{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TCB6ERXBRVO5GAIRQIVKEEKNCK","short_pith_number":"pith:TCB6ERXB","schema_version":"1.0","canonical_sha256":"9883e246e18d5dd30111822aa2114d12bf91670acd844c22c08b3c544a8ceab4","source":{"kind":"arxiv","id":"1705.08163","version":1},"attestation_state":"computed","paper":{"title":"Stochastic spikes and strong noise limits of stochastic differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Denis Bernard, Michel Bauer","submitted_at":"2017-05-23T10:17:18Z","abstract_excerpt":"Motivated by studies of indirect measurements in quantum mechanics, we investigate stochastic differential equations with a fixed point subject to an additional infinitesimal repulsive perturbation. We conjecture, and prove for an important class, that the solutions exhibit a universal behavior when time is rescaled appropriately: by fine-tuning of the time scale with the infinitesimal repulsive perturbation, the trajectories converge in a precise sense to spiky trajectories that can be reconstructed from an auxiliary time-homogeneous Poisson process. Our results are based on two main tools. T"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1705.08163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-05-23T10:17:18Z","cross_cats_sorted":["math.MP","math.PR"],"title_canon_sha256":"aca05ae193103cb68a11a1d4c1346965723f70331160d008b6d713fbf52a9143","abstract_canon_sha256":"dede3b1e843c7eb572c0b3ac68d70831005ebfe0ba6f55f4bfba0574660be370"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:41.402278Z","signature_b64":"W83Sj1YxdAil9a9IwA0sDou9qF/NhRTRnA69ZGd2qPXC3bthiemPjkAVd0UCB+OLQdA104LR21VpLEo4SGGEDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9883e246e18d5dd30111822aa2114d12bf91670acd844c22c08b3c544a8ceab4","last_reissued_at":"2026-05-18T00:10:41.401662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:41.401662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic spikes and strong noise limits of stochastic differential equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Denis Bernard, Michel Bauer","submitted_at":"2017-05-23T10:17:18Z","abstract_excerpt":"Motivated by studies of indirect measurements in quantum mechanics, we investigate stochastic differential equations with a fixed point subject to an additional infinitesimal repulsive perturbation. We conjecture, and prove for an important class, that the solutions exhibit a universal behavior when time is rescaled appropriately: by fine-tuning of the time scale with the infinitesimal repulsive perturbation, the trajectories converge in a precise sense to spiky trajectories that can be reconstructed from an auxiliary time-homogeneous Poisson process. Our results are based on two main tools. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08163","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1705.08163","created_at":"2026-05-18T00:10:41.401754+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.08163v1","created_at":"2026-05-18T00:10:41.401754+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.08163","created_at":"2026-05-18T00:10:41.401754+00:00"},{"alias_kind":"pith_short_12","alias_value":"TCB6ERXBRVO5","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TCB6ERXBRVO5GAIR","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TCB6ERXB","created_at":"2026-05-18T12:31:46.661854+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TCB6ERXBRVO5GAIRQIVKEEKNCK","json":"https://pith.science/pith/TCB6ERXBRVO5GAIRQIVKEEKNCK.json","graph_json":"https://pith.science/api/pith-number/TCB6ERXBRVO5GAIRQIVKEEKNCK/graph.json","events_json":"https://pith.science/api/pith-number/TCB6ERXBRVO5GAIRQIVKEEKNCK/events.json","paper":"https://pith.science/paper/TCB6ERXB"},"agent_actions":{"view_html":"https://pith.science/pith/TCB6ERXBRVO5GAIRQIVKEEKNCK","download_json":"https://pith.science/pith/TCB6ERXBRVO5GAIRQIVKEEKNCK.json","view_paper":"https://pith.science/paper/TCB6ERXB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.08163&json=true","fetch_graph":"https://pith.science/api/pith-number/TCB6ERXBRVO5GAIRQIVKEEKNCK/graph.json","fetch_events":"https://pith.science/api/pith-number/TCB6ERXBRVO5GAIRQIVKEEKNCK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TCB6ERXBRVO5GAIRQIVKEEKNCK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TCB6ERXBRVO5GAIRQIVKEEKNCK/action/storage_attestation","attest_author":"https://pith.science/pith/TCB6ERXBRVO5GAIRQIVKEEKNCK/action/author_attestation","sign_citation":"https://pith.science/pith/TCB6ERXBRVO5GAIRQIVKEEKNCK/action/citation_signature","submit_replication":"https://pith.science/pith/TCB6ERXBRVO5GAIRQIVKEEKNCK/action/replication_record"}},"created_at":"2026-05-18T00:10:41.401754+00:00","updated_at":"2026-05-18T00:10:41.401754+00:00"}