pith. sign in
def

c_rs

definition
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module
IndisputableMonolith.Foundation.ConstantDerivations
domain
Foundation
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plain-language theorem explainer

Researchers deriving physical constants from the Recognition Science foundation cite this definition for the speed of light. It sets c_rs to the ratio of fundamental length ell_0 to fundamental time tau_0. In native units where both are unity, this enforces c=1 as a statement of causal coherence rather than a free parameter. The definition follows directly from the unit normalization in the forcing chain.

Claim. In RS-native units the speed of light is defined by $c = ell_0 / tau_0$, with $ell_0$ the fundamental length and $tau_0$ the fundamental time.

background

The Constant Derivations module derives c, hbar, G, and alpha from the RS foundation rather than as free parameters. The chain begins with the Composition Law, defines the J-cost J(x) = 1/2(x + 1/x) - 1, forces phi as the self-similar fixed point, sets D = 3, and fixes tau_0 to eight ticks with ell_0 the matching unit length. This definition expresses c as the ratio ell_0 over tau_0.

proof idea

The declaration is a direct noncomputable definition assigning c_rs to the quotient ell_0 / tau_0. No lemmas are applied; it is the base assignment that later theorems unfold to prove equals 1.

why it matters

It is referenced by the theorem all_constants_from_phi that asserts c_rs = 1 together with hbar = phi^{-5} and G = phi^5. The module documentation places it at Level 4 of the derivation chain. It supports the subsequent definitions of Planck length and mass that reduce to 1 and phi^{-5} in native units, confirming consistency with the eight-tick octave and phi-ladder.

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