momentumQuantum_eq_cohQuantum
plain-language theorem explainer
This lemma establishes that the momentum quantum equals the coherence quantum under RS-native units. Researchers deriving particle masses or simplifying momentum expressions on the φ-ladder cite it to collapse p and E scales. The proof is a direct one-line simplification that unfolds the momentum definition and substitutes c = 1.
Claim. The momentum quantum (coherence energy divided by the speed of light) equals the coherence energy quantum: $p_0 = E_0$ when $c = 1$.
background
The RS-native unit system sets tick as the fundamental time interval and voxel as the spatial step, enforcing c = 1 with no external anchors. Coherence quantum is the base energy scale φ^{-5}; momentum quantum is defined as that energy divided by c. The module organizes all derived quantities on the φ-ladder for masses, lengths, times, and energies.
proof idea
One-line term-mode wrapper that applies simp to the definitions of momentumQuantum and c, reducing cohQuantum / 1 directly to cohQuantum.
why it matters
The equality anchors the constants module by making momentum interchangeable with energy, consistent with c = 1 and the φ-ladder scaling. It supports downstream mass and energy rung formulas without separate momentum factors. No open questions are touched; the result closes a basic conversion step in the native unit definitions.
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