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In this case we prove that for the generic $q$ the number of geodesics $\\nu(q)$ between $p$ and $q=(x,z)$ satisfies: \\[ C_1\\frac{|z|}{\\|x\\|^2} + R_1 \\leq \\nu(q) \\leq C_2\\frac{|z|}{\\|x\\|^2} + R_2\\] for some constan"},"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":"1405.4294","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-16T20:00:14Z","cross_cats_sorted":["math.MG","math.OC","math.SG"],"title_canon_sha256":"de30dc80405d3d6e4f143519555e12a8cd53240ccb8c7cb909411d80b41fb7bf","abstract_canon_sha256":"733d62352c488880a3361482e7daa4cf6b7507e8c71308fe58334195e5e8866b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:34.031928Z","signature_b64":"acNiR+zjt/nM5y5YjAsZFn8jF1vkgLK7gD5razAjKdsU66kcdGCSB6/sdsS3gG8tM9CA1XMXlgGC1bdcwmAfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28d3e53273dad209f0e35a174b250ca73fb00c672c1217653400280152ca545f","last_reissued_at":"2026-05-18T00:44:34.031521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:34.031521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"How many geodesics join two points on a contact sub-Riemannian manifold?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG","math.OC","math.SG"],"primary_cat":"math.DG","authors_text":"Antonio Lerario, Luca Rizzi","submitted_at":"2014-05-16T20:00:14Z","abstract_excerpt":"We investigate the number of geodesics between two points $p$ and $q$ on a contact sub-Riemannian manifold M. 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