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This implies that for X smooth and proper, X(R)^{+/-} is determined by the maximal 2-nilpotent quotient of Gal(C(X)) with its Gal(R)-action, where X(R)^{+/-} denotes the set of real points equipped with a real tangent direction, showing a 2-nilpotent birational real sect"},"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":"1006.0265","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-06-01T22:58:22Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"67be9f23317e89babf5dbe13aafbd136a4f6a4d2f94e5e7b61d41fcf5a20f4fb","abstract_canon_sha256":"f1bea45433145a7298759160f28e3a583a75b14492780b7060ff07dfc1cf1e8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:16.487283Z","signature_b64":"L47Yh321FX1BqdF9fZ1+TdvD9zzr0yNxei7n2j8CI9I6lA04ZeWKq/OU79mtXcH2u9SAwBGzJ7s/EcYZTiTPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f32463668e69bc61a72b80e49bc89cc787955fb25f5f83862c8b959f0a35c6f7","last_reissued_at":"2026-05-18T03:25:16.486798Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:16.486798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"2-Nilpotent Real Section Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Kirsten Wickelgren","submitted_at":"2010-06-01T22:58:22Z","abstract_excerpt":"We show a 2-nilpotent section conjecture over R: for a geometrically connected curve X over R such that each irreducible component of its normalization has R-points, pi_0(X(R)) is determined by the maximal 2-nilpotent quotient of the fundamental group with its Galois action, as the kernel of an obstruction of Jordan Ellenberg. 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