{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MNSWJEWXLOGHDEP4OHBAEUYRGZ","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":"93acc436be9c7e3c8cb2f8a5825ebafe5e6c1a064e182dc3ca985a82c48103be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-02T06:31:29Z","title_canon_sha256":"0eb3cef8f24b9ef288b6d8dd598c5d8a469f754ee0dad395fcbe8aac1b0470a2"},"schema_version":"1.0","source":{"id":"1510.00500","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00500","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00500v1","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00500","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"MNSWJEWXLOGH","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MNSWJEWXLOGHDEP4","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MNSWJEWX","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:4aac4aaee15ce86ad6c6868e400d2702ca266cb386cf4ee3a5724736690f6268","target":"graph","created_at":"2026-05-18T01:31:12Z","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":"For a large class of non-negative initial data, the solutions to the quasilinear viscous Hamilton-Jacobi equation $\\partial\\_t u-\\Delta\\_p u+|\\nabla u|^q=0$ in $(0,\\infty)\\times\\real^N$ are known to vanish identically after a finite time when $2N/(N+1) \\textless{} p \\leq 2$ and $q\\in(0,p-1)$. Further properties of this extinction phenomenon are established herein: \\emph{instantaneous shrinking} of the support is shown to take place if the initial condition $u\\_0$ decays sufficiently rapidly as $|x|\\to\\infty$, that is, for each $t \\textgreater{} 0$, the positivity set of $u(t)$ is a bounded sub","authors_text":"Christian Stinner, Philippe Lauren\\c{c}ot (IMT), Razvan Gabriel Iagar (ICMAT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-02T06:31:29Z","title":"Instantaneous shrinking and single point extinction for viscous Hamilton-Jacobi equations with fast diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00500","kind":"arxiv","version":1},"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:ed9375da3bab00904d085f1b7e13b2c98c0eaca8e8dceb8af671afce668eab8a","target":"record","created_at":"2026-05-18T01:31:12Z","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":"93acc436be9c7e3c8cb2f8a5825ebafe5e6c1a064e182dc3ca985a82c48103be","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-10-02T06:31:29Z","title_canon_sha256":"0eb3cef8f24b9ef288b6d8dd598c5d8a469f754ee0dad395fcbe8aac1b0470a2"},"schema_version":"1.0","source":{"id":"1510.00500","kind":"arxiv","version":1}},"canonical_sha256":"63656492d75b8c7191fc71c20253113674b5b60c0dfe237981335cd8c2057ffb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63656492d75b8c7191fc71c20253113674b5b60c0dfe237981335cd8c2057ffb","first_computed_at":"2026-05-18T01:31:12.897897Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:12.897897Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wSRWe/leonJFkyUBY1Xs7NlKgQSethWeNHaQv5ESF76QmvLUxeQjJY7XjjheBBStmS6Jd8pSEmVXIrsj39vsCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:12.898577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00500","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed9375da3bab00904d085f1b7e13b2c98c0eaca8e8dceb8af671afce668eab8a","sha256:4aac4aaee15ce86ad6c6868e400d2702ca266cb386cf4ee3a5724736690f6268"],"state_sha256":"d9af0b75de5dc64b73b8961285860ab83754e50f62618d5aa31efbb25d42c282"}