pith. sign in
def

f_RG_tolerance

definition
show as:
module
IndisputableMonolith.Physics.RGTransportCertificate
domain
Physics
line
36 · github
papers citing
none yet

plain-language theorem explainer

f_RG_tolerance supplies the fixed rational tolerance 1/10000 that sets the half-width of the certified interval around each computed RG transport exponent. Particle physicists certifying renormalization-group running in the Standard Model would cite this constant when checking enclosure of f^RG values. The definition is a direct rational assignment requiring no further reduction.

Claim. The tolerance parameter for the certified range of the RG transport exponent is defined as $1/10000$.

background

The RGTransportCertificate module supplies certified values for the SM RG transport exponent $f^RG_i(mu^*, mu_end)$ obtained from canonical policy. The tolerance enters the is_certified predicate, which requires the true exponent to lie inside the interval centered at the certified value with half-width equal to this tolerance. The module imports the Hypothesis structure from ClassicalBridge.Fluids.CPM2D, a bundle of constants and functionals for GalerkinState N that encodes projection-defect and energy-control bounds, together with the phi-ladder Poisson-summation hypothesis from NumberTheory.PhiLadderLattice.

proof idea

The definition is a direct one-line assignment of the rational 1/10000.

why it matters

The tolerance is invoked by certified_center_enclosed, f_RG_lower, f_RG_upper, is_certified, and is_certified_iff_abs_error_le to produce concrete enclosure statements for every fermion. It supplies the numerical criterion that closes the certification step for RG transport exponents inside the Recognition Science framework, linking the phi-ladder lattice sums to the eight-tick octave and D=3 spatial structure.

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