Interactive Lab
The theory, handed to you as running code
A real Python suite (NumPy, SciPy, SymPy, pandas, Matplotlib) checks the corpus’s own load-bearing quantitative claims by running them as live simulation and comparing against what the books state, with an explicit tolerance on every check — 16 of 17 pass. Every page below states plainly what its simulation does and does not establish.
Regular Black Hole
PASSThe regular metric's mass function keeps curvature invariants finite at r=0 for the tested core-scale parameter, with radial geodesics reaching the core in finite proper time — matching the metric as specified.
Kretschmann Scalar
PASSThe Kretschmann curvature invariant stays finite as r→0 for the regular metric, in contrast to Schwarzschild's r⁻⁶ divergence — confirmed both symbolically (from-scratch Riemann tensor derivation) and numerically.
Geodesic Completeness
PASSRadial geodesics reach the core (r=0) in finite proper time without encountering a curvature singularity — checked by direct numerical integration of the geodesic equation.
ISCO Shift Scaling
PASSThe innermost stable circular orbit's shift from the Schwarzschild value scales cubically with the core parameter g, matching the predicted exponent (fitted: 3.00024).
Black-Hole Shadow
PASSCurrent EHT shadow-diameter measurement precision (~10–17%) implies an upper bound on the core parameter, g ≲ 0.5 GM, given the ray-traced shadow-radius scaling.
Born Rule Convergence
PASSEmpirical outcome frequencies concentrate on the squared-norm (Born) weights as the number of trials N grows, with exponentially suppressed probability of atypical deviation — a large-N typicality argument, verified numerically.
Ξ World-Selection
PASSIn an illustrative toy dynamical system, Ξ-maximization favors a structured, generative, stable trajectory over trivial/frozen, chaotic, or divergent alternatives — the qualitative selection behavior the text describes.
Orbit Emergence
PASSA damped, inertial two-body reaction–diffusion field system exhibits persistent bound orbital motion rather than monotonic collapse — the actual field PDE from Ch. 7, simulated directly.
Closure History (Gravity On/Off)
PASSThe same initial condition, run at two different damping values γ, ends in opposite fates — a persistent orbit above the closure threshold ("gravity: on") versus decaying below it ("gravity: off") — demonstrating history-dependence, not just instantaneous state.
Emergent Causality
PASSA localized perturbation produces a detectable response at increasing distance only after a time proportional to that distance — i.e. a finite, horizon-robust maximum signal speed emerges from dissipation and coherence loss, using the manuscript's own operational definition (not a claimed closed-form formula).
Magnetic Memory
PASSAfter an ultrafast quench sets the current J≈0, the magnetic field B does not vanish instantaneously — it persists and decays on a finite, kernel-governed memory timescale, matching the fitted decay constant to the kernel's own τ.