Conclusion

Conclusion

We have converted a structural question , is the observable tier the physical state space, or a faithful quotient of a larger one? , into a sequence of exact theorems, and we have marked the boundary at which the mathematics stops.

The strongest justified result is this. In any model that supplies a source domain reduced by its own declared physical equivalence, an exact readout, and a witness pair of gauge-inequivalent source states with the same readout but different correct answers to a nominated target, the readout is , relative to that model and that target , a non-source projection: no deterministic function of the readout answers the target, the minimal completion properly refines the readout, and every sufficient extension surjects onto it. Two ceilings then follow, from two separate hypotheses, and we have been careful to derive neither from the other. If every admissible internal probe factors through the readout, then within a fiber all probe values coincide, and no deterministic selector or post-processing of those values can recover the distinction. If, separately, the complete outcome law factors through the readout, then within a fiber the data laws are equal, and the stronger conclusion follows: no statistic, no randomized test, and no sample size can discriminate. If instead some further probe fails to factor through the readout , or some experiment’s law depends on the fiber coordinate , the distinction becomes, in principle, empirically discriminable, and Theorem 6.2 says precisely when.

What remains outside is equally definite. The mathematics does not supply the source domain, does not certify the physical equivalence, does not adjudicate which map deserves to be called the readout, and does not exhibit a witness. Those are the tasks of physical instantiation and empirical testing, as delimited in §10.4. We prove the model-relative theorem, sharply; we do not draw the unrestricted ontological conclusion, and no argument above supports it. The value of a boundary theorem lies in both of its sides.