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Applying techniques developed in JB$^*$-triple theory, we prove that $f$ admits an extension to a surjective real linear isometry $T: E\\to B$. Among the consequences, we show that every surjective isometry between the unit spheres of two compact C$^*$-algebras $A$ and $B$ (and in particular when $A=K(H)$ and $B=K(H')$) extends to a surjective real linear isometry from $A$"},"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":"1608.06327","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-08-22T21:58:06Z","cross_cats_sorted":[],"title_canon_sha256":"67e880ee334f56e65803c78a71c27b6b5eb1b33c41c4a26ae3a6c6cf8037043d","abstract_canon_sha256":"653da39988b63ca372a07f5260d0fe08424d1f09fed5d59a12fe7bbe82c42859"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:21:43.615871Z","signature_b64":"/vPBUKALq6slc/SDQG2H00smZjHhoirQZwUMh2oM7FHuK7r9+OVYA7o+GjEEQLNkzGf0el48RHDOY7vGyKXvBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f412e350397d0c2d6ee03739c6430404fc901d6c72b6bde047ddcdaf28d15cc4","last_reissued_at":"2026-05-18T00:21:43.615166Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:21:43.615166Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A solution to Tingley's problem for isometries between the unit spheres of compact C$^*$-algebras and JB$^*$-triples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Antonio M. 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