"2026-07-05T07:21:09Z"},{"alias_kind":"pith_short_12","alias_value":"S72A4SIPG4JR","created_at":"2026-07-05T07:21:09Z"},{"alias_kind":"pith_short_16","alias_value":"S72A4SIPG4JRWN2N","created_at":"2026-07-05T07:21:09Z"},{"alias_kind":"pith_short_8","alias_value":"S72A4SIP","created_at":"2026-07-05T07:21:09Z"}],"graph_snapshots":[{"event_id":"sha256:7695593fbcc9d43ff2e1ba6d1f76993db4c17961b24fb271d02b3826838ef73e","target":"graph","created_at":"2026-07-05T07:21:09Z","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/2208.05182/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a functional transcendence theorem for the integrals of algebraic forms in families of algebraic varieties. This allows us to prove a geometric version of Andr\\'e's generalization of the Grothendieck period conjecture, which we state using the formalism of Nori motives.\n  More precisely, we prove a version of the Ax--Schanuel conjecture for the comparison between the flat and algebraic coordinates of an arbitrary admissible graded polarizable variation of integral mixed Hodge structures. This can be seen as a generalization of the recent Ax--Schanuel theorems of \\cite{chiu,GaoKlingler","authors_text":"Ben Bakker, Jacob Tsimerman","cross_cats":["math.NT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-08-10T07:00:18Z","title":"Functional Transcendence of Periods and the Geometric Andr\\'e--Grothendieck Period Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.05182","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:b1c557048328ed3ecef66dcc720ba71d1e438bccd0188caa7ee3e6bbab863497","target":"record","created_at":"2026-07-05T07:21:09Z","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":"760366cdf09dc0426ec082d8893ae0546de471e24acf4e0851708aa67f1e0212","cross_cats_sorted":["math.NT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2022-08-10T07:00:18Z","title_canon_sha256":"4885862e608518125ce15726e06f6181ae1c8518e01d4efb78b81b47d49e463a"},"schema_version":"1.0","source":{"id":"2208.05182","kind":"arxiv","version":2}},"canonical_sha256":"97f40e490f37131b374ddd1eae9395841241143a74fe4d7fd9bca4133c969e5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97f40e490f37131b374ddd1eae9395841241143a74fe4d7fd9bca4133c969e5e","first_computed_at":"2026-07-05T07:21:09.910747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:21:09.910747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UdliQ45pcyQHeri4iGIQJglxEYkoyAsnmWVsMHOWRyDiMMCwjItwKjfMmjyhXMPCeMhF58G6KuWY9vDO5qOgCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T07:21:09.911147Z","signed_message":"canonical_sha256_bytes"},"source_id":"2208.05182","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b1c557048328ed3ecef66dcc720ba71d1e438bccd0188caa7ee3e6bbab863497","sha256:7695593fbcc9d43ff2e1ba6d1f76993db4c17961b24fb271d02b3826838ef73e"],"state_sha256":"128476e3abe1797c3579be9a71cd8b059fd21873332688ccafd01d1b09b105c1"}