dim_T
plain-language theorem explainer
The definition assigns the time dimension the signature with length exponent zero, time exponent one, and mass exponent zero. Researchers deriving constants from Recognition Science primitives would cite it to maintain unit consistency when equations involve time. It is realized by a direct constructor call on the three-exponent structure with no lemmas or reductions.
Claim. The time dimension is the triple $(0,1,0)$ whose components are the integer exponents for length, time, and mass.
background
The module supplies a dimensional analysis framework in which every physical quantity carries a signature $[L^a T^b M^c]$. Fundamental units are the tick τ₀, the recognition length ℓ₀ = c·τ₀, and the golden-ratio scaling factor φ; all constants ℏ, G, c are obtained from these. The upstream Dimension structure records the three integer exponents used to track dimensions through calculations.
proof idea
This definition is a direct constructor application that supplies the exponents 0, 1, 0 to the Dimension structure.
why it matters
The definition supplies the canonical time signature needed for dimensional bookkeeping when constants are derived from the primitives τ₀, ℓ₀, and φ. It belongs to the set of fundamental dimension constants listed in the module and is required for any later consistency checks that involve time. No downstream theorems are recorded yet.
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