{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NOTQJRBWC4L2NQACXLTEUCRIVY","short_pith_number":"pith:NOTQJRBW","schema_version":"1.0","canonical_sha256":"6ba704c4361717a6c002bae64a0a28ae2868e35dea4c94464f64707296bf566d","source":{"kind":"arxiv","id":"1507.06238","version":1},"attestation_state":"computed","paper":{"title":"The Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Kay Joerg Wiese, Mathieu Delorme","submitted_at":"2015-07-22T16:10:14Z","abstract_excerpt":"Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the process and the time $t_{\\rm max}$ at which the maximum is reached. They are encoded in a path integral, which we evaluate perturbatively around a Brownian, setting $H=1/2 + \\varepsilon$. This allows us to derive analytic results beyond the scaling exponents. Extensive numerical simulations for different values of $H$ test these analytical predictions and show "},"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":"1507.06238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-07-22T16:10:14Z","cross_cats_sorted":[],"title_canon_sha256":"e7c9266a3e2853ff99583155f18219b2ff02b3f71ed19f13c3963f581e6929ff","abstract_canon_sha256":"9bca217488e0b7ce92293731b69c5116bc9e8455894ce0f20f7265374cbfc770"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:09.859059Z","signature_b64":"4pn7fLwnsWjPMALm8pkUo/NqZolX3kaZhuFLGzAwlG4MhKlW0lUcEGSL+mxXH5JLXzYfAvlahtUD4t1Cq50UCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ba704c4361717a6c002bae64a0a28ae2868e35dea4c94464f64707296bf566d","last_reissued_at":"2026-05-18T01:26:09.858273Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:09.858273Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Kay Joerg Wiese, Mathieu Delorme","submitted_at":"2015-07-22T16:10:14Z","abstract_excerpt":"Fractional Brownian motion is a non-Markovian Gaussian process $X_t$, indexed by the Hurst exponent $H$. It generalises standard Brownian motion (corresponding to $H=1/2$). We study the probability distribution of the maximum $m$ of the process and the time $t_{\\rm max}$ at which the maximum is reached. They are encoded in a path integral, which we evaluate perturbatively around a Brownian, setting $H=1/2 + \\varepsilon$. This allows us to derive analytic results beyond the scaling exponents. Extensive numerical simulations for different values of $H$ test these analytical predictions and show "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06238","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":"1507.06238","created_at":"2026-05-18T01:26:09.858546+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.06238v1","created_at":"2026-05-18T01:26:09.858546+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06238","created_at":"2026-05-18T01:26:09.858546+00:00"},{"alias_kind":"pith_short_12","alias_value":"NOTQJRBWC4L2","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NOTQJRBWC4L2NQAC","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NOTQJRBW","created_at":"2026-05-18T12:29:34.919912+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/NOTQJRBWC4L2NQACXLTEUCRIVY","json":"https://pith.science/pith/NOTQJRBWC4L2NQACXLTEUCRIVY.json","graph_json":"https://pith.science/api/pith-number/NOTQJRBWC4L2NQACXLTEUCRIVY/graph.json","events_json":"https://pith.science/api/pith-number/NOTQJRBWC4L2NQACXLTEUCRIVY/events.json","paper":"https://pith.science/paper/NOTQJRBW"},"agent_actions":{"view_html":"https://pith.science/pith/NOTQJRBWC4L2NQACXLTEUCRIVY","download_json":"https://pith.science/pith/NOTQJRBWC4L2NQACXLTEUCRIVY.json","view_paper":"https://pith.science/paper/NOTQJRBW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.06238&json=true","fetch_graph":"https://pith.science/api/pith-number/NOTQJRBWC4L2NQACXLTEUCRIVY/graph.json","fetch_events":"https://pith.science/api/pith-number/NOTQJRBWC4L2NQACXLTEUCRIVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NOTQJRBWC4L2NQACXLTEUCRIVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NOTQJRBWC4L2NQACXLTEUCRIVY/action/storage_attestation","attest_author":"https://pith.science/pith/NOTQJRBWC4L2NQACXLTEUCRIVY/action/author_attestation","sign_citation":"https://pith.science/pith/NOTQJRBWC4L2NQACXLTEUCRIVY/action/citation_signature","submit_replication":"https://pith.science/pith/NOTQJRBWC4L2NQACXLTEUCRIVY/action/replication_record"}},"created_at":"2026-05-18T01:26:09.858546+00:00","updated_at":"2026-05-18T01:26:09.858546+00:00"}