{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:FTVOH7LA72537MF74MW3DH3QXH","short_pith_number":"pith:FTVOH7LA","schema_version":"1.0","canonical_sha256":"2ceae3fd60febbbfb0bfe32db19f70b9f991008edc52dd893d15d0791f84db10","source":{"kind":"arxiv","id":"1509.07343","version":1},"attestation_state":"computed","paper":{"title":"Renewal Structure of the Brownian Taut String","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Schertzer","submitted_at":"2015-09-24T12:39:49Z","abstract_excerpt":"In a recent paper, M. Lifshits and E. Setterqvist introduced the taut string of a Brownian motion $w$, defined as the function of minimal quadratic energy on $[0,T]$ staying in a tube of fixed width $h>0$ around $w$. The authors showed a Law of Large Number (L.L.N.) for the quadratic energy spent by the string for a large time $T$.\n  In this note, we exhibit a natural renewal structure for the Brownian taut string, which is directly related to the time decomposition of the Brownian motion in terms of its $h$-extrema (as first introduced by Neveu and Pitman). Using this renewal structure, we de"},"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":"1509.07343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-24T12:39:49Z","cross_cats_sorted":[],"title_canon_sha256":"b726bf08385d8e648680ad8b830fce09a967b63cc209c29724e31d101bcb1ed4","abstract_canon_sha256":"ed90a41c81cdb805e69ef28695238d450bfd92fb158b45850a6e535ba04c55dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:09.245088Z","signature_b64":"Zv2D6OHyQ0TNrhPEUl7A4vXLn7vn8Y5eNmO23bnAlusG7wXVBTOH5yi3XuspKLqn5w40ZgwZ/38VN8cMDWTJCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ceae3fd60febbbfb0bfe32db19f70b9f991008edc52dd893d15d0791f84db10","last_reissued_at":"2026-05-18T01:32:09.244508Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:09.244508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Renewal Structure of the Brownian Taut String","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Schertzer","submitted_at":"2015-09-24T12:39:49Z","abstract_excerpt":"In a recent paper, M. Lifshits and E. Setterqvist introduced the taut string of a Brownian motion $w$, defined as the function of minimal quadratic energy on $[0,T]$ staying in a tube of fixed width $h>0$ around $w$. The authors showed a Law of Large Number (L.L.N.) for the quadratic energy spent by the string for a large time $T$.\n  In this note, we exhibit a natural renewal structure for the Brownian taut string, which is directly related to the time decomposition of the Brownian motion in terms of its $h$-extrema (as first introduced by Neveu and Pitman). Using this renewal structure, we de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07343","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":"1509.07343","created_at":"2026-05-18T01:32:09.244604+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.07343v1","created_at":"2026-05-18T01:32:09.244604+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07343","created_at":"2026-05-18T01:32:09.244604+00:00"},{"alias_kind":"pith_short_12","alias_value":"FTVOH7LA7253","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"FTVOH7LA72537MF7","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"FTVOH7LA","created_at":"2026-05-18T12:29:22.688609+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/FTVOH7LA72537MF74MW3DH3QXH","json":"https://pith.science/pith/FTVOH7LA72537MF74MW3DH3QXH.json","graph_json":"https://pith.science/api/pith-number/FTVOH7LA72537MF74MW3DH3QXH/graph.json","events_json":"https://pith.science/api/pith-number/FTVOH7LA72537MF74MW3DH3QXH/events.json","paper":"https://pith.science/paper/FTVOH7LA"},"agent_actions":{"view_html":"https://pith.science/pith/FTVOH7LA72537MF74MW3DH3QXH","download_json":"https://pith.science/pith/FTVOH7LA72537MF74MW3DH3QXH.json","view_paper":"https://pith.science/paper/FTVOH7LA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.07343&json=true","fetch_graph":"https://pith.science/api/pith-number/FTVOH7LA72537MF74MW3DH3QXH/graph.json","fetch_events":"https://pith.science/api/pith-number/FTVOH7LA72537MF74MW3DH3QXH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FTVOH7LA72537MF74MW3DH3QXH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FTVOH7LA72537MF74MW3DH3QXH/action/storage_attestation","attest_author":"https://pith.science/pith/FTVOH7LA72537MF74MW3DH3QXH/action/author_attestation","sign_citation":"https://pith.science/pith/FTVOH7LA72537MF74MW3DH3QXH/action/citation_signature","submit_replication":"https://pith.science/pith/FTVOH7LA72537MF74MW3DH3QXH/action/replication_record"}},"created_at":"2026-05-18T01:32:09.244604+00:00","updated_at":"2026-05-18T01:32:09.244604+00:00"}