{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.topic/1","content_sha256":"257ad8efdb3e3ca7d4f6c66d2a512c11008d7905fd1f0acba17c677e9adcfe47","created":"2026-10-03T07:17:52Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":[],"salt":"ad980b3f728fc37a909c7647492c421a65d834d7cbaa83c63d82324e5e1aa366","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"topic"},"content":{"external_id":"mathph.kam-stability","field":"mathph","n":"1","review_cite":"V. Kaloshin, K. Zhang, Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom, Annals of Mathematics Studies 208, Princeton University Press, 2020","review_link":"https://doi.org/10.23943/princeton/9780691202525.001.0001","review_verified":"true","summary":"Nearly regular motion such as planetary orbits is kept in order by invariant tori found by Kolmogorov, Arnold and Moser (KAM theory), but with three or more degrees of freedom orbits can slowly drift through the gaps between tori (Arnold diffusion). How general this drift is, and how fast it acts, is not settled.","title":"KAM theory, Arnold diffusion and long-term stability","topic_ref":null,"why":"It decides the long-term predictability of nearly integrable systems, from the solar system to particle accelerators and magnetic confinement."},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"cd1c7cff821fba931816a6faeec94ad21e6f069bd36505c710e41ce43b61e40a","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"fd99ba864e5500c3d85ced418ee4732899afd133d1448ea19c36032fe1f73505","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"UKTb0JbjslFkGb46nub-hZ6F_HdIbBe34Xkl0gc-HQZUSdfy5O9tQ14r0eGbPgk-SR9LJXv3cdLJBxfqvPouAA"},"schema":"pubphys.envelope/1"},"record_hash":"cd1c7cff821fba931816a6faeec94ad21e6f069bd36505c710e41ce43b61e40a","leaf_index":261}