IndisputableMonolith.Physics.VacuumDecayFromJCost
This module defines vacuum decay structures in Recognition Science by expressing tunneling actions through the J-cost function in RS-native units. Cosmologists and particle physicists modeling false vacuum stability would cite these definitions when deriving decay rates from the recognition composition law. The module consists of channel definitions, action calculations, positivity predicates, and a certification object, with no internal proofs.
claimThe module introduces the tunneling action $S(C)$ for a decay channel $C$ derived from the J-cost $J$, the action ratio and positivity checks, and the vacuum decay certificate predicate that certifies valid decay processes in units where the fundamental time quantum satisfies $τ_0 = 1$.
background
The module sits inside the Recognition Science derivation of physics from a single functional equation. It imports the RS time quantum $τ_0 = 1$ tick from Constants and builds directly on the J-cost $J(x) = (x + x^{-1})/2 - 1$ together with the recognition composition law. Sibling definitions cover decay channels, the tunneling action, action ratios, action positivity, and the vacuum decay certificate.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the vacuum decay primitives that support later derivations of cosmological observables and particle lifetimes within the Recognition Science chain. It links the J-cost directly to tunneling processes, consistent with the eight-tick octave and the emergence of three spatial dimensions.
scope and limits
- Does not compute explicit numerical decay rates for given potentials.
- Does not treat multi-field or gravitational vacuum decay.
- Does not derive decay rates from the full forcing chain T0-T8.