module module high

`IndisputableMonolith.Engineering.EnergyStorageDensityStructure`

The module defines the RS coherence energy quantum E_coh = phi^{-5} together with rung-based storage densities for chemical and nuclear regimes. Engineers deriving bounds for storage systems or turbines cite these expressions when working in RS-native units. It is a definition module that records positivity and ordering facts for the energy quantities.

claim$E_{coh} = phi^{-5}$, with phi-rung energy $E(rung) = yardstick · phi^{rung-8+gap(Z)}$ on the phi-ladder, plus chemical and nuclear storage densities and their ratio.

background

Recognition Science sets c = 1 and hbar = phi^{-5}, so the coherence energy quantum coincides with the reduced Planck constant in these units. The module imports the fundamental time quantum tau_0 = 1 tick from Constants and the J-cost functional from Cost. It introduces E_coh_storage as the base quantum, then phi_rung_energy, chemical_rung, nuclear_rung, and the comparison nuclear_exceeds_chemical.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the energy densities required by the downstream TeslaTurbineStructure. It implements the mass formula and phi-ladder energy steps that follow from the forcing chain T5-T8 and the Recognition Composition Law, placing concrete engineering quantities on the same footing as the alpha band and D = 3.

scope and limits

Does not derive phi from the functional equation.
Does not evaluate numerical energies for concrete atomic numbers.
Does not incorporate relativistic or quantum-field corrections.
Does not address 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