mass_raw
Converts an abstract mass count into its value on the raw RS scale by multiplying with the mass quantum. Researchers expressing particle masses on the phi-ladder in native units cite this conversion when working inside the tick-voxel system. The definition is a direct scalar multiplication with no reduction or lemma application required.
claimThe raw mass in RS-native units is given by $m_0 = m · m_Q$, where $m$ is a real number counting the mass and $m_Q$ is the mass quantum (equal to the coherence quantum since $c=1$).
background
The RS-native unit system takes the tick (fundamental time quantum τ₀ = 1) and voxel (spatial step with c = 1) as base standards. Derived quanta include the coherence quantum E_coh = φ^{-5} and the mass quantum defined as one coherence quantum. All measures sit on the phi-ladder φ^n, with dimensionless ratios fixed solely by φ. The module sets c = 1 and ħ = φ^{-5} (in native units), making SI conversion optional via external calibration. Upstream, the tick is defined as the base time unit and the mass quantum is set equal to cohQuantum.
proof idea
One-line definition that multiplies the input mass count (typed as real) by the pre-defined mass quantum. It directly references the upstream massQuantum definition and the Mass type alias as real numbers; no tactics or lemmas are invoked.
why it matters in Recognition Science
This definition supplies the scaling step needed to place masses on the phi-ladder inside the Recognition Science constants system. It supports the mass formula yardstick · φ^(rung - 8 + gap(Z)) by providing the raw RS value before rung adjustments. It aligns with the eight-tick octave and D = 3 spatial dimensions by keeping all quantities in native tick-voxel units. No downstream uses are recorded in the current graph.
scope and limits
- Does not convert the result to SI units.
- Does not apply phi-ladder rung or gap(Z) adjustments.
- Does not compute numerical values for specific particles.
- Does not incorporate relativistic or interaction corrections.
formal statement (Lean)
123@[simp] noncomputable def mass_raw (m : Mass) : ℝ := m * massQuantum
proof body
Definition body.
124
125/-! ## Frequency and momentum quanta -/
126
127/-- Frequency quantum: 1/tick (inverse of fundamental time). -/