IndisputableMonolith.QFT.VacuumStability
The module shows that a unique global minimum of the RS cost function precludes vacuum decay in QFT. QFT researchers working inside Recognition Science cite these results to establish stability of the vacuum. The argument is purely logical: metastability requires at least two distinct local minima, which uniqueness immediately rules out.
claimIf the cost function $J$ possesses a unique global minimum, then no lower vacuum exists into which decay can occur: uniqueness of the minimizer forbids the multiple local minima required for metastability.
background
The module sits inside the QFT domain of Recognition Science and imports the RS time quantum $ au_0 = 1$ tick from Constants. Its central object is the implication that a unique cost minimizer (unique global minimum of $J$) yields vacuum stability. The supplied module doc-comment states the core claim directly: uniqueness removes any possibility of a lower vacuum state.
proof idea
The module collects and organizes sibling theorems (uniqueness_implies_stability, rs_vacuum_stability_structural, vacuum_unique_minimum, etc.) that each encode the same logical step. No individual proof bodies are shown; the structure is that each sibling applies the observation that metastability presupposes at least two distinct minima.
why it matters in Recognition Science
The module supplies the stability guarantee needed for any RS-derived QFT vacuum. It directly implements the uniqueness-implies-stability step referenced in the module doc-comment and prepares the ground for downstream QFT constructions that assume a stable vacuum. No used-by edges are recorded, indicating it functions as a foundational block rather than an intermediate lemma.
scope and limits
- Does not compute tunneling amplitudes or decay lifetimes.
- Does not derive the explicit shape of the potential from the J-cost.
- Does not treat finite-temperature or non-vacuum initial states.
- Does not address multi-field or non-scalar potentials.