Conclusion

Conclusion

Reversible finite Gaussian dynamics can prepare a writer conditionally on its complete retained archive for a broad, explicitly non-Born class of original laws. The exact smooth map is essential: fine archive information invalidates an unrestricted writer-only premise, while full conditional physical scores and actual moments yield constructive quantitative bounds without a density cap. The same parent supports a separate physical receiver and an input-uniform finite-internal-reference instrument. These are positive mathematical results with identifiable statistical and control premises. Establishing those premises independently in a material apparatus, and extending the argument to repeated unknown inputs and arbitrary positional references, remain distinct scientific tasks.