{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:6DGDK4FHKN6IWQXSDLAE5MSAHE","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":"2b1147de90800cbea5917d083e21cde55c4dd69da339c1ee1cce744f36e60154","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-23T15:19:33Z","title_canon_sha256":"87361ed75e3e787d06955f993a753dfcce11b2456e8bb4c1ca7bc93e75bd05f0"},"schema_version":"1.0","source":{"id":"1706.07745","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07745","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07745v5","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07745","created_at":"2026-05-17T23:47:40Z"},{"alias_kind":"pith_short_12","alias_value":"6DGDK4FHKN6I","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_16","alias_value":"6DGDK4FHKN6IWQXS","created_at":"2026-05-18T12:31:03Z"},{"alias_kind":"pith_short_8","alias_value":"6DGDK4FH","created_at":"2026-05-18T12:31:03Z"}],"graph_snapshots":[{"event_id":"sha256:77b1d5824cafcc8ae03729a395d7de2fc972b00f1e30880a1ee2b265a65f20fe","target":"graph","created_at":"2026-05-17T23:47:40Z","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 article studies the dynamics of a nonlinear dissipative reaction-diffusion equation with well-separated stable states which is perturbed by infinite-dimensional multiplicative L\\'evy noise with a regularly varying component at intensity $\\epsilon>0$. The main results establish the precise asymptotics of the first exit times and locus of the solution $X^\\epsilon$ from the domain of attraction of a deterministic stable state, in the limit as $\\epsilon\\rightarrow 0$. In contrast to the exponential growth for respective Gaussian perturbations the exit times grow essentially as a power functio","authors_text":"Michael A. H\\\"ogele","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-23T15:19:33Z","title":"The first exit problem of reaction-diffusion equations for small multiplicative L\\'evy noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07745","kind":"arxiv","version":5},"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:a39b257d1a3f4b702f6994eefc3b93f249c925b102c2810498c5a2f8b4274449","target":"record","created_at":"2026-05-17T23:47:40Z","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":"2b1147de90800cbea5917d083e21cde55c4dd69da339c1ee1cce744f36e60154","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-06-23T15:19:33Z","title_canon_sha256":"87361ed75e3e787d06955f993a753dfcce11b2456e8bb4c1ca7bc93e75bd05f0"},"schema_version":"1.0","source":{"id":"1706.07745","kind":"arxiv","version":5}},"canonical_sha256":"f0cc3570a7537c8b42f21ac04eb2403934efc5cd1d59b925a9cefb5dc70e6050","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0cc3570a7537c8b42f21ac04eb2403934efc5cd1d59b925a9cefb5dc70e6050","first_computed_at":"2026-05-17T23:47:40.277559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:40.277559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yAv6PZG3+BZ6IE5QUoloCHNeEw34e/tlqtXFZY82uYTDym2b7vXyBc4wr+TbWUWU5CGNsFA0eYbtfjBGKUWZCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:40.277956Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07745","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a39b257d1a3f4b702f6994eefc3b93f249c925b102c2810498c5a2f8b4274449","sha256:77b1d5824cafcc8ae03729a395d7de2fc972b00f1e30880a1ee2b265a65f20fe"],"state_sha256":"1d847f016dcdbe67732c6304bba486f329bd3404b30801e393f64672a21f9b5a"}