3615 — Autocorrelation Polarization Is RH-Equivalent and Cannot Select a Spectral Factor
The strict radial-current theorem makes
equivalent to zero confinement. Without an independent source constructor, “zero-state polarization” is therefore RH rewritten rather than an intermediate lemma.
The deeper obstruction is spectral-factor ambiguity. The positive packets
P=1+2w and P#=2+w have identical boundary modulus, autocorrelation,
positive-real half-form, and current function, but reciprocal zeros -1/2
and -2. Reversing any finite real packet preserves all autocorrelations while
reciprocating its divisor.
Hence autocorrelation machinery cannot select the physical factor. The next noncircular target is a theta-labelled phase port distinguishing the completed factor from its reciprocal reverse and compatible with modular sewing.
Checker result: 22/22 exact gates passed.
Artifact:
research/grothendieck/autocorrelation-polarization-is-rh-equivalent-and-cannot-select-a-spectral-factor.md.