pith. sign in
module module high

IndisputableMonolith.QFT.GaugeInvariance

show as:
view Lean formalization →

This module defines ledger states as the basic encoding of physical reality and introduces U(1) gauge transformations together with global and local variants on top of the discrete 8-tick clock. It supplies the gauge primitives required for QFT derivations in the Recognition Science framework. The module contains only definitions and elementary properties of equivalence and composition; no theorems are proved.

claimA ledger state encodes physical reality. Two ledger states are physically equivalent when they differ by a gauge transformation. U(1) transformations act on field configurations via maps $U: S^1 times LedgerState to LedgerState$, with global and local versions distinguished by whether the phase is constant or position-dependent.

background

The module sits inside the QFT tier of Recognition Science and imports the fundamental time quantum τ₀ = 1 tick together with the 8-tick structure whose phases are 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4. It introduces the ledger state as the object that records physical content, the physically equivalent relation that identifies states related by gauge action, the U(1) transformation group, and the distinction between global and local gauge operations on field configurations.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the gauge-invariance layer that feeds directly into the parent QFT module for Tier 2 derivations. It links the eight-tick octave (T7) to field configurations through ledger states, providing the discrete foundation on which the Recognition Composition Law and phi-ladder are expected to generate standard-model gauge structure.

scope and limits

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

depends on (2)

Lean names referenced from this declaration's body.

declarations in this module (26)