TNFR: Resonant Fractal Nature Theory

TNFR is a Python research framework for coherent patterns on graph-coupled networks. It provides network construction, 13 registered structural operators, U1-U6 grammar, numerical evolution and diagnostics through Python and a CLI.

Each node carries form (EPI), reorganization capacity (nu_f) and circular phase. The unforced nodal relation is

$$ \frac{\partial \mathrm{EPI}}{\partial t}=\nu_f,\Delta\mathrm{NFR}(t). $$

In plain text: dEPI/dt = nu_f * DeltaNFR — form changes at a rate given by capacity times structural pressure. A runnable model also needs explicit pressure, phase, capacity, support and input laws. The equation alone does not select them. Structural time requires a declared clock; comparison with laboratory seconds requires an independent measurement bridge.

Use the engine to execute declared operator studies, observe structural fields and examine scoped mathematical models. Autonomous persistent patterns and their correspondence with physical entities remain research objectives.

Installation

Python 3.10 or later is required. Install the published package:

python -m pip install tnfr
python -m tnfr --version

To use the current checkout instead, run python -m pip install -e . from the repository root. Core dependencies include NumPy, SciPy and NetworkX. Optional extras enable additional tools:

python -m pip install -e ".[test,docs]"     # repository tests and documentation
python -m pip install -e ".[compute-jax]"   # optional JAX backend
python -m pip install -e ".[compute-torch]" # optional Torch numerical backend

Package metadata owns versions and dependency groups. The repository can be ahead of PyPI; use an explicit release tag when comparing results. The Torch extra supplies a numerical backend, without promising CUDA acceleration for every engine path.

Quick start

from tnfr.sdk import TNFR

net = TNFR.create(20, seed=42).ring()
net.evolve(steps=5, sequence="basic_activation")
print(net.results().summary())
print(net.tetrad().summary())

Output for the declared uniform preparation in the checked environment:

C=1.000, Si=1.000, N=20, E=20, rho=0.105
Phi_s=0.0000, |grad_phi|=0.0000, |K_phi|=0.0000, xi_C=4.5201 (N=20)

This creates a ring with supplied EPI=0, nu_f=1 and phase zero, then runs five complete operator words. It does not demonstrate spontaneous pattern formation. Coherence and sense index are diagnostics; a high value is not a proof of stability. The tetrad's safety flags, available separately through is_safe(), apply configured policies.

For stored-pressure observations with independent field availability, use diagnose_network(net) from tnfr.sdk. It reads a detached graph copy and retains unavailable-field reasons and coherence-length provenance. The CLI and SDK guide explains these reports, seed ownership and advanced execution routes.

Command line and reproducible studies

The CLI and SDK share a declared study runner:

tnfr network --nodes 6 --topology ring --seed 42 --steps 1 --export-spec study.json --output report.json
python -m tnfr network --spec study.json --output replay-report.json
tnfr sequences basic_activation
tnfr operators emission

In Python, use StudySpec, run_study and diagnose_network from tnfr.sdk. The report retains supplied inputs, finite endpoint state and diagnostic provenance. Cycles are operator-word passes, not elapsed physical time; a report is not a resumable checkpoint. See the CLI and SDK guide for equivalent Python examples, field availability and reproducibility scope.

Canonical structure

The scalar engine accepts signed real EPI or its uniform-real BEPIElement embedding. Scalar-only operators and diffusion reject genuinely complex or nonuniform payloads; their magnitude is not a signed form coordinate. Detailed state and execution boundaries belong to API contracts.

The nodal identity organizes the model; it does not uniquely supply the phase, capacity, support or pressure laws. Each experiment must declare those inputs and distinguish continuous flow from named operator jumps.

Explicit edge length determines field path geometry; weight is a compatibility fallback. Diffusion uses weight as conductance. The phase-wrap bounds are exact; warning thresholds are configured policies. The fitted coherence length and spectral fallback have different assumptions; reports identify the estimator used. The tetrad does not reconstruct the complete nodal state. Definitions, numerical boundaries and availability rules are centralized in Structural Fields.

Thirteen registered operators act primarily on form, capacity, phase or pressure. Their shared contracts and U1-U6 grammar define the engine interface. Grammar admission, live preconditions and trajectory stability are different claims. Si is configured telemetry used by some controllers; that use is not a derivation of spontaneous operator selection.

Named operators can introduce declared hybrid jumps; continuous solver spans use the shared nodal integrator. Immutable all-target proposals and atomic graph-owned commits have their own execution scope. Live temporal evidence, network REMESH history and rollback boundaries are specified in the API contracts, which owns these details rather than duplicating them here.

Mathematical scope

The repository contains useful conditional results and explicit counterexamples:

• Fixed reversible pure-EPI diffusion has a Dirichlet dissipation law and componentwise consensus under fixed positive capacities. Directed, forced and time-varying models require additional hypotheses: diffusion theorem.
• Projecting out nodal state can create memory. Mean closure need not preserve potential or coherence length: derived memory and scale/geometry bridge.
• A prescribed phase motion can produce a conditional periodic form response; autonomous generation of that motion remains open: phase/form foundations.
• The symplectic substrate, graph wave, polarization and arithmetic models are specified auxiliary constructions. Their identities do not establish that all engine trajectories obey them or that particles have emerged: variational scope and regime comparisons.

Conservation residuals are measured quantities; a nonnegative diagnostic energy is not automatically a Lyapunov function. Passing finite tests or reproducing arithmetic targets does not prove global stability, a Millennium conjecture or a physical theory of emergence.

The theory index distinguishes current references, conditional results, finite evidence and historical work. The research portfolio classifies the branches; the execution plan is the sole active queue. The main objective remains a predictive generative account of coherent patterns, with a separate reserved-data measurement bridge.

Repository map

src/tnfr/
├── config/          # runtime configuration and declared policy classifications
├── constants/       # canonical and operational constants
├── operators/       # operator implementations, contracts, grammar and execution
├── dynamics/        # Delta NFR computation and nodal integration
├── physics/         # tetrad, diffusion, conservation and structural diagnostics
├── metrics/         # coherence, sense index and telemetry kernels
├── core/            # service protocols, defaults and dependency container
├── services/        # orchestration facade
├── sdk/             # public network APIs, study declarations and reports
├── cli/             # command adapters, including the shared SDK study runner
├── engines/         # optimization and computation services
├── mathematics/     # numerical backends and arithmetic structures
└── research areas   # riemann, navier_stokes, yang_mills and related modules

Executable demonstrations are grouped into ten thematic folders under examples/. The full architecture and source-of-truth map are documented in ARCHITECTURE.md.

Development and verification

python -m pytest
python scripts/verify_internal_references.py --ci
python scripts/check_documentation.py
python scripts/prepare_docs.py
python -m mkdocs build --strict

The configured default test run excludes tests marked slow. See TESTING.md for focused suites, optional backends, slow tests, and reproducibility checks. See CONTRIBUTING.md for contribution requirements.

Documentation

The published site is built from these repository sources by the documentation workflow: TNFR documentation.

Citation

The DOI below identifies the project across versions. Cite the version and its release tag for the exact software snapshot.

@software{tnfr_python_engine,
  author = {Martinez Gamo, F. F.},
  title = {TNFR-Python-Engine: Resonant Fractal Nature Theory Implementation},
  year = {2026},
  version = {0.0.3.6},
  doi = {10.5281/zenodo.17602860},
  url = {https://github.com/fermga/TNFR-Python-Engine}
}

MIT licensed. See LICENSE.md.