IndisputableMonolith.Recognition.ModelingExamples
The module Recognition.ModelingExamples supplies concrete modeling examples for Recognition Science, centered on a minimal 2-vertex structure with bidirectional relations. Researchers building or auditing foundational models would cite it for basic test cases. The module consists entirely of definitions drawn from the core Recognition import, with no proofs or derivations.
claimA minimal recognition structure with two vertices $v_1, v_2$ linked by a bidirectional relation $R$ that satisfies the recognition composition law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$.
background
The module sits inside the Recognition Science setting whose upstream result states T1 (MP): Nothing cannot recognize itself. It introduces sibling definitions SimpleStructure, SimpleLedger and SimpleTicks that instantiate the J-cost function and defectDist on the smallest possible graph. All constructions inherit the phi-ladder and eight-tick octave conventions from the parent Recognition module.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the simplest concrete instances that illustrate T1 and the Recognition Composition Law. It feeds the broader Recognition framework by giving explicit objects on which later mass-formula and Berry-threshold arguments can be tested, even though no direct used-by edges are recorded yet.
scope and limits
- Does not contain any theorem statements or Lean proofs.
- Does not extend the forcing chain T0-T8 or derive new constants.
- Does not model multi-vertex or higher-dimensional recognition graphs.
- Does not compute numerical values for alpha, G or mass rungs.