pith. sign in
theorem

c_rs_eq_one

proved
show as:
module
IndisputableMonolith.Foundation.ConstantDerivations
domain
Foundation
line
105 · github
papers citing
2 papers (below)

plain-language theorem explainer

Establishes that the speed of light equals 1 in RS-native units. Researchers deriving Planck-scale quantities or forcing spacetime emergence from the Recognition Science foundation cite this normalization step. The proof is a direct term-mode reduction that unfolds the ratio definition and applies numerical simplification.

Claim. In RS-native units the speed of light satisfies $c_{rs} = 1$, where $c_{rs}$ is defined as the ratio of the fundamental length scale to the fundamental time scale.

background

The ConstantDerivations module derives the fundamental constants from the RS foundation via the Composition Law and the J-cost function. The speed of light is introduced as the ratio $c_{rs} := ℓ_0 / τ_0$, with $ℓ_0$ the unit length and $τ_0$ the eight-tick fundamental period. In the native unit system both scales are fixed to 1, so the ratio collapses to unity by construction of causal coherence.

proof idea

The term-mode proof unfolds the definition of $c_{rs}$ together with the definitions of $ℓ_0$ and $τ_0$, then invokes norm_num to reduce the resulting numerical expression to 1.

why it matters

The result is invoked by all_constants_from_phi to list every constant as an algebraic function of φ, by planck_length_eq_one and planck_mass_eq to normalize Planck units, and by the master theorems reality_forced_by_any_distinction and reality_from_one_distinction to close the forcing chain. It realizes the Level-4 step of the derivation diagram in the module documentation, fixing the causal bound at unity after the eight-tick octave and three-dimensional forcing steps.

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papers checked against this theorem (showing 2 of 2)