module module high

`IndisputableMonolith.Physics.QuantumHallEffect`

The QuantumHallEffect module formalizes the quantum Hall effect in Recognition Science by defining the Chern number as the integer topological invariant that counts filled Landau levels in the IQHE or composite-fermion levels in the FQHE. Condensed-matter physicists would cite it when deriving quantized Hall conductance from the discrete 8-tick clock. The module consists entirely of definitions and supporting declarations that import the EightTick cycle and J-cost machinery without containing any proofs.

claimThe Chern number $C$ is the integer topological invariant such that the Hall conductance equals $C e^2/h$, where $C$ equals the number of filled Landau levels for the integer quantum Hall effect or the composite-fermion Landau-level index for the fractional case.

background

The module sits inside Recognition Science's discrete 8-tick foundation, whose phases run through multiples of π/4 as stated in the upstream EightTick documentation. It draws the cost function from JcostCore to assign recognition costs to topological configurations. The central object is the ChernNumber, introduced as an integer-valued invariant that directly equals the number of filled Landau levels (IQHE) or the composite-fermion structure (FQHE).

proof idea

This is a definition module, no proofs. It declares the core objects ChernNumber, hall_conductance_quantized, chern_number_integer_from_8tick, iqhe_filling, iqhe_conductance_integer, von_klitzing_constant, RK_positive, landau_energy, landau_spacing, zero_point_energy, jain_fraction and jain_denominator_odd_plus, each built from the imported EightTick and JcostCore primitives.

why it matters in Recognition Science

The module supplies the topological interface that connects the eight-tick octave (T7) to quantized transport, preparing the ground for any later derivation of the von Klitzing constant or filling-factor formulas inside the Recognition framework. Although no downstream used_by edges are recorded yet, the sibling declarations are positioned to feed higher-level physics results that invoke the phi-ladder or the Recognition Composition Law.

scope and limits

Does not derive explicit numerical values for the von Klitzing constant.
Does not treat electron-electron interactions beyond the composite-fermion ansatz.
Does not incorporate disorder, edge states, or localization effects.
Does not address the microscopic wavefunctions such as Laughlin states.

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Cost.JcostCore module_import
IndisputableMonolith.Foundation.EightTick module_import

declarations in this module (22)

structure ChernNumber L35
theorem hall_conductance_quantized L40
theorem chern_number_integer_from_8tick L51
def iqhe_filling L60
theorem iqhe_conductance_integer L63
abbrev von_klitzing_constant L68
theorem RK_positive L71
def landau_energy L78
theorem landau_spacing L82
theorem zero_point_energy L89
def jain_fraction L99
theorem jain_denominator_odd_plus L103
theorem jain_denominator_odd_minus L110
theorem fqhe_odd_denominator L118
theorem one_third_in_jain_sequence L124
theorem two_fifth_in_jain_sequence L130
def laughlin_quasi_charge L138
theorem laughlin_charge_one_third L141
theorem quasi_charge_decreasing L146
def laughlin_exchange_phase L160
theorem electron_exchange_phase L164
theorem one_third_exchange_phase L169