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)

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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 (v11.2, PDF) — consolidated article
  • Extended notes (v11.2, PDF) — supplementary material (retrodiction, weak values, EEG analogies, cultural variation)
  • Technical core (v11.2.4, PDF) — concise 4-page technical core of v11.2, designed for citation, indexing, and quick reference. Contains all key equations and predictions in a self-contained format.
  • 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–v11.2.4 (technical core edition)) 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–v11.2.4 (technical core edition) 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

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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.