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The key point here is that $\\frac{p-3}{p-1}$ is much smaller than the critical in"},"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":"1508.00228","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-08-02T13:05:56Z","cross_cats_sorted":[],"title_canon_sha256":"c2a561e3322abbad937cc9a61d13a46f766b5e234bd2a0cc5f3f85edaeb96804","abstract_canon_sha256":"02b86796057c404a6bb833486395c9c2129ff0a3d9fb7f657a2d1fa59746e900"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:38.031623Z","signature_b64":"OqpZ0s0hM2z7g/9YI3pNU8SSJ+vTYYabynZR6EPAFK6ILoipKtF82uN+M8n3fLDnqKE8fKIH0+Gm5lIAk+hsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e510d6115c15999784405610d54d13827ee3de526dcbf1b3546f4c0911dd5431","last_reissued_at":"2026-05-18T01:29:38.031076Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:38.031076Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Probabilistic well-posedness for supercritical wave equation on $\\mathbb{T}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bo Xia, Chenmin Sun","submitted_at":"2015-08-02T13:05:56Z","abstract_excerpt":"In this article, we follow the strategies, listed in \\cite{Burq2011} and \\cite{OhPo}, in dealing with supercritical cubic and quintic wave equations, we obtain that, the equation\n  \\begin{equation*}\n  \\left\\{\n  \\begin{split}\n  &(\\partial^2_t-\\Delta)u+|u|^{p-1}u=0,\\ \\ 3<p<5\n  &\\big(u,\\partial_tu\\big)|_{t=0}=(u_0,u_1)\\in H^{s}\\times H^{s-1}=:\\mathcal{H}^s,\n  \\end{split}\n  \\right.\n  \\end{equation*} is almost surely global well-posed in the sense of Burq and Tzvetkov\\cite{Burq2011} for any $s\\in (\\frac{p-3}{p-1},1)$. 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