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This is a classical object well known in Variational Calculus, Mathematical Statistics, etc. We show that the energy of this taut string on large intervals is equivalent to $C^2 T\\, /\\, r^2$ where $C$ is some finite positive constant. While the precise value of $C$ remains unknown, we give various theoretical bounds for it as well as rather precise results of computer simulation.\n  While the taut"},"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":"1405.1651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-07T15:55:28Z","cross_cats_sorted":[],"title_canon_sha256":"3e9b369394fbde3d125e651eb7500813554bdf560cf4488edad72606c8237d5e","abstract_canon_sha256":"bc6518310d807fed6c0c58de327c0d12fa7f79c6b9b1bb25c30be6780e525683"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:37.684987Z","signature_b64":"EQrqK/DIfLkBm5voWoSP23xaXhjurLwYGBxR+o6AyeMNtNsrp7XpEhoWXlp/iczREUy2je2xk5pZEthu9Y9uDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"da1a57faff441bdceb7f50664f2a4a757f7630e9af1db827affe05e9acf5c4a3","last_reissued_at":"2026-05-17T23:41:37.684394Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:37.684394Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Energy of taut strings accompanying Wiener process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eric Setterqvist, Mikhail Lifshits","submitted_at":"2014-05-07T15:55:28Z","abstract_excerpt":"Let $W$ be a Wiener process. 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