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readme_content = """
This repository defines a formal system based on the rejection of actual infinity and the explicit inclusion of thermodynamic constraints in computation, observation, and cognition.
All logic is implemented in Coq. The system models a world where operations have finite cost, observations are limited by perceptual resolution, and computation consumes non-renewable budget.
VOID is not a metaphor. It is an alternative executable formalism — one that assumes reality, perception, and knowledge all occur within finite, budgeted processes.
The system is organized into modular Coq files grouped into conceptual layers.
| void_finite_minimal.v | Defines finite natural numbers F, bounded successor structure. |
| void_probability_minimal.v | Implements ℙ_𝔽, finite probabilities (0 < p < 1). |
| void_arithmetic.v | Arithmetic over F with cost-aware computation. |
| void_budget_flow.v | General framework for budget-aware functions f̂: A × 𝔹 → B × 𝔹. |
| void_entropy.v | Heat as computation cost, conservation axioms. |
| void_entropy_integration.v | Accumulation of entropy across composite processes. |
| void_geometry.v | Defines vector space Vₙ over ℙ_𝔽 without standard basis. |
| void_symmetry_movement.v | Budget-aware symmetry and motion operators. |
| void_geometry_basis.v | Defines shapes as fields, space as distinguishability gradient. |
| void_pattern.v | Defines pattern space 𝒫 = 𝔽 × ℙ_𝔽. |
| void_pattern_algebra_extended.v | Aggregation and interference of patterns. |
| void_pattern_thermo.v | Heat-aware pattern dynamics, refractory logic. |
| void_crisis_relocation.v | Models crisis points and adaptive pattern relocation. |
| void_memory_trace.v | Encodes decaying memory and persistence of activation. |
| void_resonance.v | Detects reinforcement through repeated stimuli. |
| void_distinguishability.v | Defines observer-based distinguishability 𝒟(O,e₁,e₂,b). |
| void_probability_minimal.v | Core definition of ℙ_𝔽 (shared). |
- Install Coq (version ≥ 8.17 recommended).
- Clone this repository.
- Start with:
- Explore void_pattern.v and void_pattern_thermo.v to understand how neural patterns activate and decay under thermodynamic constraints.
VOID is an executable alternative to formal systems based on infinite sets, continuous spaces, and cost-free computation.
It replaces:
- ℕ with F (finite natural numbers),
- [0,1] with ℙ_𝔽 (open interval rational pairs),
- metric space with observer-resolution distinguishability,
- computation with budget-aware transitions,
- perception with patterns and bounded thresholds.
It models a world where no process runs forever, no signal is infinitely fine, and no knowledge is free.
This work is released freely and openly under the MIT License.
This system was developed under constraint — physical, emotional, cognitive. It is not a protest against infinity, but a formal answer to the question: what remains when it is gone?
"""
readme_path = "/mnt/data/README.md" with open(readme_path, "w") as f: f.write(readme_content)
readme_path
