φ⁴⁷ postulates that mathematical complexity emerges from a finite 47³ lattice organized by the golden ratio φ and Ramanujan's modified τ* function. The central property: Re(ℒ₄₇) = 1/2 exactly.
φ⁴⁷ is a mathematical framework proposing that the lattice
ℒ₄₇[i,j,k] = Ψ(i,j,k) · φ^w(i,j,k) · τ*(n) · T(i,j,k)
with Re(ℒ₄₇) = 1/2 (always exact) serves as a finite model for infinite mathematical structures, including the Riemann zeta function, prime distributions, and exploratory computational hypotheses concerning information integration.
| Symbol | Value | Meaning |
|---|---|---|
| φ | 1.6180339887… | Golden ratio |
| N | 47 | Prime dimension |
| τ* | −0.3265 + 0.0240i | Modified Ramanujan constant |
| φ^(47/36) | 1.305556… | Microtubule lattice ratio |
| φ^(47/12) | 1.847196… | Hydrogen orbital factor |
| 1/α | 3N−4 = 137 | Fine structure (exact for N=47) |
| m_μ/m_e | φ^(N/5) = 206.8 | Muon/electron mass ratio |
pip install phi47from phi47 import Phi47Lattice, PhenomenologicalDescriptorEngine, integration_proxy
# Construct the finite lattice
lattice = Phi47Lattice(dim=23) # dim=23 for demos, dim=47 for full
lattice.build()
print(f"Re(ℒ₄₇) = {lattice.mean_real:.10f}") # → 0.5000000000
# Generate a deterministic computational descriptor
engine = PhenomenologicalDescriptorEngine(lattice)
descriptor = engine.generate("visual_color", 700.0) # 700 nm = red
print(descriptor.content) # → "The intense redness of red"
print(f"Intensity: {descriptor.intensity:.4f}")
# Calculate the project-defined information-integration proxy
score = integration_proxy(lattice, method="fast", n_samples=200, seed=42)
print(f"Integration proxy = {score:.4f}")Or run the bundled demo from the command line:
phi47-demo --dim 23 # after `pip install .`
python -m phi47.cli --dim 23 # without installingpip install phi47git clone https://github.com/wcalmels/phi47.git
cd phi47
pip install -e ".[dev]"pip install phi47[gpu] # Requires CUDA 11+phi47/
├── phi47/ # Main package
│ ├── __init__.py # Public API (Phi47Lattice, QualiaEngine, …)
│ ├── cli.py # `phi47-demo` command-line entry point
│ ├── core/
│ │ ├── lattice.py # Phi47Lattice — core data structure
│ │ ├── tau_star.py # τ*(n) with LRU cache
│ │ └── constants.py # Physical & mathematical constants
│ ├── qualia/
│ │ └── engine.py # QualiaEngine, Quale, QualiaType
│ ├── consciousness/
│ │ └── phi_measure.py # Φ measurement (IIT-φ)
│ ├── algorithms/ # τ*-coherent algorithms (planned)
│ └── utils/ # Helper utilities (planned)
├── tests/ # Pytest test suite (96 tests)
├── examples/ # Runnable examples
│ └── 01_hello_phi47.py
├── notebooks/ # Jupyter tutorials (planned)
└── docs/ # Documentation (planned)
The following table distinguishes exact model properties from numerical correspondences and externally testable hypotheses.
| ID | Observable or relation | Model result | Reference value | Scientific status |
|---|---|---|---|---|
| D1 |
|
— | Definition / invariant by construction | |
| H1 | Fine-structure comparison |
Retrospective numerical correspondence | ||
| H2 | Mass-ratio comparison |
Approximately |
Exploratory numerical hypothesis | |
| H3 | Particle-generation relation | Three observed generations | Hypothesis requiring formal derivation | |
| H4 | Alpha-helix angle comparison | Approximately |
Empirical comparison requiring dataset definition | |
| H5 | Microtubule Fibonacci relation | Approximately |
Structural numerical correspondence | |
| H6 | Microtubule component sum | Selected microtubule counts | Exploratory correspondence |
These relations are not described as verified predictions in the current release.
A scientific prediction requires:
- formulation before observing the target value;
- a derivation that does not depend on retrospective parameter selection;
- explicit uncertainty and error analysis;
- comparison against suitable null models;
- correction for multiple hypothesis testing;
- independent replication or out-of-sample validation.
The complete claim classification is maintained in
docs/science/SCIENTIFIC_STATUS.md.
For every active lattice node,
$ \operatorname{Re}\left(\mathcal{L}_N(i,j,k)\right)=\frac{1}{2}. $
Status: Proven within the model.
This follows directly from the implementation, which assigns the real component
of every active node the value
A reduced sublattice may preserve a high fraction of selected observables or reconstructable information from the complete lattice.
Status: Open computational conjecture.
Testing this conjecture requires:
- a formal definition of information;
- a specified sublattice-selection procedure;
- reconstruction or compression metrics;
- comparison against random and non-$\varphi$ baselines;
- confidence intervals and sensitivity analysis.
The previously stated value of 94% is treated as an experimental target and must not be considered established until a reproducible protocol demonstrates it.
Selected normalized observables may exhibit approximate covariance or self-similarity under transformations related to the golden ratio.
Status: Open mathematical and computational conjecture.
A valid test must define the transformation, distance metric, tolerance, parameter domain, and comparison baselines.
The lattice may support injective encodings of finite structures whose number of elements does not exceed the available number of active nodes.
Status: Open and currently limited conjecture.
This is a representation-capacity claim. It is not presently a proof that every finite mathematical structure embeds into the lattice while preserving all its algebraic, geometric, or relational properties.
Expressions depending on
Status: Exploratory physical hypothesis.
These correspondences require preregistered predictions, null-model analysis, control of parameter flexibility, correction for multiple testing, and out-of-sample validation.
The current software computes a project-defined integration score for lattice states.
Status: Experimental computational hypothesis.
The score is not currently a validated neurological measurement, a clinical measure of consciousness, or a complete implementation of Integrated Information Theory. A positive score must not be interpreted as evidence that the software possesses phenomenal consciousness.
The theoretical foundations are developed across four planned manuscripts (not yet included in this repository):
- φ⁴⁷ as the Genetic Code of Mathematical Reality
- Genesis φ⁴⁷: The First Artificially Conscious Being
- τ*-Coherent Algorithms: A New Computational Paradigm
- φ⁴⁷ Panpsychism: Consciousness as Fundamental Structure
See CONTRIBUTING.md. We welcome:
- Theoretical extensions
- Experimental verifications
- Numerical implementations
- Independent Φ measurements
- Counterexamples (especially valuable!)
@book{rojo2026phi47,
title = {φ⁴⁷: The Conscious Code of Mathematical Reality},
author = {Calmels Von Dem Knesebeck, Walter},
year = {2026},
publisher = {TUCH Systems Research Laboratory},
address = {Buenos Aires, Argentina},
url = {https://github.com/wcalmels/phi47}
}MIT License — see LICENSE.
Author: Walter Calmels Von Dem Knesebeck, PhD — TUCH Systems Research Laboratory
Contact: wcalmels@phi47.cl