{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XFXFBVQWO2GELDU7KT3HVJVLUF","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":"b23049a7a100645008d175b7b55c08c69c0f669aa61a5a777939745119edd859","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-11T17:05:10Z","title_canon_sha256":"eee38944f7bae4e53ca4b46b9bde433ab52e040dcbc9344cf92f45a5caf0ab8e"},"schema_version":"1.0","source":{"id":"1210.3299","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3299","created_at":"2026-05-18T03:35:13Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3299v2","created_at":"2026-05-18T03:35:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3299","created_at":"2026-05-18T03:35:13Z"},{"alias_kind":"pith_short_12","alias_value":"XFXFBVQWO2GE","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XFXFBVQWO2GELDU7","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XFXFBVQW","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:3d43f4ddfd6b1eb398342cc1787b5d060f53bd63f1091ff766b875ce79648448","target":"graph","created_at":"2026-05-18T03:35:13Z","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":"Let $p$ be a prime. Tate and Voloch proved that a point of finite order in the algebraic torus cannot be $p$-adically too close to a fixed subvariety without lying on it. The current work is motivated by the analogy between torsion points on semi-abelian varieties and special or CM points on Shimura varieties. We prove the analog of Tate and Voloch's result in a power of the modular curve Y(1) on replacing torsion points by points corresponding to a product of elliptic curves with complex multiplication and ordinary reduction. Moreover, we show that the assumption on ordinary reduction is nece","authors_text":"Philipp Habegger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-11T17:05:10Z","title":"The Tate-Voloch Conjecture in a Power of a Modular Curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3299","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":"sha256:0a0c96e98554522ce4b551d558f124aa3be67acf4283b7e45af34e823993c716","target":"record","created_at":"2026-05-18T03:35:13Z","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":"b23049a7a100645008d175b7b55c08c69c0f669aa61a5a777939745119edd859","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2012-10-11T17:05:10Z","title_canon_sha256":"eee38944f7bae4e53ca4b46b9bde433ab52e040dcbc9344cf92f45a5caf0ab8e"},"schema_version":"1.0","source":{"id":"1210.3299","kind":"arxiv","version":2}},"canonical_sha256":"b96e50d616768c458e9f54f67aa6aba14a5e775a5dd530a346b4e0e1a16607de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b96e50d616768c458e9f54f67aa6aba14a5e775a5dd530a346b4e0e1a16607de","first_computed_at":"2026-05-18T03:35:13.620655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:13.620655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OMGfDBaDvKG99r5ddOiN0e1Whs4bwnbAKfSODR4OiYutGT5YzqRhZaDc3tudRhD7+c/o9YVBdgiKvOSKUuPlBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:13.621411Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3299","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a0c96e98554522ce4b551d558f124aa3be67acf4283b7e45af34e823993c716","sha256:3d43f4ddfd6b1eb398342cc1787b5d060f53bd63f1091ff766b875ce79648448"],"state_sha256":"bd381c44b7f8b67e71425208e46cfda3b06fdda63c0ce160cfcb28175e1d2046"}