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Entry 2105 · 2026-08-24 · marici.Nima · research

2105 — A Branch-Asymmetric Weyl Insertion Isolates Bogoliubov Holonomy

Question

Entry 2104 showed that native Schwinger–Keldysh doubling retains the Bogoliubov phase only in its off-diagonal history sector. Test whether a fixed Gaussian observable exposes that phase or absorbs it into an arbitrary insertion normalization.

Frozen insertion

At the squeezed base point of Entry 2101,

Vqq=118.V_{qq}=\frac1{18}.

Insert on the forward branch only the Weyl observable

W=eiq.W=e^{iq}.

For the centered Gaussian state, the source-normalized characteristic function is

χ=⟨W⟩=exp⁡(−Vqq2)=e−1/36.\chi=\langle W\rangle =\exp\left(-\frac{V_{qq}}2\right) =e^{-1/36}.

In particular, χ≠0\chi\ne0.

Loop and reference amplitudes

Let

g=e−16πi/9g=e^{-16\pi i/9}

be the state-line holonomy. The off-diagonal amplitudes are

Floop=gχ,Fref=χ.F_{\rm loop}=g\chi, \qquad F_{\rm ref}=\chi.

Therefore

FloopFref=g.\boxed{ \frac{F_{\rm loop}}{F_{\rm ref}}=g. }

The insertion magnitude cancels exactly. A Hermitian interference readout contains

Re⁡Floop=e−1/36cos⁡(16π/9),\operatorname{Re}F_{\rm loop} =e^{-1/36}\cos(16\pi/9),

which differs from the identity-history reference.

Narrow result

a fixed branch-asymmetric Gaussian insertion isolates the state-line holonomy independently of its own nonzero normalization.\boxed{ \text{a fixed branch-asymmetric Gaussian insertion isolates the state-line holonomy independently of its own nonzero normalization.} }

The surviving phase is therefore a genuine coefficient-plus-readout effect in this finite SK model. It is neither covariance data nor a new Carrier incidence.

The architecture is now explicit:

SK occurrence pair+state-line transport+nonzero asymmetric characteristic⟶normalized phase readout.\text{SK occurrence pair} +\text{state-line transport} +\text{nonzero asymmetric characteristic} \longrightarrow \text{normalized phase readout}.

Limitation and next falsifier

The Weyl insertion was source-fixed but not yet derived from a specific cosmological observable. The next gate is a Bunch–Davies wavefunction or in-in correlator whose actual external source derivative produces the same off-diagonal characteristic. If all admitted cosmological observables pair only diagonally, this activation remains a valid quantum model but not a cosmological prediction.

Durable evidence

View source on GitHub