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The model equation is\n  \\begin{equation*}\\begin{split} \\partial_t(|u|^{q-1}u)+\\mathrm{P}.\\mathrm{V}.\\int_{\\mathbb{R}^n}\\frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{n+sp}}\\,\\mathrm{d}y=0, \\end{split} \\end{equation*} where $0<s<1$, $p>2$ and $0<q<p-1$. Under a parabolic tail condition, we show that any locally bounded and sign-changing solution is locally H\\\"older continuous. Our proof is based on a nonlocal version of De Giorgi technique and the method of intrinsic scaling."},"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":"2509.05914","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-09-07T04:16:34Z","cross_cats_sorted":[],"title_canon_sha256":"4e4d31273373b9e25e34ccc624e87a530828bdd0adc283998e4e7e37bb959d66","abstract_canon_sha256":"f0e375b6eadb0505bb4435cca9e4f42971716a9e4be8ddb59944833c656a4eae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:06:26.387866Z","signature_b64":"Qht50Gx8T88yk4wbbE/zlLn/M0/PNNGIWstyNSCgHkFfhlnb/bR7kSwTpgwJ/Xg9yWcLj3+ojFTKBdRpew8WDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d5b4a0d3095214d4b5d70492a4bc1c6964f89472544818f709d81815f19eff8","last_reissued_at":"2026-07-05T12:06:26.387457Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:06:26.387457Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"H\\\"older regularity of weak solutions to nonlocal doubly degenerate parabolic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qifan Li","submitted_at":"2025-09-07T04:16:34Z","abstract_excerpt":"We study local regularity for nonlocal doubly degenerate parabolic equations. The model equation is\n  \\begin{equation*}\\begin{split} \\partial_t(|u|^{q-1}u)+\\mathrm{P}.\\mathrm{V}.\\int_{\\mathbb{R}^n}\\frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{n+sp}}\\,\\mathrm{d}y=0, \\end{split} \\end{equation*} where $0<s<1$, $p>2$ and $0<q<p-1$. Under a parabolic tail condition, we show that any locally bounded and sign-changing solution is locally H\\\"older continuous. 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