[ZacharyHendrix]

This fixes inconsistent sampler conditionals and incorrect saved posterior scores.

• Sampler: preserve calibrated background in brightness proposals, refresh accepted-position caches, prevent endpoint likelihood double counting, and keep the MSD conditional consistent with likelihood-only tempering.
• Scoring: correct the initial-position prior sign, include the brightness prior and count-dependent Gaussian normalizers, score the initial sample, and select finite MAP/MLE candidates with validated burn-in.
• Detector/activity: stabilize SPAD likelihood calculations, preserve binary activity masks, handle inactive 3D emitters, and exclude nonfinite masked pixels before reduction.

Validation on Windows x64 with Julia 1.12.6: Pkg.test() passed all 511 assertions, including 506 new regressions covering Float32/Float64, SPAD/EMCCD, activity masks, and zero-emitter cases.

An independent one-frame, one-emitter SPAD reference check jointly varied position and brightness. Three chains retained 80,000 draws each; all nine checked moments agreed with numerical integration within 1.109 batch Monte Carlo standard errors. Quadrature refinement and domain-extension checks passed.

GPU validation remains blocked: CUDA.jl compilation fails on a basic broadcast independently of SP2T. Extension loading succeeds, but numerical GPU validation is outstanding. Julia 1.11 and other platforms also need CI.

This draft covers core correctness; reconnection, unknown-count mixing, and broader scientific performance remain separate validation work.