A realistic two-quadrature seam experiment

Date: 24 October 2026 Status: buildable interface experiment with preregistered observables; tests the seam carrier, not new gravity Evidence: machine-readable protocol Certificate: signal-model verifier

Purpose

Test the exact prediction of the sewing-response gate:

a coherent two-quadrature detector can retain an orientation-odd seam amplitude that a power-only detector necessarily squares away.

This is a test of the proposed interface type. Conventional coupled-mode theory predicts the basic effect, so observing it is theoretical engineering rather than evidence for new physics. Its value is to establish a calibrated physical carrier on which the stronger corpus intertwiners can later be tested.

Preferred platform

Use two coupled microwave resonators with a parametrically controlled complex coupling

\[ \epsilon=g_x+i g_y=r e^{i\phi}. \]

A vector network analyser or coherent microwave source plus IQ mixer measures the complex transmission amplitude. Tunable superconducting-resonator couplers and phase-sensitive microwave detection are established technologies; an optical Mach--Zehnder or programmable photonic mesh with balanced homodyne readout is a direct alternative.

The minimal effective model is

\[ H_{\rm eff}= \begin{pmatrix} \omega_1-i\kappa_1/2 & \epsilon\\ \epsilon^* & \omega_2-i\kappa_2/2 \end{pmatrix}. \]

The two independently programmed pump quadratures set \(g_x\) and \(g_y\). The seam reversal is implemented by shifting the pump phase by \(\pi\):

\[ \epsilon\longmapsto-\epsilon. \]

Measurement channels

Calibrate the background and extract the complex seam-dependent amplitude

\[ A_{\rm seam}=c\,\epsilon+O(|\epsilon|^2). \]

Measure two records from the same acquisition.

Orientation-even control

\[ P_{\rm even}=|A_{\rm seam}|^2 =|c|^2r^2+O(r^3). \]

It is unchanged under \(\epsilon\mapsto-\epsilon\).

Orientation-odd record

With a coherent reference \(A_{\rm ref}=|A_{\rm ref}|e^{i\theta}\), record

\[ X_\theta =2\operatorname{Re}(A_{\rm ref}^*A_{\rm seam}). \]

The antisymmetrized statistic

\[ D_{\rm odd} =\frac{X_\theta(+\epsilon)-X_\theta(-\epsilon)}{2} \]

is linear in \(r\), reverses sign with the seam, and varies sinusoidally with \(\phi-\theta\).

Run matrix

For each radius \(r\), acquire a randomized sequence over

\[ \phi\in \left\{ 0,\frac{\pi}{2},\pi,\frac{3\pi}{2} \right\}, \]

plus:

reference on and reference off;
\(+\epsilon\) and \(-\epsilon\);
both quadratures, \(g_x\)-only and \(g_y\)-only;
coherent averaging and deliberately phase-scrambled averaging;
coupled device and coupling-disabled baseline.

Use at least five nonzero radii spanning the linear-response range and repeat the full randomized block across multiple thermal/drift cycles.

Preregistered fits

Fit

\[ D_{\rm odd}(r,\phi) =\alpha r\cos(\phi-\phi_0)+\alpha_3r^3+\cdots \]

and

\[ P_{\rm even}(r) =\beta r^2+\beta_4r^4+\cdots. \]

The interface passes only if:

\(D_{\rm odd}\) is linear at small \(r\) and reverses under \(\epsilon\mapsto-\epsilon\);
its fitted phase follows the programmed pump phase;
it vanishes under reference removal or phase scrambling;
\(P_{\rm even}\) is unchanged by seam reversal and begins quadratically;
the result survives a held-out calibration block and a second readout phase.

Nuisance model

Fit or independently calibrate:

IQ gain imbalance and quadrature skew;
cable delay and reference-phase drift;
direct feedthrough around the resonators;
unequal linewidths and detuning;
pump leakage into the readout;
amplifier compression;
nonreciprocal or dissipative coupling;
slow temperature and bias drift.

The primary falsifier is a purported odd record reproduced by IQ leakage from the even power channel. Phase scrambling and reference-off runs directly test that failure.

The two-resonator transfer preflight adds a second essential control. Coherent direct feedthrough can manufacture a linear odd term in raw power. Measuring and subtracting the coupling-disabled complex baseline removes that false channel while retaining the calibrated homodyne reference.

Interpretation ladder

Outcome	Meaning
odd channel absent after calibration	this implementation does not retain the seam
odd channel present but removable by port rephasing	ordinary convention-dependent coherent response
odd channel obeys the full run matrix	operational two-quadrature seam carrier
response additionally follows a source-derived modular/Leech parameter map with no refit	evidence for the proposed mathematical interface
unexplained residual survives the complete conventional model and independent replication	candidate anomaly requiring a new-physics audit

The first successful experiment should be expected to stop at the third row. That is still useful: it builds the detector required by the theory without claiming the theory has already supplied the coupling.

The two-mode phase-gauge gate further limits that interpretation. A single complex coupling phase is removable inside an isolated two-mode Hamiltonian. The measured odd phase is meaningful relative to the pump and local oscillator; an intrinsic device phase requires a closed three-mode coupling loop.

Existing technical precedents

Peropadre et al., tunable complex couplings and effective gauge fields between superconducting resonators
Taballione et al., a fully tunable twelve-mode photonic interferometer
Tuite and Zuevsky, genus-two fermionic sewing

A realistic two-quadrature seam experiment

Route into this page

A realistic two-quadrature seam experiment

Purpose

Preferred platform

Measurement channels

Orientation-even control

Orientation-odd record

Run matrix

Preregistered fits

Nuisance model

Interpretation ladder

Existing technical precedents

Inbound corpus links

Outgoing corpus links