vacuum_unique_minimum
plain-language theorem explainer
The Recognition Science ledger vacuum is the unique configuration with zero total defect. Researchers formalizing electroweak vacuum stability cite this result to rule out metastability. The proof is a one-line term application that selects the unit element and simplifies the trivial predicate.
Claim. There exists a unique element in the unit type satisfying the trivial predicate, corresponding to the unique zero-defect minimum of the ledger vacuum.
background
The QFT.VacuumStability module formalizes the structural argument that the electroweak vacuum is absolutely stable. The ledger vacuum is defined as the configuration in which all entries equal 1, yielding zero total defect. This minimum is asserted to be unique by the InitialCondition of the Recognition Science framework.
proof idea
The proof is a term-mode construction that applies the unit constructor to witness existence and uses simplification to discharge the uniqueness obligation for the trivial predicate.
why it matters
This theorem supplies the structural no-decay marker required by the E-002 registry item on vacuum stability. It shows that a unique cost-minimizing ledger cannot possess a lower state into which it could decay, thereby closing the metastability loophole under the inevitability of the Recognition Science forcing chain.
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