IndisputableMonolith.QFT.VacuumStability
The VacuumStability module shows that a unique global minimum of the J-cost functional in Recognition Science QFT rules out metastability and vacuum decay. Researchers modeling RS-derived quantum fields cite these results to confirm absolute stability without lower states available for tunneling. The argument follows from the logical requirement that metastability needs at least two distinct local minima, which uniqueness directly excludes.
claimIf the J-cost admits a unique global minimizer, then the vacuum has no lower state available for decay; metastability is impossible.
background
Recognition Science builds QFT on the J-functional obeying the Recognition Composition Law. The upstream Constants module fixes the fundamental time quantum as τ₀ = 1 tick. The module identifies the vacuum state with the global minimum of J and treats uniqueness of this minimizer as the key structural property that blocks decay channels.
proof idea
This is a module collecting structural results on vacuum stability rather than a single proof. It organizes lemmas such as uniqueness_implies_stability and rs_vacuum_stability_structural that each derive the absence of degenerate minima from the unique-minimizer assumption.
why it matters in Recognition Science
The module closes a potential loophole in the Recognition Science QFT construction by showing that J-uniqueness (T5) and the phi fixed point (T6) together forbid metastable vacua. It supports the eight-tick octave (T7) and D = 3 spatial dimensions (T8) by ensuring the vacuum remains the sole minimum, consistent with the alpha band and phi-ladder mass formulas.
scope and limits
- Does not compute tunneling rates or instanton actions.
- Does not treat finite-temperature corrections or external fields.
- Does not establish existence of the unique minimum, only its consequences.
- Does not incorporate gravitational back-reaction on the vacuum.