{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"0e0bdc21076860a94c698a215f972145566be4903a1532d27b47de30df8201f3","created":"2026-10-03T07:18:07Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011","b9ac9f44652a99795b9547ff2d404bfa7120d276ceb5cc641d745b4bcd729558"],"salt":"a76c28df2cfdd7efb78c777c0802ce5a908873f8254d2d26c14d32acd926623f","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"med.pet.statistical-bound","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[{"note":"","parent_revision":"b9ac9f44652a99795b9547ff2d404bfa7120d276ceb5cc641d745b4bcd729558","relation":"special_case"}],"plain":"Light arrives at the sensor at random times, which sets a floor on how precisely the arrival can be timed. The exact floor for realistic detectors is not established.","posed_since":"2012","precise":"Derive the Cramer-Rao lower bound (the minimum variance any unbiased estimator can reach) on timing precision for a scintillation detector including non-exponential rise and decay, position-dependent light transport inside the crystal, photodetector single-photon time response and dark counts, and construct an estimator reaching it. An answer is the bound as a function of photon yield, rise time, decay time and transit-time spread, plus a realizable estimator.","problem_ref":null,"references":"","settled_by":"A derivation with an estimator demonstrated in simulation and on bench data to approach the bound.","status_note":"Bounds exist for simplified emission models since Seifert, van Dam and Schaart (2012); the realistic transport case was not closed as of 2025.","title":"Fundamental bound on scintillation timing","topic_ref":"82c46a639f6fd1f2c6c4e5f93efaf610a76f3cc0784379dd43df49391264c57d"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"9109dc573c3c9aee78d134c3e68700a2d25898a12946e47b5c68c1ca587422b6","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"1273f2245a1df7b8087cd1522427b13b0f4768e29cea57918c7c80706f18f81e","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"AelEjYBGqgm5ZCBfqKAP0YUYb7Yz8JSeg8cM555opkIylBHPe9TsQnEQ2kOfYdanFzlFO46ASyVucm-FsJsXCw"},"schema":"pubphys.envelope/1"},"record_hash":"9109dc573c3c9aee78d134c3e68700a2d25898a12946e47b5c68c1ca587422b6","leaf_index":1718}