Conditional Classification of Projection-Based Effective Theories: Witness Records, Comparison Axes, and the Limits of Inevitability in Modal Triplet Theory

Irreversible records, ultraviolet control, event-like outcomes, and consistent matter sectors are genuine demands on physical theories. They do not, by themselves, force all viable theories into one mathematical universality class. The missing information is the mechanism: which states and operations are admitted, what is projected, what counts as recovery, which dynamics stabilizes records, how ultraviolet errors are controlled, how events are generated, and which global gauge and bundle data define the matter sector. This paper replaces an earlier inevitability claim by a conditional classification framework. A theory is represented by a seven-axis witness record covering operational measurement, descent and recovery, stability, ultraviolet control, event structure, gauge and matter data, and empirical validation. We prove five bounded results: noninjective descent has no left inverse; compact cores of open record regions have positive margins; transverse crossings are locally finite; representations of a specified compact U(1) have integer weights; and multi-axis equivalence classes refine monotonically as comparison requirements are added. Explicit counterexamples show why operational irreversibility need not mean algebraic noninvertibility, low-energy predictivity does not select smooth spectral damping, countable outcomes do not create a causal set, and local anomaly cancellation or charge quantization does not determine the observed Standard Model. Collapse models, monitored circuits, effective field theory, asymptotic safety, loop quantum gravity, causal sets, noncommutative geometry, and Modal Triplet Theory are therefore compared only through completed witness rows. The result is a falsifiable taxonomy and release-ready comparison protocol, not a proof that the apparent plurality of physical theories is illusory.