---
{
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"title": "OP-QM-004 · Dynamical Origin of Born Statistics",
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---
## Established results
A linearly driven detector’s mean absorbed power is proportional to the envelope modulus squared. Fixed energy per event and negligible leakage, dead time and saturation give an event rate and a conditional position distribution after time/thickness integration. The manuscript also supplies phase-flow equivariance and a nonlinear detector-response expansion. These are established results within their stated conditions.
## Research still required
Build nonlinear competition dynamics for the core, accompanying field and detector array to obtain one record per excitation. Test relaxation toward a Born-type distribution from independently specified initial ensembles, retaining efficiency, normal-flux weighting, time windows and noise calibration.
## The next reproducible deliverable
First deliver a complete response model, conservation accounting, event definition and calibration for one detector. Provide a proof, numerical result or counterexample for single-record exclusivity and initial-state convergence, without using the target probability as a preset sampling rule.
## Scope and research links
Equivariance preserves an already matched initial ensemble; it does not prove convergence from arbitrary ensembles. Uniform efficiency alone also does not remove a varying normal-flow velocity from the count distribution.
[detection statistics](/en/theory/quantum/detection-statistics) · [master equation](/en/theory/space-dynamics/master-equation) · [detection statistics](/en/theory/quantum/detection-statistics) · [electron solution](/en/open-problems/matter/electron-solution) · [master equation](/en/theory/space-dynamics/master-equation) · [quantum](/en/theory/quantum)