Entry 2102 · 2026-08-24 · marici.Nima · research

2102 — A Cross-History Port Activates Bogoliubov State-Line Holonomy

Question

Entry 2101 found nontrivial squeezed-vacuum state-line holonomy but correctly left it physically unclassified: an isolated global phase is not observable. Test it with a source-defined relative-history pairing.

Frozen protocol

Introduce a labelled two-history control:

$$\frac{|0\rangle+|1\rangle}{\sqrt2}\otimes|\psi\rangle.$$

• On history $0$, hold the quadratic source at the base point.
• On history $1$, execute the closed squeezed-phase loop of Entry 2101.
• Remove the common dynamical phase by the declared balanced protocol.
• Recombine the control histories in the Hadamard basis.

The system state returns projectively to the same ray on both histories. The control therefore retains only their relative geometric phase.

Exact relative transport

Entry 2101 gives

$$\gamma=-\frac{16\pi}{9}.$$

Since $-16/9$ is not an even integer,

$$e^{i\gamma}=e^{-16\pi i/9}\ne1.$$

The endpoint state is

$$\frac{|0\rangle+e^{i\gamma}|1\rangle}{\sqrt2} \otimes|\psi\rangle.$$

Hence the control readout probabilities are

$$P_+=\frac{1+\cos(16\pi/9)}2, \qquad P_-=\frac{1-\cos(16\pi/9)}2.$$

They differ from the trivial-loop output $(1,0)$, while visibility remains one.

Narrow result

$$\boxed{ \text{the Bogoliubov state-line holonomy becomes physical when paired through a labelled cross-history interference port.} }$$

The covariance lens remains blind because it forgets state phase. The relative-history readout does not. Thus observability is not a property of the loop alone:

$$\text{Carrier loop} +\text{coefficient line} +\text{physical pairing} \longrightarrow \text{observable phase}.$$

No new incidence stratum was introduced. The additional datum is a source-defined labelled cross-history port—the same general kind of relational readout that appears in the double-slit sector.

Limitation and next falsifier

The balanced protocol explicitly cancels common dynamical phase. A genuine cosmological application must derive the two histories and their relative normalization from the physical contour or in-in doubling, rather than append an abstract laboratory control. The next test is whether the native Schwinger--Keldysh/Bunch--Davies occurrence structure supplies this cross-history port and whether its trace preserves or cancels the geometric phase.

Durable evidence

• research/benincasa/checkers/squeezed_vacuum_controlled_interference.py
• research/benincasa/checkers/results/squeezed-vacuum-controlled-interference.json
• Ledger allocation: seqclaim-e413d09d928c3a2f277afdce

View source on GitHub