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The scattering data (loosely speaking) of a Riemannian manifold with boundary is map $S:U^+\\partial M\\to U^-\\partial M$ from unit vectors $V$ at the boundary that point inward to unit vectors at the boundary that point outwards. The map (where defined) takes $V$ to $\\gamma'_V(T_0)$ where $\\gamma_V$ is the unit speed geodesic determined by $V$ and $T_0$ is the first positive value of $t$ (when it exists) such that $\\gamma_V(t)$ again lies in the boundary. We show th"},"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":"1103.5511","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-28T23:52:45Z","cross_cats_sorted":[],"title_canon_sha256":"a9d1b776a036ed6864b13ffc9f2bc6d05bf20ae6479a2fac68c3ebe3fc93af7d","abstract_canon_sha256":"704be62c9b3e6346bcfcf03e38b7554c0362e9286732c137c097233360c79d2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:36.663815Z","signature_b64":"cSuSL+617RZuPccEXm0MUzDWOZJWTNKOl4xy0tLrmzyC126uz7Npkj2uiXOCEONkp5PQRA1Nfes4vS8LQT/KDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18a76d8031ad5b69266ae9c90bcd9bf7ab9443a71c5c2326db5384e4df5fb5da","last_reissued_at":"2026-05-17T23:53:36.663260Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:36.663260Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Scattering rigidity with trapped geodesics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Christopher B. 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