module module high

`IndisputableMonolith.Climate.AtmosphericLayeringFromPhiLadder`

This module assigns atmospheric layer boundaries to specific rungs on the Recognition Science phi-ladder. Climate modelers and atmospheric physicists cite it to link the J-cost function and self-similar fixed point to observed tropopause, stratopause, mesopause, and thermosphere altitudes. The module consists of rung definitions, equality lemmas, a strict ordering proof, and altitude formulas derived from the phi-ladder.

claimTropopause rung = 0 (recognition-base altitude); stratopause rung, mesopause lower/upper rungs, and thermosphere rung follow on the phi-ladder with altitude_at_rung(r) = yardstick * phi^{r-8+gap(Z)} in RS-native units.

background

The module imports Constants (providing the RS time quantum τ₀ = 1 tick) and Cost (supplying the J-cost function J(x) = (x + x^{-1})/2 - 1). It operates in the setting of the forcing chain where T5 establishes J-uniqueness, T6 forces phi as the self-similar fixed point, and T7 introduces the eight-tick octave. Rung assignments build directly on the phi-ladder structure for spatial scaling.

proof idea

This is a definition module. It introduces constant rung values for each layer, states equality lemmas (tropopause_rung_eq etc.), proves rung_strict_ordering by direct comparison, and derives altitude_at_rung and altitude_geometric from the phi-ladder formula.

why it matters in Recognition Science

The module supplies the concrete rung-to-layer map that lets the phi-ladder (T6-T8) reach observable climate structure. It feeds downstream climate applications by grounding layer altitudes in the Recognition Composition Law and D=3 spatial dimensions. No parent theorems are listed in the used_by edges yet.

scope and limits

Does not derive temperature or pressure profiles inside layers.
Does not address dynamical processes such as convection or radiation.
Does not extend beyond the listed rungs to ionospheric or exospheric regimes.
Does not incorporate observational data or empirical fitting.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (22)

def tropopause_rung L104
def stratopause_rung L107
def mesopause_rung_lower L110
def mesopause_rung_upper L113
def thermosphere_rung L116
theorem tropopause_rung_eq L118
theorem stratopause_rung_eq L119
theorem thermosphere_rung_eq L120
theorem rung_strict_ordering L123
def altitude_at_rung L135
theorem altitude_at_rung_pos L137
theorem altitude_geometric L143
def stratopause_tropopause_ratio L150
theorem phi_cubed_eq L153
theorem stratopause_tropopause_ratio_gt_4 L162
theorem stratopause_tropopause_ratio_band L171
def thermosphere_tropopause_ratio L181
theorem thermosphere_tropopause_ratio_pos L183
theorem thermosphere_above_stratopause_ratio L189
structure AtmosphericLayeringFromPhiLadderCert L213
def atmosphericLayeringFromPhiLadderCert L231
theorem atmospheric_layering_one_statement L252