trivialOctave_wellPosed
plain-language theorem explainer
The trivial octave model satisfies the well-posedness predicate of the RRF core axioms by direct construction. Researchers establishing baseline consistency for Recognition Science models cite this as the degenerate case confirming the axiom bundle is satisfiable. The proof is a term-mode construction that pairs the unit state with the balanced property of the trivial ledger.
Claim. The trivial octave, whose state space is the singleton type with J-cost identically zero and ledger trivially closed, satisfies the well-posedness condition.
background
The RRF.Models.Trivial module defines the simplest model satisfying RRF axioms: state equals the unit type (one state), J equals zero (always balanced), and the ledger is 0/0 (trivially closed). This construction proves internal consistency of the core axiom bundle. The wellPosed predicate originates in RRF.Core.Octave and encodes the consistency requirements for octave models.
proof idea
The proof is a one-line term wrapper that constructs the wellPosed witness as the pair consisting of the unit element and the trivial_balanced lemma from the same module.
why it matters
This theorem supplies the base consistency check for the trivial model inside the RRF framework. It confirms that the core axioms remain satisfiable in the degenerate case and supplies a reference point for more elaborate models. No downstream uses are recorded yet; the result touches the internal-consistency step of the Recognition Science monolith but does not engage the T0-T8 forcing chain or the Recognition Composition Law.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.