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In the twisted cotangent bundle $(T^*M,\\omega_\\varepsilon)$, with $\\omega_\\varepsilon=\\omega_{\\mathrm{can}}+\\varepsilon\\,\\pi^*\\omega_{\\mathrm{KKS}}$ being the canonical plus Kirillov-Kostant-Souriau (KKS) forms, we build two canonical and commuting families of polynomial first integrals: one pulled back from the Lie algebra $\\mathfrak{g}$ of $G$ via the magnetic moment map $P$, and one pulled back 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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2601.01369","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2026-01-04T04:41:28Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1df3661dbc748778a4dcd9c6a5fb18d367a0ea2ee4fd7b3dfefc39df2c6385cb","abstract_canon_sha256":"ba8ec873b520742347a9d1ca0d5bbbb08c1f6367a9868f07cc3bb743c5a5d071"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:32.360469Z","signature_b64":"yanvr9OOEYvJzXKDh8bbko2J1DhCs+4M7hFkm6Xh3ZXIDYXpfOCnwJ2a9XokT4lWeG5WFpVajHhj/x+J5ZuPCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69ac47be5344e6ff594e7953e603b8002a89c4c74f908903df2e836e15c1d850","last_reissued_at":"2026-05-18T03:09:32.359585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:32.359585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poisson Centralisers and Polynomial Superintegrability for Magnetic Geodesic Flows on Reductive Homogeneous Spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Magnetic geodesic flows on reductive homogeneous spaces admit superintegrability through polynomial integrals from the Lie algebra and an invariant slice.","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Guorui Ma, Ian Marquette, Junze Zhang, Kai Jiang, Yao-Zhong Zhang","submitted_at":"2026-01-04T04:41:28Z","abstract_excerpt":"We provide a method for formulating superintegrable magnetic geodesic flows on reductive homogeneous spaces $M=G/A$, with $G$ a compact semisimple Lie group and $A$ a closed subgroup of $G$. In the twisted cotangent bundle $(T^*M,\\omega_\\varepsilon)$, with $\\omega_\\varepsilon=\\omega_{\\mathrm{can}}+\\varepsilon\\,\\pi^*\\omega_{\\mathrm{KKS}}$ being the canonical plus Kirillov-Kostant-Souriau (KKS) forms, we build two canonical and commuting families of polynomial first integrals: one pulled back from the Lie algebra $\\mathfrak{g}$ of $G$ via the magnetic moment map $P$, and one pulled back from a $"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Their common image generates a reduced Poisson algebra obtained from a fiber tensor product, and the natural multiplication map into a Poisson subalgebra of polynomial functions O(T^*M) subset C^infty(T^*M) is Poisson and injective. In a dense regular locus, the resulting projection chain realises a superintegrable system.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The construction assumes the existence of an Ad(A)-invariant affine slice of m congruent to T_{eA}M and that the magnetic moment map P pulls back commuting polynomial integrals from g; this is stated as part of the setup for reductive homogeneous spaces but not derived in the abstract.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Constructs two commuting families of polynomial first integrals for magnetic geodesic flows on reductive homogeneous spaces G/A, yielding a superintegrable system via a reduced Poisson algebra in a dense regular locus.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Magnetic geodesic flows on reductive homogeneous spaces admit superintegrability through polynomial integrals from the Lie algebra and an invariant slice.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"75ae7306df0050970e0096045d828f00d367044c9ca350ad8c73fb291f15d198"},"source":{"id":"2601.01369","kind":"arxiv","version":2},"verdict":{"id":"0652306f-7d56-4523-a652-bff6a6f40a23","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T18:21:02.858470Z","strongest_claim":"Their common image generates a reduced Poisson algebra obtained from a fiber tensor product, and the natural multiplication map into a Poisson subalgebra of polynomial functions O(T^*M) subset C^infty(T^*M) is Poisson and injective. In a dense regular locus, the resulting projection chain realises a superintegrable system.","one_line_summary":"Constructs two commuting families of polynomial first integrals for magnetic geodesic flows on reductive homogeneous spaces G/A, yielding a superintegrable system via a reduced Poisson algebra in a dense regular locus.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The construction assumes the existence of an Ad(A)-invariant affine slice of m congruent to T_{eA}M and that the magnetic moment map P pulls back commuting polynomial integrals from g; this is stated as part of the setup for reductive homogeneous spaces but not derived in the abstract.","pith_extraction_headline":"Magnetic geodesic flows on reductive homogeneous spaces admit superintegrability through polynomial integrals from the Lie algebra and an invariant slice."},"references":{"count":44,"sample":[{"doi":"","year":2013,"title":"W. Miller Jr, S. Post, and P. Winternitz. 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