{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:UBDRVBQE2HHROVNSCGZBMTE5GO","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":"47d89b0f1d02ebbe8846fa9da717d88dd7aab7024fefcc7c16fa31bf013f1284","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"physics.plasm-ph","submitted_at":"2000-11-03T18:31:56Z","title_canon_sha256":"17f7c2870c3bea3818987b8ed29c0d5925d457f1a6ba14e072a6ee39a2d955cf"},"schema_version":"1.0","source":{"id":"physics/0011010","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"physics/0011010","created_at":"2026-05-18T01:38:11Z"},{"alias_kind":"arxiv_version","alias_value":"physics/0011010v1","created_at":"2026-05-18T01:38:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.physics/0011010","created_at":"2026-05-18T01:38:11Z"},{"alias_kind":"pith_short_12","alias_value":"UBDRVBQE2HHR","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"UBDRVBQE2HHROVNS","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"UBDRVBQE","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:4979da6ae25b81e21b78ee7709dd3292626a0370e73e9d7271d642fbefe8fb1c","target":"graph","created_at":"2026-05-18T01:38:11Z","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":"We investigate solutions to the equation $\\partial_t{\\cal E} - {\\cal D}\\Delta {\\cal E} = \\lambda S^2{\\cal E}$, where $S(x,t)$ is a Gaussian stochastic field with covariance $C(x-x',t,t')$, and $x\\in {\\mathbb R}^d$. It is shown that the coupling $\\lambda_{cN}(t)$ at which the $N$-th moment $<{\\cal E}^N(x,t)>$ diverges at time $t$, is always less or equal for ${\\cal D}>0$ than for ${\\cal D}=0$. Equality holds under some reasonable assumptions on $C$ and, in this case, $\\lambda_{cN}(t)=N\\lambda_c(t)$ where $\\lambda_c(t)$ is the value of $\\lambda$ at which $<\\exp\\lbrack \\lambda\\int_0^tS^2(0,s)ds\\r","authors_text":"A. Asselah, J. L. Lebowitz, P. Dai Pra, Ph. Mounaix","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"physics.plasm-ph","submitted_at":"2000-11-03T18:31:56Z","title":"Diffusion Effects on the Breakdown of a Linear Amplifier Model Driven by the Square of a Gaussian Field"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"physics/0011010","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":"sha256:477bd83003e550b35c6f5dfec0324f2d74845ca7f5dc72c70391a0fa0dcd76d1","target":"record","created_at":"2026-05-18T01:38:11Z","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":"47d89b0f1d02ebbe8846fa9da717d88dd7aab7024fefcc7c16fa31bf013f1284","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"physics.plasm-ph","submitted_at":"2000-11-03T18:31:56Z","title_canon_sha256":"17f7c2870c3bea3818987b8ed29c0d5925d457f1a6ba14e072a6ee39a2d955cf"},"schema_version":"1.0","source":{"id":"physics/0011010","kind":"arxiv","version":1}},"canonical_sha256":"a0471a8604d1cf1755b211b2164c9d33a98ba964b1762fc6a030b4582e349744","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0471a8604d1cf1755b211b2164c9d33a98ba964b1762fc6a030b4582e349744","first_computed_at":"2026-05-18T01:38:11.341228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:11.341228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kulceC71VAWhfjW7pmLwCAkDFCaSRM7H9tbF81X7OgIPjSl63Lm+3dHnLrewhL/jru8zvqOa70NzCfYB9cz7Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:11.341895Z","signed_message":"canonical_sha256_bytes"},"source_id":"physics/0011010","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:477bd83003e550b35c6f5dfec0324f2d74845ca7f5dc72c70391a0fa0dcd76d1","sha256:4979da6ae25b81e21b78ee7709dd3292626a0370e73e9d7271d642fbefe8fb1c"],"state_sha256":"11a8ee2fa2999931714159c169aaca5948f1dfc15d5d7a4115781470a26d27fe"}