IndisputableMonolith.QFT.VacuumStability
The QFT.VacuumStability module establishes that a unique global minimum of the cost function precludes vacuum decay. QFT researchers in the Recognition Science program cite it to rule out metastability. The module collects several theorems each reducing the claim to the logical requirement that metastability needs at least two distinct minima.
claimIf the cost function $J$ admits a unique global minimum, then no lower vacuum exists for decay; metastability requires at least two distinct local minima.
background
The module sits in the QFT domain of Recognition Science and imports the fundamental time quantum from Constants, where τ₀ = 1 tick. It works with the J-cost whose uniqueness is the sole hypothesis needed for the stability claim. The supplied module doc-comment states the core observation: uniqueness of the minimizer forbids the multiple minima required for metastability.
proof idea
This is a module containing multiple sibling declarations rather than a single proof. Each declaration (uniqueness_implies_stability and its companions) applies the uniqueness assumption directly to the definition of metastability, showing that decay channels cannot open when only one global minimum exists.
why it matters in Recognition Science
The module supplies the stability result required by the QFT section of the Recognition framework. It closes the logical gap between the unique-minimum property (itself forced by the J-uniqueness step T5 and the phi fixed point T6) and the absence of vacuum decay, consistent with the eight-tick octave and D = 3. No downstream declarations are recorded, indicating it functions as a terminal lemma for this topic.
scope and limits
- Does not treat theories possessing multiple local minima.
- Does not compute tunneling rates or lifetimes.
- Does not incorporate explicit particle content or spectra.
- Does not address finite-temperature or non-vacuum initial states.