{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6B5EPR6A6BZ6QFWC3G54XE2OQW","short_pith_number":"pith:6B5EPR6A","canonical_record":{"source":{"id":"1407.2696","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-10T05:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"5d81a36dfad39fc84956f1967e4c55b053acc840cd7a7bd803eec758917b0894","abstract_canon_sha256":"dbf7b952ce3b2e03268d8d70bb8d432c918fe7ceedb0deeb1f58913b19c00efc"},"schema_version":"1.0"},"canonical_sha256":"f07a47c7c0f073e816c2d9bbcb934e85ad7f465c129dbf99f5b44db20862e296","source":{"kind":"arxiv","id":"1407.2696","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2696","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2696v2","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2696","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"6B5EPR6A6BZ6","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6B5EPR6A6BZ6QFWC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6B5EPR6A","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6B5EPR6A6BZ6QFWC3G54XE2OQW","target":"record","payload":{"canonical_record":{"source":{"id":"1407.2696","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-10T05:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"5d81a36dfad39fc84956f1967e4c55b053acc840cd7a7bd803eec758917b0894","abstract_canon_sha256":"dbf7b952ce3b2e03268d8d70bb8d432c918fe7ceedb0deeb1f58913b19c00efc"},"schema_version":"1.0"},"canonical_sha256":"f07a47c7c0f073e816c2d9bbcb934e85ad7f465c129dbf99f5b44db20862e296","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:47.183095Z","signature_b64":"RvB3Xf53s3fm+BngBbCzdyjE3D4kk7fNSghVs0uC1fqCP/enaf7tIh5GaoxuCQy+ncp4mxvRfhmwSt28pHy4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f07a47c7c0f073e816c2d9bbcb934e85ad7f465c129dbf99f5b44db20862e296","last_reissued_at":"2026-05-18T02:35:47.182711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:47.182711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.2696","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:35:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7wqxj+Y3VxkSrS1fno7kXNKhnE5p3ehYGuIOU/uHcCdRcf7ezMGx2iX9DUYZzMAdO4vsvTP0Y81EdnyPozI7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:27:52.094917Z"},"content_sha256":"b4d4454d50b9d31202c5185e893886ed18f3858897045126187940c0bc52cb5a","schema_version":"1.0","event_id":"sha256:b4d4454d50b9d31202c5185e893886ed18f3858897045126187940c0bc52cb5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6B5EPR6A6BZ6QFWC3G54XE2OQW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic behaviour of solutions of the fast diffusion equation near its extinction time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kin Ming Hui","submitted_at":"2014-07-10T05:37:13Z","abstract_excerpt":"Let $n\\ge 3$, $0<m<\\frac{n-2}{n}$, $\\rho_1>0$, $\\beta\\ge\\frac{m\\rho_1}{n-2-nm}$ and $\\alpha=\\frac{2\\beta+\\rho_1}{1-m}$. For any $\\lambda>0$, we will prove the existence and uniqueness (for $\\beta\\ge\\frac{\\rho_1}{n-2-nm}$) of radially symmetric singular solution $g_{\\lambda}\\in C^{\\infty}(R^n\\setminus\\{0\\})$ of the elliptic equation $\\Delta v^m+\\alpha v+\\beta x\\cdot\\nabla v=0$, $v>0$, in $R^n\\setminus\\{0\\}$, satisfying $\\displaystyle\\lim_{|x|\\to 0}|x|^{\\alpha/\\beta}g_{\\lambda}(x)=\\lambda^{-\\frac{\\rho_1}{(1-m)\\beta}}$. When $\\beta$ is sufficiently large, we prove the higher order asymptotic beha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2696","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:35:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QG7W+ZjWT86hxAFn+9w5R5JvOgh/f8sRhp+QcoapagVhUdwVqHU4Qj0hM3aUOfZFcGFhyR+E/UrxcDnHZLi+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T16:27:52.095737Z"},"content_sha256":"0f237cb69d748632f160d34fd5f4c77d1bf302286d3637fed50905d5cffdfa51","schema_version":"1.0","event_id":"sha256:0f237cb69d748632f160d34fd5f4c77d1bf302286d3637fed50905d5cffdfa51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6B5EPR6A6BZ6QFWC3G54XE2OQW/bundle.json","state_url":"https://pith.science/pith/6B5EPR6A6BZ6QFWC3G54XE2OQW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6B5EPR6A6BZ6QFWC3G54XE2OQW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T16:27:52Z","links":{"resolver":"https://pith.science/pith/6B5EPR6A6BZ6QFWC3G54XE2OQW","bundle":"https://pith.science/pith/6B5EPR6A6BZ6QFWC3G54XE2OQW/bundle.json","state":"https://pith.science/pith/6B5EPR6A6BZ6QFWC3G54XE2OQW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6B5EPR6A6BZ6QFWC3G54XE2OQW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6B5EPR6A6BZ6QFWC3G54XE2OQW","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dbf7b952ce3b2e03268d8d70bb8d432c918fe7ceedb0deeb1f58913b19c00efc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-10T05:37:13Z","title_canon_sha256":"5d81a36dfad39fc84956f1967e4c55b053acc840cd7a7bd803eec758917b0894"},"schema_version":"1.0","source":{"id":"1407.2696","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2696","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2696v2","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2696","created_at":"2026-05-18T02:35:47Z"},{"alias_kind":"pith_short_12","alias_value":"6B5EPR6A6BZ6","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6B5EPR6A6BZ6QFWC","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6B5EPR6A","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:0f237cb69d748632f160d34fd5f4c77d1bf302286d3637fed50905d5cffdfa51","target":"graph","created_at":"2026-05-18T02:35:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $n\\ge 3$, $0<m<\\frac{n-2}{n}$, $\\rho_1>0$, $\\beta\\ge\\frac{m\\rho_1}{n-2-nm}$ and $\\alpha=\\frac{2\\beta+\\rho_1}{1-m}$. For any $\\lambda>0$, we will prove the existence and uniqueness (for $\\beta\\ge\\frac{\\rho_1}{n-2-nm}$) of radially symmetric singular solution $g_{\\lambda}\\in C^{\\infty}(R^n\\setminus\\{0\\})$ of the elliptic equation $\\Delta v^m+\\alpha v+\\beta x\\cdot\\nabla v=0$, $v>0$, in $R^n\\setminus\\{0\\}$, satisfying $\\displaystyle\\lim_{|x|\\to 0}|x|^{\\alpha/\\beta}g_{\\lambda}(x)=\\lambda^{-\\frac{\\rho_1}{(1-m)\\beta}}$. When $\\beta$ is sufficiently large, we prove the higher order asymptotic beha","authors_text":"Kin Ming Hui","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-10T05:37:13Z","title":"Asymptotic behaviour of solutions of the fast diffusion equation near its extinction time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2696","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b4d4454d50b9d31202c5185e893886ed18f3858897045126187940c0bc52cb5a","target":"record","created_at":"2026-05-18T02:35:47Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dbf7b952ce3b2e03268d8d70bb8d432c918fe7ceedb0deeb1f58913b19c00efc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-10T05:37:13Z","title_canon_sha256":"5d81a36dfad39fc84956f1967e4c55b053acc840cd7a7bd803eec758917b0894"},"schema_version":"1.0","source":{"id":"1407.2696","kind":"arxiv","version":2}},"canonical_sha256":"f07a47c7c0f073e816c2d9bbcb934e85ad7f465c129dbf99f5b44db20862e296","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f07a47c7c0f073e816c2d9bbcb934e85ad7f465c129dbf99f5b44db20862e296","first_computed_at":"2026-05-18T02:35:47.182711Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:47.182711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RvB3Xf53s3fm+BngBbCzdyjE3D4kk7fNSghVs0uC1fqCP/enaf7tIh5GaoxuCQy+ncp4mxvRfhmwSt28pHy4CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:47.183095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2696","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b4d4454d50b9d31202c5185e893886ed18f3858897045126187940c0bc52cb5a","sha256:0f237cb69d748632f160d34fd5f4c77d1bf302286d3637fed50905d5cffdfa51"],"state_sha256":"e8443cc29e0ae17ad6c11b93eebc6b10716ba3d69c130ae63d75d1af3a02fb06"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3F1kHLnAKqk23nMkgTG1ri2jJiwpEV4StmyILJPfb4TTiZ/BQSZz+QNTgs07cOUtKgYcViiv53uUpfjAbj8LCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T16:27:52.098947Z","bundle_sha256":"41909c9aa4a780a0b836af5d75b6ddd6a3e998becf75058de1dcbce2f2088564"}}