IndisputableMonolith.RSBridge.Anchor
The RSBridge.Anchor module supplies the closed-form display function F(Z) = ln(1 + Z/φ)/ln(φ) together with the auxiliary maps ZOf, gap and residueAtAnchor that equate the integrated RG residue to the phi-ladder label at the single anchor scale μ⋆. Mass-ladder and flavor-structure authors cite it when they need an explicit, auditable replacement for the Standard-Model residue. The module is purely definitional; it contains no theorems or proofs.
claim$F(Z) = {ln(1 + Z/φ)}/{ln φ}$ with the asserted equality $f_i(μ⋆) = gap(ZOf i)$ for each fermion sector i, where F(0) = 0, F is strictly increasing for Z > -φ, and F(Z) ∼ log_φ(Z) for large Z.
background
The module lives in the RSBridge domain and depends only on the RS time quantum τ₀ = 1 tick from Constants. It introduces the single-anchor scale μ⋆ and the display function F that is claimed to equal the integrated mass anomalous dimension at that scale. Auxiliary definitions include Sector and Fermion, the map sectorOf, the effective label tildeQ, ZOf (the rung or charge-squared label), gap (the phi-ladder defect), residueAtAnchor, anchorEquality and equalZ_residue.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
AnchorPolicy, AnchorPolicyCertified and AnchorPolicyModel import the module to obtain an explicit, Lean-native stand-in for the RG residue, removing the need for an opaque axiom. RungConstructor.Proofs and ElectronMass.Defs use the same F and ZOf to reproduce the charged-lepton table and the cube-geometry derivation of lepton constants. AnomalousMoments relies on the universal Z = 1332 value for the RS correction to (g-2).
scope and limits
- Does not implement multi-loop RG kernels or numerical integration inside Lean.
- Does not prove that the integrated residue equals F(ZOf i).
- Does not address radiative stability or flavor-mixing beyond the interface definitions.
- Does not contain the full mass-ladder construction or rung proofs.
used by (22)
-
IndisputableMonolith.Masses.RungConstructor.Proofs -
IndisputableMonolith.Physics.AnchorPolicy -
IndisputableMonolith.Physics.AnchorPolicyCertified -
IndisputableMonolith.Physics.AnchorPolicyModel -
IndisputableMonolith.Physics.AnomalousMoments -
IndisputableMonolith.Physics.ElectronMass.Defs -
IndisputableMonolith.Physics.ElectronMass.Necessity -
IndisputableMonolith.Physics.Hadrons -
IndisputableMonolith.Physics.LeptonGenerations.Defs -
IndisputableMonolith.Physics.MassResidueNoGo -
IndisputableMonolith.Physics.PMNS.Types -
IndisputableMonolith.Physics.RecognitionCoupling -
IndisputableMonolith.Physics.RGTransport -
IndisputableMonolith.Physics.RGTransportCertificate -
IndisputableMonolith.Physics.SectorYardsticks -
IndisputableMonolith.Physics.SterileExclusion -
IndisputableMonolith.RRF.Physics.ElectronMass.Defs -
IndisputableMonolith.RRF.Physics.LeptonGenerations.Defs -
IndisputableMonolith.RSBridge.GapFunctionForcing -
IndisputableMonolith.RSBridge.GapProperties -
IndisputableMonolith.RSBridge.ResidueData -
IndisputableMonolith.RSBridge.ZMapDerivation
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