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In particular, we show that the restriction map $(C^{\\infty}(T^*M))^G \\rightarrow (C^{\\infty}(T^* \\Sigma))^{\\Pi}$ is a surjective homomorphism of Poisson algebras. As a corollary, the singular symplectic reductions $T^*M // G $ and $T^* \\Sigma // \\Pi$ are isomorphic as stratif"},"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":"1701.07985","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-01-27T09:43:45Z","cross_cats_sorted":[],"title_canon_sha256":"b547e4a5b35907464965cee5d2076aa0f0085228bd2d67fbd74f5bfa5b3ae0e0","abstract_canon_sha256":"b27a4af2bbbd753c2fbd35c0186461022f195e72b8098d031e4ea22582be6024"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:59.234614Z","signature_b64":"E+V+w2idsep4XjwVL/bLMZu4v8y/ewk8vEkiY6aPmmr0bC0YnyS6aV/GtBPlu3NEK9P918/zF/ZX1ZkzM5VxDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffe72cbf7502a4b46eb6ce05284fc9eb5682c49c33445c850f06ff2080bda97c","last_reissued_at":"2026-05-18T00:51:59.234140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:59.234140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symplectic aspects of polar actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jianyu Ou, Xiaoyang Chen","submitted_at":"2017-01-27T09:43:45Z","abstract_excerpt":"An isometric compact group action $G \\times (M,g) \\rightarrow (M,g)$ is called polar if there exists a closed embedded submanifold $\\Sigma \\subseteq M$ which meets all orbits orthogonally. 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