monatomicModes
plain-language theorem explainer
The definition monatomicModes fixes the quadratic mode count for monatomic ideal gases at three, corresponding to the three translational degrees of freedom. A physicist computing classical heat capacities for helium or argon in the Recognition Science setting would cite this constant when applying equipartition. It is introduced as a direct integer assignment with no computation or further reduction.
Claim. For a monatomic ideal gas the number of quadratic modes is $3$.
background
The Thermodynamics.HeatCapacity module derives heat capacity from 8-tick mode counting. Classical equipartition assigns $kT/2$ energy to each quadratic mode. Recognition Science links each 8-tick mode to contributions in $C_V$ and $C_P$, with quantum corrections arising from 8-tick discreteness.
proof idea
The definition is a direct constant assignment of the integer 3.
why it matters
This supplies the mode count used to obtain the monatomic heat capacity $C_V = (3/2)R$ in the classical limit. It aligns with the eight-tick octave (T7) before quantum corrections from the phi-ladder are applied. No open questions are closed by this definition.
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