IndisputableMonolith.Verification.DimensionKepler
Module packaging the closed-form apsidal angle and the Kepler selection principle used to specialize Recognition geometry to planetary orbits. A verifier checking the D=3 forcing step would cite it when linking orbital precession structure to the eight-tick and dimension chain. Content is definitional plus a selection lemma, not a long derivation.
claimThe module supplies a closed-form apsidal angle $\psi$ for the Kepler problem and a selection principle that isolates the admissible orbital geometry in the Recognition specialization (tied to spatial dimension $D=3$).
background
Recognition Science forces spatial dimension $D=3$ at step T8 of the unified forcing chain, after the eight-tick octave (period $2^3$) and the self-similar fixed point $\varphi$. Classical celestial mechanics encodes the same three-dimensional geometry in the apsidal angle of a bound Kepler orbit: the angle between successive periapsis passages, fixed by the inverse-square law in $D=3$.
This verification module sits in the Verification domain and introduces that closed-form apsidal angle together with a Kepler selection principle. The intent is to make the classical orbital invariant available as a named object when the framework specializes abstract Recognition geometry to planetary motion, rather than re-deriving Newtonian orbits from scratch inside Lean.
proof idea
Definition-plus-lemma module. It records a closed-form expression for the apsidal angle and states a selection principle that picks the Kepler-compatible case. No extended tactic script or multi-lemma derivation is indicated at module scope; the argument structure is the pair of sibling declarations (apsidal angle object, selection principle) against Mathlib only.
why it matters in Recognition Science
Gives the Verification layer a concrete classical handle on the $D=3$ landmark (T8) via Kepler's apsidal structure. Downstream dimension or orbital specialization arguments can cite the closed-form apsidal angle and the selection principle instead of importing raw celestial-mechanics folklore. It does not itself prove T8; it packages the Kepler side of the specialization so forcing-chain and verification results can align on the same orbital invariant.
scope and limits
- Does not prove spatial dimension $D=3$ from the forcing chain.
- Does not derive Newtonian gravity or the inverse-square law inside Lean.
- Does not treat relativistic perihelion precession or multi-body perturbations.
- Does not export numerical ephemerides or observational fits.