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Moreover, for any stopping time T, the restriction of T to {T = σ_z^λ} is totally inaccessible, while its restriction to {T ≠ σ_z^λ} is predictable."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The analysis assumes the standard construction of Brownian motion with positive drift λ > 0 and the usual augmentation of the natural filtration generated by the stopped process ξ^λ,z; no additional regularity beyond continuity of paths is postulated."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"The last passage time of a drifted Brownian motion is the unique totally inaccessible stopping time in its stopped filtration; the extended process with an indicator of whether time is before the passage is Feller."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The last passage time of Brownian motion with positive drift is the unique totally inaccessible stopping time in the filtration of the stopped process."}],"snapshot_sha256":"b0d296ca7f80607a05245ad5bd95dddaa8d5bd3cf75b373e76eecbfb11055817"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"d0a838084676955933440e830c04a8ca01cb1153f6a41f4395546c551feda3eb"},"paper":{"abstract_excerpt":"We investigate the structural properties of the last passage time $\\sigma_z^{\\lambda}$ at level $z > 0$ of a Brownian motion with positive drift $\\lambda > 0$, denoted $B^{\\lambda} = (B_t + \\lambda t)_{t \\geq 0}$, in the filtration generated by the process $\\xi^{\\lambda,z} = (B^{\\lambda}_{t \\wedge \\sigma_z^{\\lambda}})_{t \\geq 0}$. 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