Quantum gravity in PT: from sieve to ringdown

The usual conflict comes from asking the wrong question: should the continuum be quantized, or should the discrete manufacture the continuum? The PT reading says something else: there is a continuous wave mechanics, and the sieve marks its points of persistence.

In plain language: think of a wave whose specific places become stable, like nodes or resonances. The sieve does not replace the wave; it indicates the positions, channels, and closures where that wave becomes readable.

On this reading, the question is no longer “how do we quantize the metric?”, but “why does this continuous mechanics select precisely these remarkable points?”. PT quantum gravity is therefore a theory of persistent selection.

The classical sector comes from informational geometry: the distribution family of the sieve carries a Fisher metric $g^F$, then the active restriction gives Fisher-Bianchi geometry, Lorentzian signature, and Einstein equations.

The minimal quantum sector adds dynamics: transfer matrices $T_m$ define the CRT Hilbert space, canonical constraints select persistent states, and boundary amplitudes give the covariant version of the calculation.

The decisive conceptual point is the dissolution of the “continuum limit”. PT does not start from a geometric mesh whose spacing must go to zero: it starts from a continuous mechanics of phase, metric, and holonomy, whose persistent points are marked by the sieve.

For black holes, ringdown becomes a selection observable. Kerr phase follows a spin half-holonomy; the dissipative $d\tau$ channel is read as a surface-gravity candidate, still to be separated from start-time and overtone effects.

The technical level unfolds the chain without shortcuts: continuous Fisher/holonomy mechanics, selection of persistent points by the sieve, CRT Hilbert space, GR sector, constraints, covariant amplitudes, foams, then Kerr observables. Every step preserves the same PT logic: exclusion of self-copying, spin involution, boundary covariance, and persistence of admissible channels.

The continuous support is $g^F$ with its associated phases and holonomies. It is defined on the distribution family and directly gives informational geometry: the wave-like support on which channels are read.

Discrete selection is carried by $T_m$. By CRT, it marks remarkable points of this continuous mechanics, factorizes into primes, and supplies a tensor structure. The inductive limit $\mathcal H_\infty=\varinjlim\bigotimes_p\mathcal H_p$ preserves these persistent selections without postulating primitive continuous spacetime.

Covariance requires the amplitude not to depend on an arbitrary history slicing. Arbitrary-boundary amplitudes compose, the finite Dirac algebra lifts cylindrically, and topology changes remain physical foams when they respect admissible channels.

The test observable is Kerr. The macroscopic selector uses $M\Omega_H(a)=a/(2(1+\sqrt{1-a^2}))$ and forces the phase correction $\phi(a)=\phi_0+\pi M\Omega_H(a)$, hence $M\omega(a)=M\omega_0+\Omega_H(a)/2$.