{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:CFVARTVNVMBIEHXTD7LUFRBKKH","short_pith_number":"pith:CFVARTVN","canonical_record":{"source":{"id":"1406.2675","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-10T19:39:15Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"45b67820f7b087f8b6271411712c5a65e57eaa18f60d8679cf243cb0d21a444b","abstract_canon_sha256":"64555fcb190f761157bf0137eabe06f73396a9488a9b88c08403b81c3294774a"},"schema_version":"1.0"},"canonical_sha256":"116a08ceadab02821ef31fd742c42a51c9b546180832a061d00ef32acf4bacb8","source":{"kind":"arxiv","id":"1406.2675","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2675","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2675v1","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2675","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"pith_short_12","alias_value":"CFVARTVNVMBI","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CFVARTVNVMBIEHXT","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CFVARTVN","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:CFVARTVNVMBIEHXTD7LUFRBKKH","target":"record","payload":{"canonical_record":{"source":{"id":"1406.2675","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-10T19:39:15Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"45b67820f7b087f8b6271411712c5a65e57eaa18f60d8679cf243cb0d21a444b","abstract_canon_sha256":"64555fcb190f761157bf0137eabe06f73396a9488a9b88c08403b81c3294774a"},"schema_version":"1.0"},"canonical_sha256":"116a08ceadab02821ef31fd742c42a51c9b546180832a061d00ef32acf4bacb8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:32.170157Z","signature_b64":"fMfavhqtUZUpZwZVsOz2IqFi9gUAMHV23EsU381aDOdnPLYlZGzNoY9He2Dd665c0W5Pd07r1oEN31sjB9arDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"116a08ceadab02821ef31fd742c42a51c9b546180832a061d00ef32acf4bacb8","last_reissued_at":"2026-05-17T23:54:32.169631Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:32.169631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.2675","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zxlBW2nzcMWzmDuj6lI1xDgb2z4Sr0hCPKfqDZXoaQaOqcv7XhyajqpvqTBFVGTcmYa3dX10VKCqEs/w4pRvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:18:13.897409Z"},"content_sha256":"ddf4f6c6b7433308e3565fbc595b593dd20b4ddce355a9f60fedabebbedd381a","schema_version":"1.0","event_id":"sha256:ddf4f6c6b7433308e3565fbc595b593dd20b4ddce355a9f60fedabebbedd381a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:CFVARTVNVMBIEHXTD7LUFRBKKH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Front Propagation in Stochastic Neural Fields: A Rigorous Mathematical Framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Jennifer Kr\\\"uger, Wilhelm Stannat","submitted_at":"2014-06-10T19:39:15Z","abstract_excerpt":"We develop a complete and rigorous mathematical framework for the analysis of stochastic neural field equations under the influence of spatially extended additive noise. By comparing a solution to a fixed deterministic front profile it is possible to realise the difference as strong solution to an $L^2(\\mathbb{R})$-valued SDE. A multiscale analysis of this process then allows us to obtain rigorous stability results. Here a new representation formula for stochastic convolutions in the semigroup approach to linear function-valued SDE with adapted random drift is applied. Additionally, we introdu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2675","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:54:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BDO4HPLfJZpGlIETZq+bVwMgbuT13gw/TVzZau9ndICStMA4I206bY7WqOughSxwnOd9Nz+zt3uygx2NCK8mCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T23:18:13.897777Z"},"content_sha256":"271f28cd71114879e0f53b03be81a33baca4e3edc130cf7f783007501b748841","schema_version":"1.0","event_id":"sha256:271f28cd71114879e0f53b03be81a33baca4e3edc130cf7f783007501b748841"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CFVARTVNVMBIEHXTD7LUFRBKKH/bundle.json","state_url":"https://pith.science/pith/CFVARTVNVMBIEHXTD7LUFRBKKH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CFVARTVNVMBIEHXTD7LUFRBKKH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T23:18:13Z","links":{"resolver":"https://pith.science/pith/CFVARTVNVMBIEHXTD7LUFRBKKH","bundle":"https://pith.science/pith/CFVARTVNVMBIEHXTD7LUFRBKKH/bundle.json","state":"https://pith.science/pith/CFVARTVNVMBIEHXTD7LUFRBKKH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CFVARTVNVMBIEHXTD7LUFRBKKH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:CFVARTVNVMBIEHXTD7LUFRBKKH","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":"64555fcb190f761157bf0137eabe06f73396a9488a9b88c08403b81c3294774a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-10T19:39:15Z","title_canon_sha256":"45b67820f7b087f8b6271411712c5a65e57eaa18f60d8679cf243cb0d21a444b"},"schema_version":"1.0","source":{"id":"1406.2675","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2675","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2675v1","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2675","created_at":"2026-05-17T23:54:32Z"},{"alias_kind":"pith_short_12","alias_value":"CFVARTVNVMBI","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"CFVARTVNVMBIEHXT","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"CFVARTVN","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:271f28cd71114879e0f53b03be81a33baca4e3edc130cf7f783007501b748841","target":"graph","created_at":"2026-05-17T23:54:32Z","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":"We develop a complete and rigorous mathematical framework for the analysis of stochastic neural field equations under the influence of spatially extended additive noise. By comparing a solution to a fixed deterministic front profile it is possible to realise the difference as strong solution to an $L^2(\\mathbb{R})$-valued SDE. A multiscale analysis of this process then allows us to obtain rigorous stability results. Here a new representation formula for stochastic convolutions in the semigroup approach to linear function-valued SDE with adapted random drift is applied. Additionally, we introdu","authors_text":"Jennifer Kr\\\"uger, Wilhelm Stannat","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-10T19:39:15Z","title":"Front Propagation in Stochastic Neural Fields: A Rigorous Mathematical Framework"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2675","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:ddf4f6c6b7433308e3565fbc595b593dd20b4ddce355a9f60fedabebbedd381a","target":"record","created_at":"2026-05-17T23:54:32Z","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":"64555fcb190f761157bf0137eabe06f73396a9488a9b88c08403b81c3294774a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-10T19:39:15Z","title_canon_sha256":"45b67820f7b087f8b6271411712c5a65e57eaa18f60d8679cf243cb0d21a444b"},"schema_version":"1.0","source":{"id":"1406.2675","kind":"arxiv","version":1}},"canonical_sha256":"116a08ceadab02821ef31fd742c42a51c9b546180832a061d00ef32acf4bacb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"116a08ceadab02821ef31fd742c42a51c9b546180832a061d00ef32acf4bacb8","first_computed_at":"2026-05-17T23:54:32.169631Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:32.169631Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fMfavhqtUZUpZwZVsOz2IqFi9gUAMHV23EsU381aDOdnPLYlZGzNoY9He2Dd665c0W5Pd07r1oEN31sjB9arDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:32.170157Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2675","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddf4f6c6b7433308e3565fbc595b593dd20b4ddce355a9f60fedabebbedd381a","sha256:271f28cd71114879e0f53b03be81a33baca4e3edc130cf7f783007501b748841"],"state_sha256":"c56eaae1bbd16d17d80200a07742f6f346cd68903b4e9ffb0fd12ebef56ecfb5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B6B0/3wCy1rtnez4A+xb383fz5GMZqyZsbmyh4oMnExbS0mgvXXklHTasMCb5VIBfdT1XLeDVrPUWo7vUJXrAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T23:18:13.899700Z","bundle_sha256":"d962c16fa18ba249e0654f983ab06977fe6b96487216a64b0beb314423cbd733"}}