Animations from the calculations

Every animation starts paused and provides a time or parameter slider, static export, data, and text description.

Figure gallery · Technical report

A01 · The relative nuclear energy controls the rate

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

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.

A02 · Composition and the burning clock

Baseline and perturbed helium, carbon and oxygen fractions can be compared at the same elapsed time or helium depletion. Density compensation nearly restores composition while changing the clock.

Stored parcel trajectories are linearly sampled in physical time, preserving nonnegative mass fractions and the baryon invariant. The density-compensated case raises the resonance by 39.9 keV and increases density by the derived exponential factor. It is a controlled parcel identity, not a stellar density prediction.

A03 · A boundary evolved in physical time

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

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.

A04 · Conditioning selects histories

The upper graph identifies included realizations. The lower graph compares their nearby phase statistics with the unconditioned ensemble, including a past-light-cone view.

Each dot is one saved random realization, not an invented civilization or a map cell. Selection changes the statistical sample. Past-light-cone mode evaluates the target at emission and applies the same duration requirement. These are opportunity diagnostics without a measured emergence law.

A05 · Slow and rapid molecular passages

A moving cursor shows the computed H2 excited population and matching molecular energy change and background work. The population scale is fixed across slow and rapid cases.

A time-dependent Hamiltonian supplies both excitation and field-to-matter work. The same final change has different responses at different durations. No environment, dissociation continuum or biological repair system is represented. The alpha scan is a response experiment, not a demonstrated viable field history.

A06 · A temporary history and its released material

Baseline, early and late histories evolve their gas carbon-to-oxygen ratio and gas mass. A rapid-mixing comparison shows how transport changes the contrast.

The phase windows are prescribed historical response scenarios, not a derived probability of field formation or reversal. Stars return their computed winds after delays; remaining material stays locked. Multiple generations, transport and dilution can weaken or imitate the surviving pattern. Stable ground-state masses are held fixed in the resonance diagnostic.

A07 · A clock template and its false positive

Six synthetic clock channels reveal a field injection, a calibration event with a similar matched score, or noise alone.

A known-arrival template score alone is insufficient: a common calibration step can have the same projection onto the field template. The channel relationships supply additional information. The accompanying E12 ensemble quantifies recovery; this single realization is illustrative and is not GPS evidence.

A08 · Persistence under boundary and perturbation checks

Saved radial field snapshots appear above the complete fixed-core energy history. Three-dimensional leakage differs sharply from the one-dimensional control.

The camera remains fixed while field energy leaves the original core. Larger-box, initial-perturbation and dimensional controls remain selectable. Conversion to seconds requires a scalar mass; the displayed 25-GeV choice yields microscopic durations and is not an allowed cosmological model.

A09 · Field and matter respond together

Four panels show field, matter density, both radii, and exchanged energy. The boundary expands beyond the cloud while the energy changes nearly balance.

Saved real-time field evolution and a dynamically coupled homologous cloud. The converted boundary escapes the shrinking material source during this finite interval. Density is reconstructed from the exact ansatz and saved radius; field samples are decimated for display only. This is not a full local field–fluid conservation or compact-object calculation. Grid refinement reduces the final energy residual to about 0.35% of exchanged matter energy. A later unresolved interval is not animated as a valid prediction.

A10 · A finite inflationary history need not equilibrate

Probability curves starting in opposite minima retain different weights over a finite duration. A central initial state spreads into both wells, and all are compared with the stationary reference.

Positive, conservative Fokker–Planck evolution for a specified light spectator at fixed H, compared with the stationary distribution. Explicit initial conditions remain important. Only five saved times are played, with their unequal e-fold spacing labeled. This does not derive reheating, late domains or a cosmological measure.