# A boundary evolved in physical time

This is the saved Lorentzian evolution, initialized from a tunneling solution. Euclidean radius is not used as a clock. The flat-space calculation includes field energy but no material medium or collisions; the independently calculated stellar screening profile is in V10.

An expanding spherical boundary moves through fixed radii; a second graph records the field measured by a stationary probe.

## Bias 0.04; probe radius 5

Real Lorentzian spherical evolution from a stationary initial bubble, with refined grids. The time unit is 1.86×10⁻²⁶ s at lambda=0.125, f=100 GeV.

First: Real time = 0.000 / (sqrt(lambda) f); fixed probe r = 5, local field = -1.00000.

Last: Real time = 20.000 / (sqrt(lambda) f); fixed probe r = 5, local field = -1.00000.

## Bias 0.04; probe radius 10

Real Lorentzian spherical evolution from a stationary initial bubble, with refined grids. The time unit is 1.86×10⁻²⁶ s at lambda=0.125, f=100 GeV.

First: Real time = 0.000 / (sqrt(lambda) f); fixed probe r = 10, local field = -1.00000.

Last: Real time = 20.000 / (sqrt(lambda) f); fixed probe r = 10, local field = -1.00000.

## Bias 0.04; probe radius 20

Real Lorentzian spherical evolution from a stationary initial bubble, with refined grids. The time unit is 1.86×10⁻²⁶ s at lambda=0.125, f=100 GeV.

First: Real time = 0.000 / (sqrt(lambda) f); fixed probe r = 20, local field = -1.00000.

Last: Real time = 20.000 / (sqrt(lambda) f); fixed probe r = 20, local field = -1.00000.

## Bias 0.2; probe radius 5

Real Lorentzian spherical evolution from a stationary initial bubble, with refined grids. The time unit is 1.86×10⁻²⁶ s at lambda=0.125, f=100 GeV.

First: Real time = 0.000 / (sqrt(lambda) f); fixed probe r = 5, local field = -0.99999.

Last: Real time = 20.000 / (sqrt(lambda) f); fixed probe r = 5, local field = -1.00000.

## Bias 0.2; probe radius 10

Real Lorentzian spherical evolution from a stationary initial bubble, with refined grids. The time unit is 1.86×10⁻²⁶ s at lambda=0.125, f=100 GeV.

First: Real time = 0.000 / (sqrt(lambda) f); fixed probe r = 10, local field = -0.99291.

Last: Real time = 20.000 / (sqrt(lambda) f); fixed probe r = 10, local field = -1.00002.

## Bias 0.2; probe radius 20

Real Lorentzian spherical evolution from a stationary initial bubble, with refined grids. The time unit is 1.86×10⁻²⁶ s at lambda=0.125, f=100 GeV.

First: Real time = 0.000 / (sqrt(lambda) f); fixed probe r = 20, local field = +0.99949.

Last: Real time = 20.000 / (sqrt(lambda) f); fixed probe r = 20, local field = -1.00000.

## Bias 1; probe radius 5

Real Lorentzian spherical evolution from a stationary initial bubble, with refined grids. The time unit is 1.86×10⁻²⁶ s at lambda=0.125, f=100 GeV.

First: Real time = 0.000 / (sqrt(lambda) f); fixed probe r = 5, local field = +0.89901.

Last: Real time = 20.000 / (sqrt(lambda) f); fixed probe r = 5, local field = -1.00113.

## Bias 1; probe radius 10

Real Lorentzian spherical evolution from a stationary initial bubble, with refined grids. The time unit is 1.86×10⁻²⁶ s at lambda=0.125, f=100 GeV.

First: Real time = 0.000 / (sqrt(lambda) f); fixed probe r = 10, local field = +0.99890.

Last: Real time = 20.000 / (sqrt(lambda) f); fixed probe r = 10, local field = -1.00308.

## Bias 1; probe radius 20

Real Lorentzian spherical evolution from a stationary initial bubble, with refined grids. The time unit is 1.86×10⁻²⁶ s at lambda=0.125, f=100 GeV.

First: Real time = 0.000 / (sqrt(lambda) f); fixed probe r = 20, local field = +1.00000.

Last: Real time = 20.000 / (sqrt(lambda) f); fixed probe r = 20, local field = -0.43417.