IndisputableMonolith.Foundation.QRFT.SMLagrangianSkeleton
This module introduces the four canonical sectors of the Standard Model Lagrangian and associated cost functions in the Recognition Science setting. A researcher constructing the QRFT Lagrangian or verifying vacuum properties would cite these definitions when assembling total cost from sector contributions. The module consists entirely of definitions and property statements with no proofs.
claimLet the four canonical sectors of the SM Lagrangian be denoted $S_1, S_2, S_3, S_4$. Define a cost map $c$ on each sector such that $c(s)=0$ at the vacuum configuration, $c(s) eq 0$ off vacuum, $c(s) o c(s^{-1})$ under reciprocal symmetry, and the total cost is the sum over sectors. The certification object asserts that the resulting Lagrangian satisfies the required non-negativity and vacuum-zero conditions.
background
The module imports the RS time quantum $ au_0=1$ tick from Constants and the general cost machinery from the Cost module. It works inside the QRFT sector of the Foundation layer, where the Standard Model Lagrangian is decomposed into four canonical sectors whose individual costs must obey the Recognition Composition Law and the J-cost functional.
Sector cost is required to vanish exactly at the vacuum, remain non-negative everywhere, and exhibit reciprocal symmetry. The total cost is the direct sum of the four sector costs. These properties are stated as named declarations that later modules can invoke when building the full Lagrangian or its certification.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the sector decomposition and cost skeleton that higher-level QRFT constructions rely on when assembling the complete SM Lagrangian and its certification object. It directly supports the transition from the abstract cost axioms to concrete particle-sector assignments inside the Recognition Science framework.
scope and limits
- Does not derive the explicit Lagrangian densities for each sector from the J-functional.
- Does not prove that the four sectors exhaust the SM field content.
- Does not connect the sector costs to the phi-ladder mass formula.
- Does not address gauge fixing or renormalization within the sectors.
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