{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:S6IKYPFI76SBCGF3B52BLVLHMN","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":"3c981743afed2295a7b56a7afb9dadeccf4387c5343e03189da68fc1df3eb447","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-26T05:44:31Z","title_canon_sha256":"7d91d645cbb197ef4a6fdbccec2660af8290fe9dada34d7be8525e7170b72cc2"},"schema_version":"1.0","source":{"id":"1501.06258","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06258","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06258v1","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06258","created_at":"2026-05-18T02:28:41Z"},{"alias_kind":"pith_short_12","alias_value":"S6IKYPFI76SB","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S6IKYPFI76SBCGF3","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S6IKYPFI","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:5674a854aa0b7f6429c61294caa7ae7c65c1afc21cd6da343289b49dfafb5596","target":"graph","created_at":"2026-05-18T02:28:41Z","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":"This paper continues the investigation of Du and Lou (J. European Math Soc, to appear), where the long-time behavior of positive solutions to a nonlinear diffusion equation of the form $u_t=u_{xx}+f(u)$ for $x$ over a varying interval $(g(t), h(t))$ was examined. Here $x=g(t)$ and $x=h(t)$ are free boundaries evolving according to $g'(t)=-\\mu u_x(t, g(t))$, $h'(t)=-\\mu u_x(t,h(t))$, and $u(t, g(t))=u(t,h(t))=0$. We answer several intriguing questions left open in the paper of Du and Lou.First we prove the conjectured convergence result in the paper of Du and Lou for the general case that $f$ i","authors_text":"Bendong Lou, Maolin Zhou, Yihong Du","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-26T05:44:31Z","title":"Nonlinear diffusion problems with free boundaries: Convergence, transition speed and zero number arguments,"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06258","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":"sha256:32c7c5325b96628f9febc537d5fb9bf027665f49ef8049994c04a4ba18aa0221","target":"record","created_at":"2026-05-18T02:28:41Z","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":"3c981743afed2295a7b56a7afb9dadeccf4387c5343e03189da68fc1df3eb447","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-26T05:44:31Z","title_canon_sha256":"7d91d645cbb197ef4a6fdbccec2660af8290fe9dada34d7be8525e7170b72cc2"},"schema_version":"1.0","source":{"id":"1501.06258","kind":"arxiv","version":1}},"canonical_sha256":"9790ac3ca8ffa41118bb0f7415d56763631ecbaed9d978289830eda290cc4723","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9790ac3ca8ffa41118bb0f7415d56763631ecbaed9d978289830eda290cc4723","first_computed_at":"2026-05-18T02:28:41.903442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:41.903442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nax+u4esHMhAOs9Ph/6HFOljkiFk2AcQobf9IhW7WmIkuwkqpyGCfxPZFzfAEj+m+Qufz7TW8xZ9JuBmu7k7Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:41.903888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06258","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32c7c5325b96628f9febc537d5fb9bf027665f49ef8049994c04a4ba18aa0221","sha256:5674a854aa0b7f6429c61294caa7ae7c65c1afc21cd6da343289b49dfafb5596"],"state_sha256":"4c8ccf5fe29cb2e2fbb323c9e6ed884cf848ef0b7d596601e2234cb5965c4fb3"}