``mathxlab.experiments.number_theory_suite``
============================================

Number theory experiment suite (E094–E123).

.. contents:: On this page
   :local:
   :depth: 2

Quickstart
----------


.. code-block:: python

   from mathxlab.experiments.number_theory_suite import run_e094, run_e095, ParamsE094



.. list-table:: Public API
   :header-rows: 1
   :widths: 20 10 70



   * - Name
     - Kind
     - Summary
   * - ``ParamsE094``
     - class
     - Parameters for E094.
   * - ``run_e094``
     - function
     - E094: ω(n) vs Ω(n): Erdős–Kac side-by-side.
   * - ``ParamsE095``
     - class
     - Parameters for E095.
   * - ``run_e095``
     - function
     - E095: Squarefree filter: ω(n)=Ω(n) when μ(n)≠0.
   * - ``ParamsE096``
     - class
     - Parameters for E096.
   * - ``run_e096``
     - function
     - E096: Record-holders for τ(n).
   * - ``ParamsE097``
     - class
     - Parameters for E097.
   * - ``run_e097``
     - function
     - E097: σ(n)/n landscape: deficient, perfect, abundant.
   * - ``ParamsE098``
     - class
     - Parameters for E098.
   * - ``run_e098``
     - function
     - E098: Extremals of σ(n)/n^α across α.
   * - ``ParamsE099``
     - class
     - Parameters for E099.
   * - ``run_e099``
     - function
     - E099: Jordan totients J_k: atlas and identities.
   * - ``ParamsE100``
     - class
     - Parameters for E100.
   * - ``run_e100``
     - function
     - E100: Carmichael λ(n) vs Euler φ(n).
   * - ``ParamsE101``
     - class
     - Parameters for E101.
   * - ``run_e101``
     - function
     - E101: Reduced residues: (Z/qZ)^× as a concrete set.
   * - ``ParamsE102``
     - class
     - Parameters for E102.
   * - ``run_e102``
     - function
     - E102: Dirichlet convolution identity zoo.
   * - ``ParamsE103``
     - class
     - Parameters for E103.
   * - ``run_e103``
     - function
     - E103: Chebyshev ψ(x): prime powers drive the jumps.
   * - ``ParamsE104``
     - class
     - Parameters for E104.
   * - ``run_e104``
     - function
     - E104: Von Mangoldt Λ: support and statistics.
   * - ``ParamsE105``
     - class
     - Parameters for E105.
   * - ``run_e105``
     - function
     - E105: Mertens function M(x): scaling views.
   * - ``ParamsE106``
     - class
     - Parameters for E106.
   * - ``run_e106``
     - function
     - E106: Real vs complex Dirichlet characters (small moduli).
   * - ``ParamsE107``
     - class
     - Parameters for E107.
   * - ``run_e107``
     - function
     - E107: Conductor distribution for characters.
   * - ``ParamsE108``
     - class
     - Parameters for E108.
   * - ``run_e108``
     - function
     - E108: Character orthogonality matrix heatmap.
   * - ``ParamsE109``
     - class
     - Parameters for E109.
   * - ``run_e109``
     - function
     - E109: Gauss sums τ(χ) for prime modulus.
   * - ``ParamsE110``
     - class
     - Parameters for E110.
   * - ``run_e110``
     - function
     - E110: Dirichlet L-series partial sums (toy).
   * - ``ParamsE111``
     - class
     - Parameters for E111.
   * - ``run_e111``
     - function
     - E111: Euler product vs Dirichlet series for L(s,χ).
   * - ``ParamsE112``
     - class
     - Parameters for E112.
   * - ``run_e112``
     - function
     - E112: Prime race π(x;q,a) − π(x;q,b).
   * - ``ParamsE113``
     - class
     - Parameters for E113.
   * - ``run_e113``
     - function
     - E113: First prime in each reduced residue class.
   * - ``ParamsE114``
     - class
     - Parameters for E114.
   * - ``run_e114``
     - function
     - E114: ζ(1/2+it) via η-series: truncation error curves.
   * - ``ParamsE115``
     - class
     - Parameters for E115.
   * - ``run_e115``
     - function
     - E115: Hardy Z(t): sign-change scan near low zeros.
   * - ``ParamsE116``
     - class
     - Parameters for E116.
   * - ``run_e116``
     - function
     - E116: Zero-count proxy vs Riemann–von Mangoldt main term.
   * - ``ParamsE117``
     - class
     - Parameters for E117.
   * - ``run_e117``
     - function
     - E117: Functional equation check: ζ(s) ≈ χ(s) ζ(1−s).
   * - ``ParamsE118``
     - class
     - Parameters for E118.
   * - ``run_e118``
     - function
     - E118: Euler product approximation vs ζ(s): where it degrades.
   * - ``ParamsE119``
     - class
     - Parameters for E119.
   * - ``run_e119``
     - function
     - E119: ψ(x)−x with simple smoothing.
   * - ``ParamsE120``
     - class
     - Parameters for E120.
   * - ``run_e120``
     - function
     - E120: Pretentious distance toy: sum_{p<=x} (1−Re χ(p))/p.
   * - ``ParamsE121``
     - class
     - Parameters for E121.
   * - ``run_e121``
     - function
     - E121: Multiplicativity stress tests (random coprime pairs).
   * - ``ParamsE122``
     - class
     - Parameters for E122.
   * - ``run_e122``
     - function
     - E122: Arithmetic function atlas: μ(n), ω(n), φ(n)/n heatmaps.
   * - ``ParamsE123``
     - class
     - Parameters for E123.
   * - ``run_e123``
     - function
     - E123: Correlation matrix: arithmetic functions on 1..N.

Reference
---------

Classes
~~~~~~~



.. autoclass::  mathxlab.experiments.number_theory_suite.ParamsE094
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE095
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE096
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE097
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE098
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE099
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE100
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE101
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE102
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE103
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE104
   :members:
   :member-order: bysource
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.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE105
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE106
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE107
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE108
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE109
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE110
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE111
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE112
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE113
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE114
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE115
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE116
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE117
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE118
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE119
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE120
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE121
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE122
   :members:
   :member-order: bysource
   :show-inheritance:





.. autoclass:: mathxlab.experiments.number_theory_suite.ParamsE123
   :members:
   :member-order: bysource
   :show-inheritance:



Functions
~~~~~~~~~



.. autofunction:: mathxlab.experiments.number_theory_suite.run_e094





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e095

   .. autofunction:: mathxlab.experiments.number_theory_suite.run_e096





.. autofunction::  mathxlab.experiments.number_theory_suite.run_e097





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e098





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e099

   .. autofunction:: mathxlab.experiments.number_theory_suite.run_e100





.. autofunction::  mathxlab.experiments.number_theory_suite.run_e101





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e102





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e103

   .. autofunction:: mathxlab.experiments.number_theory_suite.run_e104





.. autofunction::  mathxlab.experiments.number_theory_suite.run_e105





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e106





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e107

   .. autofunction:: mathxlab.experiments.number_theory_suite.run_e108





.. autofunction::  mathxlab.experiments.number_theory_suite.run_e109





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e110





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e111

   .. autofunction:: mathxlab.experiments.number_theory_suite.run_e112





.. autofunction::  mathxlab.experiments.number_theory_suite.run_e113





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e114





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e115

   .. autofunction:: mathxlab.experiments.number_theory_suite.run_e116





.. autofunction::  mathxlab.experiments.number_theory_suite.run_e117





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e118





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e119

   .. autofunction:: mathxlab.experiments.number_theory_suite.run_e120





.. autofunction::  mathxlab.experiments.number_theory_suite.run_e121





.. autofunction:: mathxlab.experiments.number_theory_suite.run_e122



.. autofunction:: mathxlab.experiments.number_theory_suite.run_e123