scaleFactor
scaleFactor supplies the multiplicative prefactor phi raised to beta times P for rescaling observables under environment pressure. Chemists or modelers using the Recognition framework for display adjustments on energy streams would reference this helper when composing rescaleEnergy. The definition is a direct one-line application of real exponentiation to the phi constant drawn from the CPM bundle.
claimThe scale factor is defined by $s = {phi}^{beta P}$ for real parameters $beta, P$, where $phi$ is the golden-ratio constant supplied by the CPM Constants structure.
background
The Environment Display Rescale module provides display-only helpers that adjust observables via the map E maps to E times phi to the power beta P while leaving integer scaffolding untouched. Beta is imported either as the constant 1 from the PPN beta definition or as the inverse temperature 1 over k_B T from the PartitionFunction module. The base phi is taken from the Constants structure in LawOfExistence, which packages CPM quantities including the nonnegative Knet parameter. The upstream E definition from SpectralEmergence counts the edges of the D-cube as D times 2 to the D-1, consistent with the D equals 3 spatial dimension fixed by the forcing chain.
proof idea
This is a one-line definition that applies Real.rpow to the phi constant from IndisputableMonolith.Constants with exponent beta times P.
why it matters in Recognition Science
The definition is consumed directly by the sibling rescaleEnergy helper, which multiplies an input energy by the scale factor. It realizes the display rescale E to E phi to the beta P described in the module doc-comment, preserving the phi-ladder structure and the self-similar fixed point from T6 of the unified forcing chain. The construction leaves integer scaffolding intact, closing one small interface in the chemistry environment layer.
scope and limits
- Does not derive or constrain the value of beta from neutrality tests.
- Does not modify the integer scaffolding of any observable.
- Does not apply the rescaling to non-display or non-energy quantities.
- Does not introduce physical units or interpret beta P as a thermodynamic variable.
formal statement (Lean)
19def scaleFactor (beta P : ℝ) : ℝ :=
proof body
Definition body.
20 Real.rpow IndisputableMonolith.Constants.phi (beta * P)
21
22/‑ Display rescale: E' = E · φ^{β P}. -/