Cognitive Projection and Observer Entropy: A Minimal Model of Subjective Physics

This repository contains simulation code and data supporting the article:

"Cognitive Projection and Observer Entropy: A Minimal Model of Subjective Physics"
by Vladimir Khomyakov
(Zenodo DOI: 10.5281/zenodo.15719389)

Subjective Physics (Version 12.0) explores how perception shapes physical reality.
This project models an observer as an adaptive system that filters information, balancing accuracy and simplicity — a principle called Cognitive Uncertainty.
It introduces the concept of observer entropy to describe how perception, energy, and information interact.
All results are fully reproducible through open Python simulations linking cognition, thermodynamics, and information theory.

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Versions

• v1_entropy_hierarchy/ — Initial minimal observer entropy simulation.

• v2_adaptive_thresholds/ — Adaptive perceptual threshold ε(t) and extended visualizations.

• v3_tradeoff_functional/ — Trade-off functional simulation with λ-parameter analysis, Landauer energetic cost analysis.

• v4_discriminability_entropy/ — Adds adaptive entropy suppression, dynamic perceptual thresholds, phase transition tracking, and multi-condition comparisons.

• v5_entropy_rt_coupling/ — Models the coupling between subjective entropy and reaction time under Dirichlet uncertainty; includes large-scale simulation, entropy–RT correlation, and confidence interval estimation.

• v6_cognitive_geodesics/ — Introduces geodesic simulation in cognitive metric space, action-based dynamics, and curvature-driven discriminability analysis; implements cognitive trajectory integration and entropy functional regularization.

• v7_cognitive_reconstruction/ — Introduces cognitive retrodiction as a boundary value problem minimizing retrodictive entropy. Implements:

  • Damped geodesic simulation of cognitive trajectories using quadratic potential V(y; B) = (y − B)²
  • Entropy reduction analysis ΔH = H(A) − H(A|B) under belief intervention
  • Visualization of reconstructed cognitive states, entropy flow, and potential landscapes
  • Simulation scripts: cognitive_entropy_reduction_simulation.py, cognitive_retrodiction_simulation.py

• v7.4_noise_augmented/ — Adds noise-augmented cognitive retrodiction under uncertainty in final observations:

  • noise_dynamics_simulation.py — explores perturbed final conditions B′ = B + δ
  • retrodiction_noise_variation.py — simulates reconstructions from noisy boundaries
  • Generates figures: noise_dynamics.pdf, cog_reconstruction_noise.pdf

• v8_cognitive_dynamics/ — Introduces a fully dynamical framework for subjective physics based on cognitive entropy filtering, Σ-projection, and feedback-driven evolution:

  • cognitive_decoherence_with_sigma.py — simulates dynamic evolution of projected cognitive states under entropy-weighted filtering and boundary conditions; includes Σ-projection and parameter dependency analysis (region size, field types, and boundary conditions)
  • dynamic_weight_feedback_enhanced.py — implements cognitive feedback loops with bifurcation mechanisms, retrospection window for future prediction, and adaptive reconfiguration under entropy/flux constraints
  • Generates article figures: sigma_projection_result.pdf, dynamic_evolution.gif, parameter_study.pdf, dynamic_weight_feedback_results.pdf, and geometry_effects.pdf

• v9_dynamic_phase_portrait/ — Introduces entropy-driven cognitive phase space simulation with stochastic jumps, EEG feedback, and fluctuation-theorem compliance:

  • phase_portrait.py — simulates 3D/4D trajectories with Tsallis entropy, entropy gradient dynamics, stochastic cognitive jumps with ΔE and P₊/P₋ annotations, and EEG synchronization
  • plot_entropy_flux_and_jumps.py — plots time-resolved entropy flux, jump detection, and energy dissipation across perceptual transitions
  • Visualizes Lyapunov stability, energy thresholds, and observer weight evolution in subjective phase space
  • Generates figures: subjective_phase_portrait.pdf, 4d_phase_portrait.pdf, entropy_flux_and_jumps_real.pdf

• v10_multi_agent_shared_reality/ — Extends the framework to multi-agent systems with M ≥ 2 and introduces a refined Shared Reality Index (SRI) that scales with variance across heterogeneous discrete state spaces. Features include:

  • Generalised multi-agent cognitive dynamics
  • Σ-projection with expectation-level alignment
  • Dual diagnostics: distributional overlap A(t) and expectation alignment (SRI)
  • Overlap matrix visualization and PCA-projected cognitive trajectories
  • Provides operational markers for intersubjective convergence and shared reality constitution

• v11_core_observer_entropy/ — Consolidates the framework into a minimal, self-contained formalism unifying entropy scaling, Σ-projection, and multi-agent dynamics. Provides:

  • Core definitions: projection operator Fε, observer entropy S(ε), and trade-off functional L(ε)
  • Numerical experiments: entropy scaling, adaptive thresholds, RT distributions, and convergence in multi-agent settings.

• Documentation Split

  • Main article (v12.0, PDF subjective_physics_simulation_v12.0_main_article.pdf)
    Main theoretical article (primary citation target).

  • Technical core (v12.0, PDF a-technical-summary-of-subjective-physics-v12.0-2025.pdf)
    Technical and mathematical formalization of the v12.0 model.

  • Extended notes (v11.2, PDF subjective_physics_simulation_v11.2_extended_notes.pdf)
    Supplementary historical and experimental material (archival, unchanged from v11.2).

  • Serves as the stable reference version for future theoretical and experimental work.

Each version folder (e.g., v1_entropy_hierarchy/) contains a complete and self-contained implementation of that version's simulations.
For example, to reproduce all three main plots from version 1, run main.py inside v1_entropy_hierarchy/:

cd v1_entropy_hierarchy  
python main.py  

This will generate:

• entropy_vs_epsilon.pdf
• norm_vs_time.pdf
• trace_distance_vs_epsilon.pdf

All dependencies are resolved via the shared Conda environment defined in environment.yml.

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Main Features

• Cognitive entropy model with geodesic integration
• Landauer-bound energy dissipation under cognitive constraints
• Subjective metric tensor 𝒢ᵢⱼ(δ) and curvature effects
• Trade-off functional and cognitive action computation
• Thermodynamic cost estimation from observer-centric perspective
• Noise-augmented cognitive reconstruction under boundary uncertainty
• Publication-ready figures and data tables

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🔧 Installation

To install all required dependencies for all published versions (v1–v12.0) of the article:

pip install -r requirements.txt  

The requirements.txt file specifies the minimal set of Python packages needed to reproduce all simulations, figures, and numerical results described in the following publication:

Khomyakov, V. (2025). Cognitive Projection and Observer Entropy: A Minimal Model of Subjective Physics. Zenodo. https://doi.org/10.5281/zenodo.15719389

Python Environment

All scripts in versions v1–v12.0 are fully reproducible using the following Conda environment:

name: cogfun  
channels:  
  - pytorch  
  - conda-forge  
  - defaults  
dependencies:  
  - python=3.11.7  
  - numpy=2.2.5  
  - scikit-learn=1.6.1  
  - matplotlib=3.10.3  
  - pandas=2.2.3  
  - pytorch=2.3.0  
  - networkx=3.3  
  - pygame=2.6.1  
  - pip=24.0  
  - pip:  
    - galois==0.4.6  
    - ogb==1.3.6  
    - umap-learn==0.5.7  
    - tqdm==4.67.1  
    - torch-geometric==2.5.0  
    - pytest==7.4.4  

You can activate this environment with:

conda env create -f environment.yml  
conda activate cogfun  

The file environment.yml is included in the root of this repository.

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How to Run

Each version directory (e.g., v3_tradeoff_functional/) contains its own README.md describing how to:

• Reproduce the key results
• Rerun simulations
• Regenerate all figures and data exports

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DOI Versioning and Archive

• All versions
• Version 1 only
• Version 2 only
• Version 3 only
• Version 4 only
• Version 5 only
• Version 6 only
• Version 7 only
• Version 7.4 only
• Version 8.0 only
• Version 9.0 only
• Version 10.0 only
• Version 11.0 only
• Version 11.1 only
• Version 11.2.4 (technical core edition) only
• Version 12.0 only

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📜 License

MIT License (see individual LICENSE files per version).

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📖 Citation

Use the corresponding BibTeX entry from each version’s README.md or CITATION.cff.