{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RLRPB6NQ374JKJEOWDS6KVM54S","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":"05ebf9b729abe487571a394ac4ff68f6857ded1bf383ac4c9ec0c25a08490ec7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-16T06:53:21Z","title_canon_sha256":"b5bfd6c44a2d18808c4fb7e469426b4e3248777f365e24aea3871e75dc243272"},"schema_version":"1.0","source":{"id":"1009.3102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.3102","created_at":"2026-05-18T02:50:32Z"},{"alias_kind":"arxiv_version","alias_value":"1009.3102v1","created_at":"2026-05-18T02:50:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3102","created_at":"2026-05-18T02:50:32Z"},{"alias_kind":"pith_short_12","alias_value":"RLRPB6NQ374J","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RLRPB6NQ374JKJEO","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RLRPB6NQ","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:f4a72c2bf1e4f5433dd04683f519be588cfe28b8554c215d35dfcbf62e85cfa4","target":"graph","created_at":"2026-05-18T02:50:32Z","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 concerns the formation of a coincidence set for the positive solution of $p$-Laplacian elliptic problems of monostable type. It is proved that for any small parameter of diffusion term, the solution coincides with the stable zero-function $a(x)$ of reaction term in an open set if $a(x)$ is $p$-harmonic (but, not constant) and a zero of order less than 1. Inversely, it is also shown that the solution is less than $a(x)$ if $a(x)$ is a zero of order greater than or equal to 1. The proof rely on comparison theorems and an energy method for obtaining local comaprison functions.","authors_text":"Shingo Takeuchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-16T06:53:21Z","title":"Coincidence sets in quasilinear elliptic problems of monostable type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3102","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":"sha256:18f7a9020a71740690d91f28489ea0468f05270de0aded146c061c2714c685fc","target":"record","created_at":"2026-05-18T02:50:32Z","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":"05ebf9b729abe487571a394ac4ff68f6857ded1bf383ac4c9ec0c25a08490ec7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-16T06:53:21Z","title_canon_sha256":"b5bfd6c44a2d18808c4fb7e469426b4e3248777f365e24aea3871e75dc243272"},"schema_version":"1.0","source":{"id":"1009.3102","kind":"arxiv","version":1}},"canonical_sha256":"8ae2f0f9b0dff895248eb0e5e5559de4a9caac80f8d4fbad042ee2edce482c25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ae2f0f9b0dff895248eb0e5e5559de4a9caac80f8d4fbad042ee2edce482c25","first_computed_at":"2026-05-18T02:50:32.709627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:32.709627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WMio/92QB0cS6hfy1OpSwuojqYiWi1/JmCU1RQt2EQHYeCnDimt0saMGbDVLl3U2MDDApWKbOZAVJcYMQa3cAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:32.710084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.3102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18f7a9020a71740690d91f28489ea0468f05270de0aded146c061c2714c685fc","sha256:f4a72c2bf1e4f5433dd04683f519be588cfe28b8554c215d35dfcbf62e85cfa4"],"state_sha256":"e25648277323e7a257ffe1676fb7e0f368b408659a6d2de57bfc7609b6be4f81"}