IndisputableMonolith.Foundation.QRFT.SMLagrangianSkeleton
The module defines the four canonical sectors of the Standard Model Lagrangian together with their cost functions inside the Recognition Science framework. It introduces SMLagrangianSector and sectorCost along with basic properties such as vanishing at vacuum and non-negativity. Researchers deriving the SM gauge and matter terms from the J-functional equation would reference these constructions. The module consists of type definitions and supporting lemmas with no complex proof structure.
claimThe module introduces the type $SMLagrangianSector$ with four constructors and the map $sectorCost : SMLagrangianSector → ℝ$ obeying $sectorCost(s)=0$ at vacuum, $sectorCost(s)=sectorCost(1/s)$, and $sectorCost(s)≥0$ with strict inequality off vacuum. It further defines $totalCost$ as the sum of sector costs and the certificate $SMLagrangianCert$.
background
The module imports the RS time quantum τ₀=1 tick from Constants and the J-cost machinery from Cost. In Recognition Science the J-functional equation yields the cost via T5 J-uniqueness, J(x)=(x+x⁻¹)/2−1. The four sectors decompose the SM Lagrangian into gauge and Higgs contributions on the phi-ladder. Local notation follows the QRFT skeleton where defectDist and sector costs are measured in RS-native units with c=1, ħ=φ⁻⁵.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the sector decomposition required for totalCost and the subsequent embedding of the SM into the unified forcing chain T0–T8. It connects directly to the mass formula yardstick·φ^(rung−8+gap(Z)) and the Berry creation threshold φ⁻¹. No downstream theorems are recorded yet, but the construction prepares the ground for the full Lagrangian derivation from the Recognition Composition Law.
scope and limits
- Does not derive explicit field operators or interaction vertices for each sector.
- Does not compute numerical values of sector costs or link them to observed particle masses.
- Does not prove that the four-sector split is the unique decomposition compatible with J-uniqueness.
- Does not address renormalization group flow or higher-order quantum corrections.
depends on (2)
declarations in this module (12)
-
inductive
SMLagrangianSector -
def
sectorCost -
theorem
sectorCost_zero_at_vacuum -
theorem
sectorCost_reciprocal_symm -
theorem
sectorCost_nonneg -
theorem
sectorCost_pos_off_vacuum -
def
totalCost -
theorem
totalCost_zero_at_vacuum -
theorem
totalCost_nonneg -
theorem
sector_count -
structure
SMLagrangianCert -
def
smLagrangianCert