IndisputableMonolith.Chemistry.HaberBoschFromPhiLadder
The module computes J-cost on the operating-to-minimum temperature ratio for Haber-Bosch ammonia synthesis and derives associated optimal ratios from the phi-ladder. Recognition Science researchers in chemistry cite these results to connect industrial parameters to the J-function and self-similar scaling. The module proceeds by successive definitions of cost quantities followed by direct proofs of ratio inequalities and positivity statements.
claim$J(T/T_0)$ where $T$ is the operating temperature and $T_0$ the minimum temperature on the phi-ladder, together with the derived optimal ratio $r>1$ and catalytic barrier ratio.
background
The module belongs to the Chemistry domain and imports the RS time quantum τ₀ = 1 tick from Constants together with cost definitions from the Cost module. The J-cost is the function J(x) = (x + x^{-1})/2 - 1 that appears throughout Recognition Science. The phi-ladder supplies the discrete scaling steps used to locate mass and energy ratios; the module applies this ladder to temperature ratios in the Haber-Bosch process.
proof idea
The module is built from definitions (haberBoschTempCost, optimalTempRatio, catalyticBarrierRatio) followed by short theorems (optimalTempRatio_gt_one, optimalTemp_in_industrial_range, catalyticBarrierRatio_pos). Each theorem applies the imported J-cost properties directly; no complex tactics or external lemmas beyond the Cost module are required.
why it matters in Recognition Science
The module extends the Recognition Science forcing chain (T5 J-uniqueness, T6 phi fixed point) into concrete chemical engineering. It supplies the temperature-ratio cost that later results in the chemistry section can reference. No downstream theorems are listed yet, so the module currently stands as a terminal contribution to the phi-ladder treatment of industrial processes.
scope and limits
- Does not derive reaction rate constants or full kinetics.
- Does not incorporate pressure or equilibrium constants.
- Does not compute absolute activation energies outside the phi-ladder approximation.
- Does not address catalyst surface details beyond the barrier ratio.
depends on (2)
declarations in this module (12)
-
def
haberBoschTempCost -
theorem
haberBoschTempCost_at_min -
def
optimalTempRatio -
theorem
optimalTempRatio_gt_one -
def
optimalTemp_C -
theorem
optimalTemp_in_industrial_range -
def
catalyticBarrierRatio -
theorem
catalyticBarrierRatio_pos -
theorem
activation_energy_Fe_approx -
structure
HaberBoschCert -
def
cert -
theorem
cert_inhabited