IndisputableMonolith.Masses.RSBridge.Anchor
The module supplies the closed-form anchor display function F(Z) = ln(1 + Z/φ)/ln(φ) for the integrated renormalization-group residue at the anchor scale μ⋆. Mass derivations in the Recognition Science framework cite this when equating the residue to the gap function for charged fermions. It is a definition module that states the explicit formula together with its basic properties such as F(0) = 0 and monotonicity for Z > -φ.
claim$F(Z) = ln(1 + Z/φ)/ln(φ)$ with the property that the integrated mass anomalous dimension at the anchor equals $F(Z_i)$ for each species $i$, where $F(0) = 0$ and $F(Z) ≈ log_φ(Z)$ for large $Z$.
background
Recognition Science derives masses on a phi-ladder with a residue term supplied by the gap function. This module introduces the display function F as the closed form claimed to match the integrated RG residue at the anchor scale μ⋆. Upstream the time quantum τ₀ = 1 tick from Constants fixes the native units used throughout the mass framework.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the explicit residue formula used by GapFunctionForcing to close the affine-log family and by QuarkAnchorDerivation to obtain RS-native heavy-quark masses without PDG input. It bridges the geometric phi-ladder to the perturbative RG side as described in the CouplingLaw module.
scope and limits
- Does not prove that the integrated RG residue equals this F.
- Does not specify the value of Z for each fermion species.
- Does not connect to the J-uniqueness or forcing chain steps.
- Does not compute numerical masses or compare to experiment.
used by (6)
depends on (1)
declarations in this module (19)
-
inductive
Sector -
inductive
Fermion -
def
sectorOf -
def
tildeQ -
def
ZOf -
def
gap -
def
residueAtAnchor -
theorem
anchorEquality -
theorem
equalZ_residue -
def
rung -
def
M0 -
theorem
M0_pos -
def
massAtAnchor -
theorem
anchor_ratio -
structure
ResidueCert -
def
genOf -
theorem
genOf_surjective -
def
rungResidueClass -
structure
AdmissibleFamily