# Reality Revision 1.52 — phase is an ensemble property

The proposed “vibrational families” become testable only after separating an
isolated molecule from the interacting bulk system.

The isolated H2O fundamental vector (1595, 3657, 3756 cm^-1) is identical in
three frozen controls whose thermodynamic states are solid at 260 K, liquid at
298.15 K, and gas at 400 K, all at one atmosphere. Any deterministic rule that
uses only that identical vector must give all three the same label. On this
balanced control it can be correct at most once: 1/3 accuracy and 2/3 error.
Thus isolated molecular vibrations cannot uniquely determine phase.

Release 0.9.0 adds a collective spectrum

\[
F(\omega)=f_gF_g(\omega)+(1-f_g)F_s(\omega),
\quad F_g(0)>0,\ F_s(0)=0,
\]

motivated by primary velocity-autocorrelation and two-phase-thermodynamic work.
For fixed bases, \(f_g=F(0)/F_g(0)\). The engine recovers all 101 constructed
fractions with maximum error \(1.11\times10^{-16}\), while low-frequency
spectral mass rises monotonically. The solid-, liquid-, and gas-like reference
curves are distinguishable, but the full scan is continuous. No measured
boundary converts that coordinate into three universal phase boxes.

This corrects the theory: collective coupling, diffusion, temperature,
pressure, density, and free energy are candidate state variables. Vibrations
can diagnose those dynamics, but no single molecular frequency causes or
identifies phase. The curves are finite synthetic constructions anchored to
published water modes and argon parameters, not molecular dynamics or measured
condensed-phase spectra.

All 98 tests pass, and an independent scalar replay checks 2,401 spectral rows,
101 continuum states, three distances, and the exact counterexample. No result
establishes a physical fourth/fifth dimension, universal tick, or theological
cause. The next test is a frozen train/holdout molecular-dynamics experiment on
independently labeled thermodynamic state points.