CriticalExponentsFalsifier
This structure packages the conditions that would refute the Recognition Science derivation of critical exponents via φ-scaling. A condensed-matter physicist comparing universality classes to numerical or experimental data would cite it when checking for absence of golden-ratio structure. The definition is a direct record of three propositions plus an implication that produces inconsistency from the first two.
claimA falsifier for the φ-scaling derivation of critical exponents consists of propositions asserting that the exponents lack any connection to the golden ratio, that high-precision values diverge from the predicted φ-values, and that new universality classes violate the expected patterns, together with the implication that the first two propositions together yield a contradiction.
background
Near a critical point, thermodynamic quantities diverge as power laws in the reduced temperature t: specific heat ~ |t|^{-α}, order parameter ~ (-t)^β, susceptibility ~ |t|^{-γ}, and correlation length ~ |t|^{-ν}. These exponents are universal, depending only on spatial dimension and symmetry class, with the 3D Ising values serving as the standard benchmark. The module states that Recognition Science obtains this universality from φ-structured fluctuations in J-cost near criticality, constraining the exponents through the same scaling that fixes D = 3 and the eight-tick octave.
proof idea
The declaration is a pure definition with an empty proof body. It assembles the four fields directly: three independent propositions followed by the implication that no φ-connection conjoined with diverging precision produces falsehood.
why it matters in Recognition Science
The structure supplies the explicit falsification interface for the THERMO-005 derivation of universal critical exponents from φ-scaling. It directly implements the three failure modes listed in the module doc-comment and thereby closes the empirical test loop for the paper proposition on golden-ratio scaling. It leaves open the question of whether measured exponents remain inside the RS-predicted bands once higher-precision data arrive.
scope and limits
- Does not derive or compute any numerical exponent values.
- Does not reference the forcing chain T0-T8 or the Recognition Composition Law.
- Does not incorporate actual experimental or simulation datasets.
- Does not address the individual exponent derivations such as α_3D_Ising.
formal statement (Lean)
234structure CriticalExponentsFalsifier where
235 no_phi_connection : Prop
236 precision_diverges : Prop
237 pattern_violated : Prop
238 falsified : no_phi_connection ∧ precision_diverges → False
239
240end CriticalExponents
241end Thermodynamics
242end IndisputableMonolith