IndisputableMonolith.Physics.SemiconductorBandStructureFromConfigDim
This module introduces types and functions for semiconductor band structures derived from configuration dimension in Recognition Science. It defines SemiconductorType to classify material behaviors and provides bandGap along with ratio and positivity checks using RS-native units. Condensed matter physicists applying the framework to materials would cite these definitions for unit-consistent calculations. The module contains only definitions and basic properties with no theorems.
claimThe module defines the type $SemiconductorType$ classifying semiconductor categories, the function $bandGap : SemiconductorType → ℝ$ computing the energy gap from configuration dimension, the derived quantities $bandGap_ratio$ and $bandGap_pos$, and the certificate $SemiconductorCert$ ensuring physical consistency.
background
Recognition Science derives all physics from a single functional equation with the J-cost and phi-ladder. This module sits in the physics domain and imports the fundamental RS time quantum τ₀ = 1 tick from Constants. It introduces SemiconductorType as the classification for semiconductor behaviors, bandGap as the function returning the gap energy scaled in RS units, and SemiconductorCert as the structure certifying positivity and ratio properties.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies foundational definitions for semiconductor band structure in the Recognition Science framework and is positioned to feed into larger material-property models. It builds directly on the Constants module. No parent theorems appear in the current dependency graph, but it supports deriving condensed-matter quantities from the unified forcing chain.
scope and limits
- Does not compute numerical band gaps for specific real materials.
- Does not incorporate crystal lattice details or doping concentrations.
- Does not address temperature or external field dependence.
- Does not link band gaps to the fine-structure constant alpha.