IndisputableMonolith.URCAdapters.UnitsIdentity
The URCAdapters.UnitsIdentity module defines the units identity as a proposition asserting that c times the fundamental time quantum equals the fundamental length for all anchors. Researchers adapting RS-native constants for dimensional checks would reference it when confirming base relations with c set to 1. The module imports the Constants definition of τ₀ as 1 tick and structures the identity through sibling declarations for the Prop and its holding status.
claimThe units identity states that $c · τ_0 = ℓ_0$ for all anchors, where $τ_0$ is the RS time quantum equal to one tick.
background
The module operates inside the URCAdapters domain and imports Mathlib together with the Constants module. The upstream Constants module supplies the definition of the fundamental RS time quantum τ₀ = 1 tick in the native units where c = 1. The units identity is introduced as a Prop enforcing that the length scale ℓ₀ equals the product of c and τ₀, which maintains dimensional consistency across the Recognition Science framework.
proof idea
This is a definition module, no proofs. It declares the units identity proposition and relies on sibling declarations units_identity_prop and units_identity_holds to formalize the statement and its validity.
why it matters in Recognition Science
The module supplies the units identity proposition that anchors dimensional analysis in the Recognition Science framework. It builds directly on the Constants module where τ₀ is defined as 1 tick and supports adapters in the URCAdapters domain. The identity aligns with the setting of c = 1 and the phi-ladder structure, though no downstream uses are listed.
scope and limits
- Does not derive the identity from the J-function or Recognition Composition Law.
- Does not assign an independent numerical value to ℓ₀.
- Does not extend the relation beyond RS-native units with c = 1.