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Explain the Lean theorem `c_rs_eq_one` in module `IndisputableMonolith.Foundation.ConstantDerivations`. Write for an educated reader who knows science and programming but may not know Lean. Cover: (1) what the declaration says in plain English, (2) why it matters in Recognition Science, (3) how to read the formal statement, (4) visible dependencies or certificates in the supplied source, and (5) what this declaration does not prove. Cite only declarations present in the supplied Recognition source.

Big AI job. Grok 4.3 reads the canon and writes a Lean-grounded derivation; usually 20 seconds to 2 minutes. Your answer will appear below.
confidence: high in recognition cached

(1) Plain English. The declaration c_rs_eq_one asserts that the RS-native speed of light equals exactly one voxel per tick.

(2) Why it matters in Recognition Science. In the framework, c is not an empirical input but the structural ratio ℓ₀/τ₀ where both fundamental length and time are defined as unit. This makes causal propagation a unit coherence bound rather than a fitted constant; all other constants (ℏ, G, α) are then expressed algebraically in φ.

(3) How to read the formal statement. The Lean statement is theorem c_rs_eq_one : c_rs = 1 := by unfold c_rs ℓ₀ τ₀ norm_num. It first defines c_rs : ℝ := ℓ₀ / τ₀, then unfolds the definitions (both ℓ₀ and τ₀ equal 1) and normalizes to obtain equality. The proof is a direct computation with no external axioms.

(4) Visible dependencies or certificates. The theorem lives in IndisputableMonolith.Foundation.ConstantDerivations and depends only on the local definitions c_rs, ℓ₀, and τ₀. It is referenced verbatim as ConstantDerivations.c_rs_eq_one inside the master certificate reality_from_one_distinction and the propositional form reality_forced_by_any_distinction. Related local results include c_pos and all_constants_from_phi.

(5) What this declaration does not prove. It does not derive why ℓ₀ = τ₀ = 1 from the forcing chain (that occurs upstream in PhiForcing and DimensionForcing), does not address SI calibration or empirical measurement (handled in SingleAnchor), and does not prove the full physical emergence of spacetime or the light cone (those appear in SpacetimeEmergence and RealityFromDistinction).

cited recognition theorems

outside recognition

Aspects Recognition does not yet address:

  • Derivation of ℓ₀ = τ₀ = 1 from the absolute-floor or J-cost axioms (present only conceptually in the supplied slice).
  • SI-unit calibration or empirical falsifiers for c (addressed in separate calibration modules).

recognition modules consulted

The Recognition library is at github.com/jonwashburn/shape-of-logic. The model is restricted to the supplied Lean source and instructed not to invent theorem names. Treat output as a starting point, not a verified proof.