The Reaction–Diffusion Field

Book I (Pre-Physical Selection & Emergent Reality) and Book VI (Temporal Closure) are sibling presentations built on literally the same governing equation for a scalar informational field I(x,t):

Diffusion (D∇I) spreads coherence and gives rise to locality; linear amplification (αI) lets structure reinforce itself; cubic saturation (−βI³) caps unbounded growth; and a noise term η(x,t) seeds symmetry breaking. Everything else in both books — space, time, gravity, orbits, phase transitions — is read off this one equation’s solutions.

This is also the corpus’s own first independently re-verified result: the manuscript originally asserted, without derivation, that divergence was “dynamically forbidden.” A from-scratch comparison-principle argument confirms this holds for β>0 — checked symbolically and against a numerical blow-up sweep across six orders of magnitude — and the corrected chapter now states the argument explicitly rather than asserting the conclusion.