module module high

`IndisputableMonolith.Engineering.EnergyStorageDensityStructure`

This module defines the RS coherence energy quantum E_coh = phi^{-5} and related storage densities on the phi-ladder for chemical and nuclear rungs. Energy engineers mapping device performance to RS-native units would cite these when scaling storage capacities. The module consists of direct definitions plus simple positivity lemmas that establish rung ordering.

claim$E_{coh} = phi^{-5}$, with rung energies $E_{chemical}$ and $E_{nuclear}$ obtained by scaling the base quantum along the phi-ladder; positivity statements confirm $E_{nuclear} > E_{chemical} > 0$.

background

Recognition Science fixes the base time quantum tau_0 = 1 tick in the Constants module. The Cost module supplies the J-cost functional whose self-similar fixed point is phi. This module assembles energy storage densities by placing the coherence quantum E_coh = phi^{-5} at the base of the phi-ladder and assigning chemical and nuclear rungs above it.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The definitions feed the TeslaTurbineStructure module, supplying the energy densities required for turbine scaling arguments. They implement the hbar = phi^{-5} value from the RS constants and close the step from abstract Cost structures to concrete engineering quantities.

scope and limits

Does not derive phi from the T0-T8 forcing chain.
Does not compute numerical device efficiencies.
Does not incorporate relativistic or quantum-field corrections.
Does not address the fine-structure constant alpha.

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Engineering.TeslaTurbineStructure module_import

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (25)

def E_coh_storage L55
theorem E_coh_storage_pos L58
def phi_rung_energy L63
theorem phi_rung_energy_pos L66
theorem phi_rung_energy_ratio L71
def chemical_rung L81
def nuclear_rung L84
def E_chemical L87
def E_nuclear L90
theorem nuclear_exceeds_chemical L93
def nuclear_chemical_ratio L100
theorem nuclear_chemical_ratio_gt_one L103
def jcost_energy L110
theorem jcost_energy_nonneg L113
theorem jcost_energy_zero_iff_ground L119
theorem jcost_energy_min_at_ground L139
theorem phi_rung_jcost_energy L147
theorem phi_coherent_minimizes_jcost_per_energy L153
def storage_density_ratio L162
theorem storage_density_ratio_pos L165
theorem higher_rung_denser L170
theorem energy_storage_density_hierarchy L177
theorem phi_ladder_energy_strictly_increasing L191
theorem rs_energy_storage_hierarchy L201
def en004_certificate L210