trivialVantageTriple
plain-language theorem explainer
The trivial model supplies a vantage triple over the single-point state space in which the inside, acting, and outside components are identical. Model builders verifying internal consistency of the RRF axiom bundle cite this construction as the base case. The definition is a direct one-line application of the unified constructor to the unit state.
Claim. Let $U$ be the one-point state space. The vantage triple over $U$ is the structure $V = (x,x,x)$ where $x$ is the unique element of $U$.
background
The RRF layer expresses recognition quantities via vantage triples, each recording the same underlying value from three indexed perspectives (inside, acting, outside). The trivial model reduces the state space to the unit type, sets all strains to zero, and closes the ledger trivially, thereby satisfying the core RRF axioms by construction. The module documentation identifies this as the minimal witness proving internal consistency of the axiom bundle.
proof idea
The definition is a one-line wrapper that applies the unified constructor to the trivial state, producing a triple whose three components are equal by construction.
why it matters
This definition supplies the concrete vantage triple required by the downstream theorem that verifies the triple is unified. It completes the base case for the trivial model, which the module documentation identifies as the simplest witness that the RRF axiom bundle is internally consistent. Within the Recognition Science framework it anchors the RRF layer before models with nonzero J-cost or defect distances are introduced.
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