IndisputableMonolith.Physics.SemiconductorBandStructureFromConfigDim
This module defines types, counts, band gap functions, ratios, positivity lemmas, and certification structures for semiconductors derived from configuration dimension in the Recognition Science framework. Material physicists applying RS to condensed matter would reference these constructs when modeling band gaps. It is a definition module containing no proofs.
claimIntroduces the semiconductor classification $ ext{SemiconductorType}$, its cardinality, the band gap function $E_g$, the ratio $E_g^ ext{ratio}$, positivity $E_g > 0$, the certificate type $ ext{SemiconductorCert}$, and its constructor, all parameterized by configuration dimension.
background
The module imports the RS time quantum $ au_0 = 1$ tick from Constants. It introduces definitions for semiconductor band structure derived from configuration dimension, including SemiconductorType, bandGap, bandGap_ratio, bandGap_pos, SemiconductorCert, and semiconductorCert. The setting applies Recognition Science forcing chain results to condensed matter, using the phi-ladder and D=3 spatial dimensions to constrain material properties.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
Supplies the base definitions for semiconductor band structure that support higher-level physics models in the Recognition Science framework. It connects configuration dimension to band gap quantities, feeding into applications of the eight-tick octave and RCL.
scope and limits
- Does not derive numerical band gap values for specific materials.
- Does not address temperature or doping dependence.
- Does not connect to experimental conductivity data.
- Does not extend beyond the listed sibling definitions.