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By contrast to the similar questions for the Teichm\\\"uller space, it is known that for $N\\ge 2$ there does not exist a finite spectrally rigid subset of $F_N$.\n  In this paper we prove that for $N\\ge 3$ if $H\\le Aut(F_N)$ is a subgr"},"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":"1106.0688","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2011-06-03T15:40:49Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"940b039cbb2b93545d769c716dfaccd2402c5ee791cc99dcc2aa2a9bb7398220","abstract_canon_sha256":"11513c296fbc52dd6e21c1f6e9e905d52fb0e306cd1b6e2e6bcbc41a509886d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:54.677526Z","signature_b64":"Ls6GK8qfUATa5EiYUHLOTFIWJs2ZAi2lhXFrUF9vwDyY2yMQfcEwa6XokJBF3osRGe2q14kVmd6buFnyAjJ8Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2931ffdafb93edfdcbae3fb77ccfd9f7738a261e3d957d8eb41f045de9c997bd","last_reissued_at":"2026-05-18T02:32:54.677109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:54.677109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spectral rigidity of automorphic orbits in free groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Armando Martino, Ilya Kapovich, Mathieu Carette, Stefano Francaviglia","submitted_at":"2011-06-03T15:40:49Z","abstract_excerpt":"It is well-known that a point $T\\in cv_N$ in the (unprojectivized) Culler-Vogtmann Outer space $cv_N$ is uniquely determined by its \\emph{translation length function} $||.||_T:F_N\\to\\mathbb R$. 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