module module high

`IndisputableMonolith.Engineering.RoomTempSuperconductivityStructure`

The module defines the RS coherence quantum E_coh = φ^{-5} together with thermal ratios and gap functions on the phi-ladder for room-temperature superconductivity models. Condensed matter researchers applying Recognition Science cite these quantities when estimating pairing scales and critical temperatures. The module consists of the central definition plus supporting positivity and monotonicity lemmas.

claim$E_{coh} = φ^{-5}$ (RS-native units) with value ≈0.090 eV; thermal ratios and superconducting gap are defined on the φ-ladder with positivity and monotonicity properties.

background

Recognition Science obtains all constants from the J-functional equation and the T0-T8 forcing chain. The imported Constants module fixes the time quantum τ₀ = 1 tick. The Cost module supplies the J-cost functions that underlie coherence definitions. This engineering module applies those primitives to superconductivity by introducing E_coh as the fundamental pairing energy scale.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the energy scale that feeds into T_c rung and superconducting gap calculations. It connects the T5 J-uniqueness step of the forcing chain to concrete engineering models. No downstream theorems are listed yet; the definitions close the link between abstract RS constants and room-temperature superconductivity thresholds.

scope and limits

Does not derive E_coh from the J-equation inside this module.
Does not incorporate material-specific lattice parameters.
Does not perform dynamical or many-body simulations.
Does not claim experimental verification of any compound.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (24)

def E_coh L51
theorem rs_coherence_quantum_pos L54
def thermal_ratio_room_temp L61
theorem thermal_ratio_lt_one L65
theorem thermal_ratio_pos L70
def T_c_rung L79
theorem tc_rung_pos L82
theorem phi_ladder_tc_monotone L88
theorem phi_ladder_unbounded L97
def superconducting_gap L110
theorem superconducting_gap_positive L114
theorem gap_zero_above_tc L124
theorem gap_max_at_zero L131
def ambient_sc_condition L140
theorem ambient_superconductivity_possible L144
theorem cooper_pair_binding_exceeds_thermal L152
structure CoherenceCoupling L165
theorem coherent_material_has_positive_tc L175
theorem coherent_coupling_pos L179
theorem room_temperature_superconductivity_from_ledger L187
theorem room_temp_superconductivity_structure L197
def predicted_tc_ratio L205
theorem tc_ratio_formula L208
def en002_certificate L214