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docs: establish mathematical debugger and incubator protocols
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‎experiments/__init__.py‎

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# you may not use this file except in compliance with the License.
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#
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"""Experiments: Mathematical debugger and validation suite."""
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"""Experiments: Mathematical debuggers and radical idea incubator."""

experiments/lorentz_debugger.py renamed to experiments/dbg_lorentz.py

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# you may not use this file except in compliance with the License.
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#
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"""Lorentz Transformation Debugger in Spacetime Algebra Cl(3,1).
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"""
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==============================================================================
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VERSOR EXPERIMENT: MATHEMATICAL DEBUGGER
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==============================================================================
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This script is designed to validate topological and algebraic phenomena
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rather than to achieve State-of-the-Art (SOTA) on traditional benchmarks.
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Our primary focus here is to explore pure geometric intuition within the
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Clifford Algebra framework.
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Please kindly note that as an experimental module, formal mathematical proofs
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and exhaustive literature reviews may still be in progress. We warmly invite
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you to run the code, test your own hypotheses, and open a GitHub Issue if you
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discover any fascinating geometric behaviors or encounter structural limitations.
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==============================================================================
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Lorentz Transformation Debugger in Spacetime Algebra Cl(3,1).
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Validates Versor's geometric algebra operations against known physical
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laws of special relativity. Spacetime events are grade-1 vectors,
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5. Invariant mass: m^2 = -s^2 preserved under transformation
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6. Rapidity extraction: recover phi from learned rotor (pure boost)
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7. Velocity addition: R(phi1)R(phi2) = R(phi1 + phi2)
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Usage:
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uv run python -m experiments.lorentz_debugger --epochs 200
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uv run python -m experiments.lorentz_debugger --strict-ortho --boost-type combined
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uv run python -m experiments.lorentz_debugger --save-plots --output-dir my_plots
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uv run python -m experiments.lorentz_debugger --rapidity-max 2.0 --diag-interval 10
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"""
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from __future__ import annotations
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import sys
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from core.algebra import CliffordAlgebra
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from core.metric import (
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signature_norm_squared, hermitian_distance, hermitian_norm,
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signature_norm_squared, hermitian_distance,
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hermitian_grade_spectrum, signature_trace_form,
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)
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from layers import CliffordLinear

experiments/minkowski_lattice.py renamed to experiments/dbg_minkowski_lattice.py

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# you may not use this file except in compliance with the License.
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#
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"""Minkowski's Theorem and Lattice Geometry via Geometric Algebra.
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"""
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==============================================================================
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VERSOR EXPERIMENT: MATHEMATICAL DEBUGGER
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==============================================================================
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This script is designed to validate topological and algebraic phenomena
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rather than to achieve State-of-the-Art (SOTA) on traditional benchmarks.
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Our primary focus here is to explore pure geometric intuition within the
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Clifford Algebra framework.
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Please kindly note that as an experimental module, formal mathematical proofs
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and exhaustive literature reviews may still be in progress. We warmly invite
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you to run the code, test your own hypotheses, and open a GitHub Issue if you
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discover any fascinating geometric behaviors or encounter structural limitations.
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==============================================================================
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Minkowski's Theorem and Lattice Geometry via Geometric Algebra.
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This experiment demonstrates Minkowski's First and Second Fundamental Theorems
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using the Clifford Algebra Cl(n,0).

experiments/navier_stokes.py renamed to experiments/dbg_navier_stokes.py

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# you may not use this file except in compliance with the License.
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#
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"""Navier-Stokes as Gauge Theory in Cl(3,0).
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"""
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==============================================================================
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VERSOR EXPERIMENT: MATHEMATICAL DEBUGGER
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==============================================================================
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This script is designed to validate topological and algebraic phenomena
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rather than to achieve State-of-the-Art (SOTA) on traditional benchmarks.
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Our primary focus here is to explore pure geometric intuition within the
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Clifford Algebra framework.
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Please kindly note that as an experimental module, formal mathematical proofs
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and exhaustive literature reviews may still be in progress. We warmly invite
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you to run the code, test your own hypotheses, and open a GitHub Issue if you
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discover any fascinating geometric behaviors or encounter structural limitations.
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==============================================================================
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Navier-Stokes as Gauge Theory in Cl(3,0).
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Reinterprets fluid dynamics through the lens of gauge theory:
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- Velocity field u is a gauge connection (grade-1 vector)

experiments/riemann_zeta.py renamed to experiments/dbg_riemann_zeta.py

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# you may not use this file except in compliance with the License.
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#
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"""Riemann Zeta Function Reconstruction via Geometric Algebra.
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"""
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==============================================================================
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VERSOR EXPERIMENT: MATHEMATICAL DEBUGGER
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==============================================================================
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This script is designed to validate topological and algebraic phenomena
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rather than to achieve State-of-the-Art (SOTA) on traditional benchmarks.
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Our primary focus here is to explore pure geometric intuition within the
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Clifford Algebra framework.
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Please kindly note that as an experimental module, formal mathematical proofs
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and exhaustive literature reviews may still be in progress. We warmly invite
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you to run the code, test your own hypotheses, and open a GitHub Issue if you
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discover any fascinating geometric behaviors or encounter structural limitations.
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==============================================================================
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Riemann Zeta Function Reconstruction via Geometric Algebra.
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Uses Cl(2,0,r) where the even subalgebra {1, e_12} is isomorphic to C.
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Complex numbers s = sigma + it are encoded as multivectors s = sigma*1 + t*e_12.
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- Monitors cross-grade coupling
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- Tests reconstruction on known analytic properties (functional equation,
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location of trivial zeros, behavior near the pole at s=1)
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Usage:
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uv run python -m experiments.riemann_zeta
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uv run python -m experiments.riemann_zeta --strict-ortho --epochs 300
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uv run python -m experiments.riemann_zeta --strict-ortho --save-plots --output-dir zeta_plots
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uv run python -m experiments.riemann_zeta --r-dim 1 --strict-ortho --epochs 300
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uv run python -m experiments.riemann_zeta --sigma-min 0.5 --sigma-max 3.0
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"""
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from __future__ import annotations

experiments/yang_mills.py renamed to experiments/dbg_yang_mills.py

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# you may not use this file except in compliance with the License.
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#
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"""Yang-Mills SU(2) Gauge Theory in Cl(3,0).
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"""
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==============================================================================
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VERSOR EXPERIMENT: MATHEMATICAL DEBUGGER
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==============================================================================
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This script is designed to validate topological and algebraic phenomena
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rather than to achieve State-of-the-Art (SOTA) on traditional benchmarks.
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Our primary focus here is to explore pure geometric intuition within the
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Clifford Algebra framework.
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Please kindly note that as an experimental module, formal mathematical proofs
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and exhaustive literature reviews may still be in progress. We warmly invite
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you to run the code, test your own hypotheses, and open a GitHub Issue if you
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discover any fascinating geometric behaviors or encounter structural limitations.
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==============================================================================
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Yang-Mills SU(2) Gauge Theory in Cl(3,0).
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Validates Geometric Algebra as a natural framework for non-abelian gauge theory.
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SU(2) ≅ Spin(3) = unit even subalgebra of Cl(3,0).

experiments/gdo.py renamed to experiments/inc_gdo.py

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# you may not use this file except in compliance with the License.
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#
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"""
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DISCLAIMER: AHEAD OF THE LITERATURE
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The theoretical foundations of this Geometric Deterministic Optimizer (GDO)
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-- including Lorentz Warp and Topological Signature Annealing
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-- are not derived from any existing academic papers.
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They are the pure materialization of my personal geometric intuition and hypotheses.
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"""
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==============================================================================
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VERSOR EXPERIMENT: IDEA INCUBATOR (SPIN-OFF CONCEPT)
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==============================================================================
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No Whining: This is a highly experimental, non-Euclidean architecture.
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If it shatters your standard models or fails on your specific edge cases,
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do not complain. You are just stepping outside the safety of standard SGD.
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This script serves as an early-stage proof-of-concept for radical, non-Euclidean
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architectures. The concepts demonstrated here are strongly driven by geometric
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intuition and may currently reside ahead of established academic literature.
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Complexity: The concepts of dimensional lift-up and manifold unbending are abstract.
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Comprehensive documentation and mathematical proofs are planned for the future.
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Please understand that rigorous mathematical proofs or comprehensive citations
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might be incomplete at this stage. If this geometric hypothesis proves structurally
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sound, it is planned to be spun off into a dedicated, independent repository
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for detailed research.
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The Truth is in the Code: If you cannot understand the topological mechanics right now,
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wait for the docs. Otherwise, the source code is the ultimate proof. Read it.
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may be fun.
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"""
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==============================================================================
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from __future__ import annotations
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"""Geometric Deterministic Optimizer (GDO): Topology-Aware Optimization.
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Geometric Deterministic Optimizer (GDO): Topology-Aware Optimization.
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HYPOTHESIS
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==========
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- Stop probing, ignore curvature; just follow the path
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"""
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from __future__ import annotations
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import sys
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import os
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import argparse

experiments/sta_trajectory.py renamed to experiments/inc_sta_trajectory.py

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# you may not use this file except in compliance with the License.
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#
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r"""STA Trajectory Reconstruction: 3D Handwriting from Noisy IMU Data.
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"""
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==============================================================================
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VERSOR EXPERIMENT: IDEA INCUBATOR (SPIN-OFF CONCEPT)
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==============================================================================
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This script serves as an early-stage proof-of-concept for radical, non-Euclidean
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architectures. The concepts demonstrated here are strongly driven by geometric
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intuition and may currently reside ahead of established academic literature.
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Please understand that rigorous mathematical proofs or comprehensive citations
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might be incomplete at this stage. If this geometric hypothesis proves structurally
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sound, it is planned to be spun off into a dedicated, independent repository
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for detailed research.
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==============================================================================
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This project requires data.
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Arbitrary synthetic data may be used.
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- Multi-sensor fusion (magnetometer, UWB)
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If you use ideas from this experiment, please cite the Versor framework:
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@software{Kim_Versor_Universal_Geometric_2026,
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author = {Kim, Eunkyum},
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doi = {10.5281/zenodo.18939519},
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month = mar,
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title = {{Versor: Universal Geometric Algebra Neural Network}},
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url = {https://github.com/Concode0/versor},
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version = {1.0.0},
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year = {2026}
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}
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"""
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from __future__ import annotations

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