module module high

`IndisputableMonolith.Engineering.EnergyStorageDensityStructure`

This module defines the RS coherence energy quantum together with storage densities and rung-scaled energies for chemical and nuclear cases. Engineers modeling storage systems in the Recognition framework would cite these objects when scaling energies on the phi-ladder. The module consists entirely of definitions and elementary positivity statements.

claim$E_ {coh} = phi^{-5}$ is the coherence energy quantum; $E_{coh,storage}$ is the associated storage density, with rung energies $phi^{rung} E_{coh}$ defined separately for chemical and nuclear cases together with their ratio and positivity statements.

background

Recognition Science expresses all scales via the J-cost function and the phi-ladder fixed point. The imported Constants module supplies the native time quantum tau_0 = 1 tick. The imported Cost module supplies the underlying cost structure used to define energies. The present module translates those primitives into concrete energy-storage objects using the supplied value E_coh = phi^{-5}.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the energy-storage objects required by the downstream TeslaTurbineStructure module. It therefore closes the engineering layer that converts the abstract phi-ladder into storage densities for concrete device models.

scope and limits

Does not derive E_coh from the forcing chain T5-T6.
Does not convert any quantity to SI units.
Does not treat time-dependent storage dynamics.

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