Pith. sign in
def

canonicalThreshold

definition
show as:
module
IndisputableMonolith.StandardModel.RS_STD_Structural_010
domain
StandardModel
line
20 · github
papers citing
none yet

plain-language theorem explainer

The canonical threshold is the fixed real constant φ − 3/2 used as a universal cutoff in RS Standard Model structural comparisons. Anyone calibrating domain costs against the electron-fixed coherence scale would cite it. It is a pure definitional constant (no proof obligation), built from the golden ratio forced at T6.

Claim. The canonical threshold is the real number $\varphi - 3/2$, where $\varphi$ denotes the golden ratio (self-similar fixed point of the Recognition forcing chain).

background

Module RS_STD_Structural_010 is a structural Standard Model layer in Recognition Science: the coherence energy $E_{\mathrm{coh}}$ is fixed once by the electron mass, after which all predictions are parameter-free. The module status is a structural theorem block (zero sorry, zero axiom).

The golden ratio $\varphi$ enters from the Constants import and is the unique self-similar fixed point forced at T6 of the unified forcing chain. The Cost import supplies the J-cost infrastructure against which domain costs are compared. Sibling material in the same file defines a domain cost functional and proves it is nonnegative, then compares that cost to this threshold.

Numerically $\varphi \approx 1.618$, so the threshold sits near $0.118$, a small positive scale natural for residual structural defects once the leading RS ladder is fixed.

proof idea

Definitional abbreviation only: the name is bound to the real expression $\varphi - 3/2$. No tactics, no lemmas, no proof term beyond the defining equality.

why it matters

Gives a single named cutoff for RS-to-Standard-Model structural certificates in this module. With $E_{\mathrm{coh}}$ pinned by the electron mass, residual domain costs are meant to sit below a universal φ-native scale rather than an ad hoc SM parameter. The constant sits downstream of T6 (φ forced) and upstream of the module's positivity and certificate inhabitants (siblings such as the positivity lemma for the threshold and the structural certificate). It does not itself close a forcing-chain step; it packages the cutoff those certificates compare against.

Switch to Lean above to see the machine-checked source, dependencies, and usage graph.