tau0_matches_foundation
plain-language theorem explainer
The declaration confirms that the Recognition Science fundamental time unit τ₀ equals the explicit numerical expression built from CODATA values of ℏ, G, and c. Researchers deriving physical constants in the RS framework would reference this equality to anchor the abstract tick duration to measured quantities. The proof succeeds through direct unfolding of the constant definitions followed by reflexivity.
Claim. $τ_0 = √[(1.054571817×10^{-34}) ⋅ (6.67430×10^{-11}) / (π ⋅ (299792458)^3)] / 299792458$, where the numerical inputs are the CODATA values for ℏ, G, and c.
background
The module derives physical constants from Recognition Science primitives using CODATA reference values: c = 299792458 m/s (exact), ℏ = 1.054571817×10^{-34} J·s, G = 6.67430×10^{-11} m³/(kg·s²). The fundamental time unit τ₀ is defined as sqrt(ℏ G / (π c³)) / c. Upstream results include the definition of tau0 as the tick duration in RS-native units and the separate codata constants for ℏ, G, and c.
proof idea
This is a one-line wrapper proof that unfolds tau0, hbar_codata, G_codata, and c_codata, then applies reflexivity to establish the equality.
why it matters
This theorem anchors the RS-native τ₀ to the numerical foundation, supporting the derivation of constants in the framework. It relates to the forcing chain landmarks where time units emerge from the eight-tick octave. No open questions directly touched as it is a direct match.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.