c
plain-language theorem explainer
The declaration sets the speed of light to exactly 1 in RS-native units of voxel per tick. Researchers normalizing calculations in the Recognition Science framework cite this choice when handling light propagation or relativistic effects. It is implemented as a direct constant definition with no lemmas or computational steps.
Claim. In Recognition Science the speed of light is defined by $c = 1$ in native units where distance is measured in voxels and time in ticks.
background
The module sets the fundamental RS time quantum to τ₀ = 1 tick. This normalizes the speed of light c to the value 1 in voxel-per-tick units. Sibling definitions in the same module introduce the golden ratio φ and the discrete tick, which together support the phi-ladder scaling and the eight-tick octave structure used throughout the framework.
proof idea
The declaration is a direct assignment of the real number 1 to c. No upstream lemmas are applied and no tactics are used; the @[simp] attribute simply marks the constant for automatic simplification in later proofs.
why it matters
This definition fixes the unit system for the Recognition Science framework, allowing c = 1 to be used consistently with ħ = φ^{-5} and G = φ^5 / π. It aligns with the forcing chain landmarks by normalizing light speed, which supports the later derivation of D = 3 spatial dimensions. No open questions are addressed here, but the choice underpins all subsequent constant and mass-ladder constructions.
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papers checked against this theorem (showing 1 of 1)
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Lensed GWs forecast cosmic dipole detection in 10 years
"d_L(z) = (1+z) r(z) with r(z) = ∫ c/H(z) dz and H(z) = H0 √[Ωm,0(1+z)^3 + ΩΛ,0]"