module module high

`IndisputableMonolith.Astrophysics.TidalLockingFromPhiResonance`

The module supplies resonance conditions for Moon-Earth, Mercury, and Venus spin-orbit ratios based on phi resonance in the J-cost function. Celestial dynamicists applying Recognition Science to solar system observations would cite these. The structure consists of parameter definitions and band checks without embedded proofs.

claimMoon-Earth tidal locking satisfies the resonance condition with spin-orbit ratio $1:1$ at zero $J$-cost deviation inside the phi band, where $J(x) = (x + x^{-1})/2 - 1$ and the ratio aligns with the phi-ladder scaling.

background

The module sits in the astrophysics domain and imports the RS time quantum τ₀ = 1 tick from Constants together with the J-cost function from Cost. It defines resonance predicates using the phi-ladder and defectDist to encode observed spin-orbit ratios for the Moon, Mercury, and Venus. Upstream results fix native units with c = 1 and ħ = φ^{-5}.

proof idea

This is a definition module, no proofs. The argument is organized as a sequence of resonance definitions (moon_resonance_pq, mercury_resonance_pq, venus_resonance_pq) followed by zero-cost and band-membership checks (moon_J_cost_zero, mercury_deviation_in_J_phi_band, venus_deviation_in_inverse_phi_sq_band).

why it matters in Recognition Science

The module contributes to the Recognition Science account of tidal locking by encoding the observed 1:1 Moon-Earth ratio as a phi-resonance outcome. It connects to the forcing chain steps T5-T8 through the self-similar fixed point phi and the eight-tick octave. No direct parent theorems appear in the current dependency graph.

scope and limits

Does not derive resonance from Newtonian orbital equations.
Does not treat multi-body tidal evolution.
Does not predict resonances for bodies outside the listed set.
Does not incorporate relativistic or dissipative corrections.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (17)

def moon_resonance_pq L87
def mercury_resonance_pq L90
def venus_resonance_pq L94
theorem moon_resonance_eq L99
theorem moon_J_cost_zero L102
theorem mercury_deviation_eq_J_phi L110
theorem mercury_deviation_in_J_phi_band L116
def phi_cubed L127
theorem phi_cubed_eq L130
theorem phi_cubed_band L141
theorem venus_deviation_in_inverse_phi_sq_band L149
def J_phi_ceiling L159
theorem J_phi_ceiling_pos L161
theorem J_phi_ceiling_band L165
structure TidalLockingFromPhiResonanceCert L189
def tidalLockingFromPhiResonanceCert L202
theorem tidal_locking_one_statement L226