# The relative nuclear energy controls the rate

The three-alpha threshold defines zero energy. The published derivative changes the Hoyle energy relative to that threshold. A common translation is an analytic null. Separate absolute threshold motions are not available for every nuclear scenario and are not invented here. Stellar temperature is held fixed.

A moving cursor connects a small relative energy shift with the exponential triple-alpha rate response; the common-translation control stays at zero.

## T = 0.1 GK; response 3.9 MeV

Radiative width fixed. Response scenarios are the published central coefficient and ± one reported error, not a joint nuclear posterior.

First: Alpha displacement -200 ppm; E_R = 378.5423 keV; fixed-temperature rate / baseline = 1.09475. This slider is a parameter scan, not physical time.

Last: Alpha displacement +200 ppm; E_R = 380.1023 keV; fixed-temperature rate / baseline = 0.91347. This slider is a parameter scan, not physical time.

## T = 0.1 GK; response 3.99 MeV

Radiative width fixed. Response scenarios are the published central coefficient and ± one reported error, not a joint nuclear posterior.

First: Alpha displacement -200 ppm; E_R = 378.5243 keV; fixed-temperature rate / baseline = 1.09704. This slider is a parameter scan, not physical time.

Last: Alpha displacement +200 ppm; E_R = 380.1203 keV; fixed-temperature rate / baseline = 0.91156. This slider is a parameter scan, not physical time.

## T = 0.1 GK; response 4.08 MeV

Radiative width fixed. Response scenarios are the published central coefficient and ± one reported error, not a joint nuclear posterior.

First: Alpha displacement -200 ppm; E_R = 378.5063 keV; fixed-temperature rate / baseline = 1.09933. This slider is a parameter scan, not physical time.

Last: Alpha displacement +200 ppm; E_R = 380.1383 keV; fixed-temperature rate / baseline = 0.90966. This slider is a parameter scan, not physical time.

## T = 0.2 GK; response 3.9 MeV

Radiative width fixed. Response scenarios are the published central coefficient and ± one reported error, not a joint nuclear posterior.

First: Alpha displacement -200 ppm; E_R = 378.5423 keV; fixed-temperature rate / baseline = 1.04630. This slider is a parameter scan, not physical time.

Last: Alpha displacement +200 ppm; E_R = 380.1023 keV; fixed-temperature rate / baseline = 0.95576. This slider is a parameter scan, not physical time.

## T = 0.2 GK; response 3.99 MeV

Radiative width fixed. Response scenarios are the published central coefficient and ± one reported error, not a joint nuclear posterior.

First: Alpha displacement -200 ppm; E_R = 378.5243 keV; fixed-temperature rate / baseline = 1.04740. This slider is a parameter scan, not physical time.

Last: Alpha displacement +200 ppm; E_R = 380.1203 keV; fixed-temperature rate / baseline = 0.95476. This slider is a parameter scan, not physical time.

## T = 0.2 GK; response 4.08 MeV

Radiative width fixed. Response scenarios are the published central coefficient and ± one reported error, not a joint nuclear posterior.

First: Alpha displacement -200 ppm; E_R = 378.5063 keV; fixed-temperature rate / baseline = 1.04849. This slider is a parameter scan, not physical time.

Last: Alpha displacement +200 ppm; E_R = 380.1383 keV; fixed-temperature rate / baseline = 0.95376. This slider is a parameter scan, not physical time.

## T = 0.3 GK; response 3.9 MeV

Radiative width fixed. Response scenarios are the published central coefficient and ± one reported error, not a joint nuclear posterior.

First: Alpha displacement -200 ppm; E_R = 378.5423 keV; fixed-temperature rate / baseline = 1.03063. This slider is a parameter scan, not physical time.

Last: Alpha displacement +200 ppm; E_R = 380.1023 keV; fixed-temperature rate / baseline = 0.97028. This slider is a parameter scan, not physical time.

## T = 0.3 GK; response 3.99 MeV

Radiative width fixed. Response scenarios are the published central coefficient and ± one reported error, not a joint nuclear posterior.

First: Alpha displacement -200 ppm; E_R = 378.5243 keV; fixed-temperature rate / baseline = 1.03135. This slider is a parameter scan, not physical time.

Last: Alpha displacement +200 ppm; E_R = 380.1203 keV; fixed-temperature rate / baseline = 0.96961. This slider is a parameter scan, not physical time.

## T = 0.3 GK; response 4.08 MeV

Radiative width fixed. Response scenarios are the published central coefficient and ± one reported error, not a joint nuclear posterior.

First: Alpha displacement -200 ppm; E_R = 378.5063 keV; fixed-temperature rate / baseline = 1.03207. This slider is a parameter scan, not physical time.

Last: Alpha displacement +200 ppm; E_R = 380.1383 keV; fixed-temperature rate / baseline = 0.96893. This slider is a parameter scan, not physical time.