Position
plain-language theorem explainer
Position is the real line serving as the spatial coordinate for potential functions in coherence-based gravity. It is referenced in structures for extended objects, external phase fields, and energy processing gradients. The declaration is a direct abbreviation with no derivation or lemmas required.
Claim. The position coordinate is an arbitrary element of the real numbers, written $h, h_{cm} : x$ with $x$ ranging over $x : x$.
background
The CoherenceFall module models gravitational effects through coherence defects on a one-dimensional line. ProcessingField carries a potential map from Position to reals. ExtendedObject records a center-of-mass location in Position together with positive extent. These structures feed calculations of coherence restoration under falling and external acoustic contributions.
proof idea
The declaration is a direct abbreviation of the real numbers as the position type.
why it matters
This definition supports sixteen downstream declarations, including ExternalPhaseField for acoustic levitation, energy_creates_processing_gradient, and w_mass_implies_ew_scale. It supplies the coordinate domain for the phi-ladder and coherence defect expansions. The real-line choice is consistent with the eight-tick octave and D = 3 in the Recognition Science forcing chain.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.