Position
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.
claimThe 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 in Recognition Science
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.
scope and limits
- Does not encode vector positions in three dimensions.
- Does not incorporate time or relativistic effects.
- Does not define a distance metric or inner product on the line.
formal statement (Lean)
32abbrev Position := ℝ
proof body
Definition body.
33
used by (16)
-
p_neq_np_assembled -
w_mass_implies_ew_scale -
ExternalPhaseField -
ExternalPhaseField -
ExtendedObject -
ProcessingField -
energy_creates_processing_gradient -
EnergyDistribution -
energy_distribution_creates_gravity_modifier -
gradient_superposition -
SuperpositionJustification -
LedgerEntry -
NewtonianParticle -
PointerState -
pointer_states_are_neutral_windows -
preferredBasisExamples