{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MT3BWQ6NU2H57ZK7HB2FVSK5GW","short_pith_number":"pith:MT3BWQ6N","canonical_record":{"source":{"id":"1810.03585","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T17:23:55Z","cross_cats_sorted":[],"title_canon_sha256":"a1a82a0389ffeaa49e772a2b624cc070420923857d3b48fcffd2f725669ceb49","abstract_canon_sha256":"40724b7ebc18d4ffd2f7f18121a56464f6034471541d31d86209a425a153ab31"},"schema_version":"1.0"},"canonical_sha256":"64f61b43cda68fdfe55f38745ac95d35a7343d574f2a456c30804b9d84ad47ae","source":{"kind":"arxiv","id":"1810.03585","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03585","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03585v2","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03585","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"pith_short_12","alias_value":"MT3BWQ6NU2H5","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MT3BWQ6NU2H57ZK7","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MT3BWQ6N","created_at":"2026-05-18T12:32:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MT3BWQ6NU2H57ZK7HB2FVSK5GW","target":"record","payload":{"canonical_record":{"source":{"id":"1810.03585","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T17:23:55Z","cross_cats_sorted":[],"title_canon_sha256":"a1a82a0389ffeaa49e772a2b624cc070420923857d3b48fcffd2f725669ceb49","abstract_canon_sha256":"40724b7ebc18d4ffd2f7f18121a56464f6034471541d31d86209a425a153ab31"},"schema_version":"1.0"},"canonical_sha256":"64f61b43cda68fdfe55f38745ac95d35a7343d574f2a456c30804b9d84ad47ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:14.481382Z","signature_b64":"/EbbsPdugJVNhY6l9wQH/Gq7gvGOpP/C4cx9mMi735SGK8Rz9s5DYIQdBQIkiyLHWRTflpnwdQK8r/rf2B+3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64f61b43cda68fdfe55f38745ac95d35a7343d574f2a456c30804b9d84ad47ae","last_reissued_at":"2026-05-18T00:03:14.480840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:14.480840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.03585","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+yjzfUr4ShD1rV43Q5ciczheO9V36/Qs2JocTjjo9fJa/7pJOvMgFv1jTCL4Slt+4Bj/CyoSkqcw++D4Zi8oBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:03:46.604623Z"},"content_sha256":"45875414c594a06a0bb1be351ff33db2edc673ae3f736498e3bf173229e1c4c5","schema_version":"1.0","event_id":"sha256:45875414c594a06a0bb1be351ff33db2edc673ae3f736498e3bf173229e1c4c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MT3BWQ6NU2H57ZK7HB2FVSK5GW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Simultaneous Small Noise Limit for Singularly Perturbed Slow-Fast Coupled Diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"K. Suresh Kumar, Rajesh Sundaresan, Siva R. Athreya, Vivek S. Borkar","submitted_at":"2018-10-08T17:23:55Z","abstract_excerpt":"We consider a simultaneous small noise limit for a singularly perturbed coupled diffusion described by \\begin{eqnarray*} dX^{\\varepsilon}_t &=& b(X^{\\varepsilon}_t, Y^{\\varepsilon}_t)dt + \\varepsilon^{\\alpha}dB_t,\n  dY^{\\varepsilon}_t &=& - \\frac{1}{\\varepsilon} \\nabla_yU(X^{\\varepsilon}_t, Y^{\\varepsilon}_t)dt + \\frac{s(\\varepsilon)}{\\sqrt{\\varepsilon}} dW_t, \\end{eqnarray*} where $B_t, W_t$ are independent Brownian motions on ${\\mathbb R}^d$ and ${\\mathbb R}^m$ respectively, $b : \\mathbb{R}^d \\times \\mathbb{R}^m \\rightarrow \\mathbb{R}^d$, $U : \\mathbb{R}^d \\times \\mathbb{R}^m \\rightarrow \\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03585","kind":"arxiv","version":2},"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":"2026-05-18T00:03:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SVRlcMXbk0slXTuaepch1GegY1ahRsq/XLnvQAYK65Jr8u6Ub2q+Oo4UKPP3oUWCCqC8TnQ1esIK2sDqSKS8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T04:03:46.604976Z"},"content_sha256":"4e010c5f864a083ecf517fa61593573413b11033b706577cdf402b5c22f3b7ef","schema_version":"1.0","event_id":"sha256:4e010c5f864a083ecf517fa61593573413b11033b706577cdf402b5c22f3b7ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MT3BWQ6NU2H57ZK7HB2FVSK5GW/bundle.json","state_url":"https://pith.science/pith/MT3BWQ6NU2H57ZK7HB2FVSK5GW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MT3BWQ6NU2H57ZK7HB2FVSK5GW/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":"2026-06-23T04:03:46Z","links":{"resolver":"https://pith.science/pith/MT3BWQ6NU2H57ZK7HB2FVSK5GW","bundle":"https://pith.science/pith/MT3BWQ6NU2H57ZK7HB2FVSK5GW/bundle.json","state":"https://pith.science/pith/MT3BWQ6NU2H57ZK7HB2FVSK5GW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MT3BWQ6NU2H57ZK7HB2FVSK5GW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MT3BWQ6NU2H57ZK7HB2FVSK5GW","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":"40724b7ebc18d4ffd2f7f18121a56464f6034471541d31d86209a425a153ab31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T17:23:55Z","title_canon_sha256":"a1a82a0389ffeaa49e772a2b624cc070420923857d3b48fcffd2f725669ceb49"},"schema_version":"1.0","source":{"id":"1810.03585","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.03585","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"arxiv_version","alias_value":"1810.03585v2","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.03585","created_at":"2026-05-18T00:03:14Z"},{"alias_kind":"pith_short_12","alias_value":"MT3BWQ6NU2H5","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MT3BWQ6NU2H57ZK7","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MT3BWQ6N","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:4e010c5f864a083ecf517fa61593573413b11033b706577cdf402b5c22f3b7ef","target":"graph","created_at":"2026-05-18T00:03:14Z","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 consider a simultaneous small noise limit for a singularly perturbed coupled diffusion described by \\begin{eqnarray*} dX^{\\varepsilon}_t &=& b(X^{\\varepsilon}_t, Y^{\\varepsilon}_t)dt + \\varepsilon^{\\alpha}dB_t,\n  dY^{\\varepsilon}_t &=& - \\frac{1}{\\varepsilon} \\nabla_yU(X^{\\varepsilon}_t, Y^{\\varepsilon}_t)dt + \\frac{s(\\varepsilon)}{\\sqrt{\\varepsilon}} dW_t, \\end{eqnarray*} where $B_t, W_t$ are independent Brownian motions on ${\\mathbb R}^d$ and ${\\mathbb R}^m$ respectively, $b : \\mathbb{R}^d \\times \\mathbb{R}^m \\rightarrow \\mathbb{R}^d$, $U : \\mathbb{R}^d \\times \\mathbb{R}^m \\rightarrow \\ma","authors_text":"K. Suresh Kumar, Rajesh Sundaresan, Siva R. Athreya, Vivek S. Borkar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T17:23:55Z","title":"Simultaneous Small Noise Limit for Singularly Perturbed Slow-Fast Coupled Diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.03585","kind":"arxiv","version":2},"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":"sha256:45875414c594a06a0bb1be351ff33db2edc673ae3f736498e3bf173229e1c4c5","target":"record","created_at":"2026-05-18T00:03:14Z","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":"40724b7ebc18d4ffd2f7f18121a56464f6034471541d31d86209a425a153ab31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-08T17:23:55Z","title_canon_sha256":"a1a82a0389ffeaa49e772a2b624cc070420923857d3b48fcffd2f725669ceb49"},"schema_version":"1.0","source":{"id":"1810.03585","kind":"arxiv","version":2}},"canonical_sha256":"64f61b43cda68fdfe55f38745ac95d35a7343d574f2a456c30804b9d84ad47ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64f61b43cda68fdfe55f38745ac95d35a7343d574f2a456c30804b9d84ad47ae","first_computed_at":"2026-05-18T00:03:14.480840Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:14.480840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/EbbsPdugJVNhY6l9wQH/Gq7gvGOpP/C4cx9mMi735SGK8Rz9s5DYIQdBQIkiyLHWRTflpnwdQK8r/rf2B+3Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:14.481382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.03585","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45875414c594a06a0bb1be351ff33db2edc673ae3f736498e3bf173229e1c4c5","sha256:4e010c5f864a083ecf517fa61593573413b11033b706577cdf402b5c22f3b7ef"],"state_sha256":"ce2dbc196bc43fc9bbbc310a587114696ca39fa82d8f3bda5e3b929ff6e212c7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZ8jWG1N4oiNCCGhU/DcghpYQfLAYti4JHnrrA56qvF5+zDT7u/0TcBWKikF9sEYdcizfbinJU0iLt48cf0NCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T04:03:46.606862Z","bundle_sha256":"d0e18f9979e5acb489b3f5892f125ba4d83f522be8d04202dd184d4020cd09f6"}}