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We investigate their fine asymptotics near the extinction time $T$ in terms of a separable solution of the form ${\\mathcal V}(r,t)=(1-t/T)^{1/(1-m)}V^{1/m}(r)$, where $V$ is the unique positive energy solution, radial w.r.t. $o$, to $-\\Delta V=c\\,V^{1/m}$ for a suitable $c>0$, a semilinear elliptic problem thorough"},"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":"1302.4093","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-02-17T17:40:50Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"44bbdcef8e8d3deb6b052c38ed53dcde5b6a0c29f76275c4c1924e4cc34d6d43","abstract_canon_sha256":"95f8e5e3297b6a6b6e7f6b541ab4c7dbd15ae50d6c31aea188eb9811cb7b8b49"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:30.024858Z","signature_b64":"zI/jQTuo7QM4HTg1CxPe3owj8AhB1GTrdwxGgiyMynFJGL7o0zxMwb1m6kmP2ZiJKkd/irxfMWE+8of0ml25Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe1dc99c6ad4d58aaf7c4b2776361968ee5ccc49b116cb4f3d1ed16d02512183","last_reissued_at":"2026-05-18T00:44:30.024383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:30.024383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Radial Fast Diffusion on the Hyperbolic Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Gabriele Grillo, Matteo Muratori","submitted_at":"2013-02-17T17:40:50Z","abstract_excerpt":"We consider radial solutions to the fast diffusion equation $u_t=\\Delta u^m$ on the hyperbolic space $\\mathbb{H}^{N}$ for $N \\ge 2$, $m\\in(m_s,1)$, $m_s=\\frac{N-2}{N+2}$. 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We investigate their fine asymptotics near the extinction time $T$ in terms of a separable solution of the form ${\\mathcal V}(r,t)=(1-t/T)^{1/(1-m)}V^{1/m}(r)$, where $V$ is the unique positive energy solution, radial w.r.t. $o$, to $-\\Delta V=c\\,V^{1/m}$ for a suitable $c>0$, a semilinear elliptic problem thorough"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4093","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1302.4093","created_at":"2026-05-18T00:44:30.024453+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.4093v3","created_at":"2026-05-18T00:44:30.024453+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4093","created_at":"2026-05-18T00:44:30.024453+00:00"},{"alias_kind":"pith_short_12","alias_value":"7YO4THDK2TKY","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"7YO4THDK2TKYVL34","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"7YO4THDK","created_at":"2026-05-18T12:27:38.830355+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7YO4THDK2TKYVL34JMTXMNQZND","json":"https://pith.science/pith/7YO4THDK2TKYVL34JMTXMNQZND.json","graph_json":"https://pith.science/api/pith-number/7YO4THDK2TKYVL34JMTXMNQZND/graph.json","events_json":"https://pith.science/api/pith-number/7YO4THDK2TKYVL34JMTXMNQZND/events.json","paper":"https://pith.science/paper/7YO4THDK"},"agent_actions":{"view_html":"https://pith.science/pith/7YO4THDK2TKYVL34JMTXMNQZND","download_json":"https://pith.science/pith/7YO4THDK2TKYVL34JMTXMNQZND.json","view_paper":"https://pith.science/paper/7YO4THDK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.4093&json=true","fetch_graph":"https://pith.science/api/pith-number/7YO4THDK2TKYVL34JMTXMNQZND/graph.json","fetch_events":"https://pith.science/api/pith-number/7YO4THDK2TKYVL34JMTXMNQZND/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7YO4THDK2TKYVL34JMTXMNQZND/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7YO4THDK2TKYVL34JMTXMNQZND/action/storage_attestation","attest_author":"https://pith.science/pith/7YO4THDK2TKYVL34JMTXMNQZND/action/author_attestation","sign_citation":"https://pith.science/pith/7YO4THDK2TKYVL34JMTXMNQZND/action/citation_signature","submit_replication":"https://pith.science/pith/7YO4THDK2TKYVL34JMTXMNQZND/action/replication_record"}},"created_at":"2026-05-18T00:44:30.024453+00:00","updated_at":"2026-05-18T00:44:30.024453+00:00"}