{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:K77EL2YURJVPQNMDTPNR5C34CU","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":"08ed93fa86483a5c7ab389d681eafafbae6e46a43f344bc3d0677c2881ddd2f0","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-09T11:10:47Z","title_canon_sha256":"466b863f0b23658b60c639588d7fa22b8802a678ec669e54b17657ef748fd1a4"},"schema_version":"1.0","source":{"id":"1802.03204","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03204","created_at":"2026-05-18T00:23:58Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03204v1","created_at":"2026-05-18T00:23:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03204","created_at":"2026-05-18T00:23:58Z"},{"alias_kind":"pith_short_12","alias_value":"K77EL2YURJVP","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"K77EL2YURJVPQNMD","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"K77EL2YU","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:c0b173119c3a0da34979c5fb08eb570d70c167ddc8e0a0d39fa302c8516cd0d3","target":"graph","created_at":"2026-05-18T00:23:58Z","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"},"paper":{"abstract_excerpt":"Given a point $\\xi$ on a complex abelian variety $A$, its abelian logarithm can be expressed as a linear combination of the periods of $A$ with real coefficients, the Betti coordinates of $\\xi$. When $(A, \\xi)$ varies in an algebraic family, these coordinates define a system of multivalued real-analytic functions. Computing its rank (in the sense of differential geometry) becomes important when one is interested about how often $\\xi$ takes a torsion value (for instance, Manin's theorem of the kernel implies that this coordinate system is constant in a family without fixed part only when $\\xi$ ","authors_text":"Pietro Corvaja, Umberto Zannier, Yves Andr\\'e","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-09T11:10:47Z","title":"The Betti map associated to a section of an abelian scheme (with an appendix by Z. Gao)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03204","kind":"arxiv","version":1},"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":"sha256:50534ccc9e65473ec87693fe2a52e6a4e4f5cf7d7521aed27bd068c9adc6b64b","target":"record","created_at":"2026-05-18T00:23:58Z","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":"08ed93fa86483a5c7ab389d681eafafbae6e46a43f344bc3d0677c2881ddd2f0","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-02-09T11:10:47Z","title_canon_sha256":"466b863f0b23658b60c639588d7fa22b8802a678ec669e54b17657ef748fd1a4"},"schema_version":"1.0","source":{"id":"1802.03204","kind":"arxiv","version":1}},"canonical_sha256":"57fe45eb148a6af835839bdb1e8b7c1515d0ed5755e12fe20bbd12be46bfbc3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"57fe45eb148a6af835839bdb1e8b7c1515d0ed5755e12fe20bbd12be46bfbc3e","first_computed_at":"2026-05-18T00:23:58.311355Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:58.311355Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"81uGRSBGsnflKto0kSwpbTa7jjZItkCh1bMqqBrt4/1F64DHICUiS7YzWJBj4LjoqWwMnMJQ43biUl+RiSN3Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:58.312206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03204","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50534ccc9e65473ec87693fe2a52e6a4e4f5cf7d7521aed27bd068c9adc6b64b","sha256:c0b173119c3a0da34979c5fb08eb570d70c167ddc8e0a0d39fa302c8516cd0d3"],"state_sha256":"7842c840c74db25bc92e5e34b4f3826ba7c1a18870310ba340189d3dbb34dda7"}