SymPhi-Engine

Physics-aware symbolic implication kernel. Applies conserved-energy grammar to the GDk9 alphabet — classifying letters by symmetry type, computing energy invariants, and transforming words through morphisms that preserve the fundamental conservation law: ΣE(before) = ΣE(after).

python main.py FWEM
# Energy: 42.04
# Classes: ['asymmetric', 'idempotent', 'biphasic', 'idempotent']
# Vector: [63. 60. 41. -0.95]
# Conserved: True

Concepts

Symmetry types — every letter is one of four classes:

Type	Letters	Equation	Role
Idempotent	A H I M O T U V W X Y / a m o t u v w x y	x² = x	Stabiliser — preserves identity
Biphasic	B C D E K / b c d e k	x² = f(x)	Oscillator — dual-phase modulation
Involutive	N S Z / n s z	x² = 1	Flipper — reversible inversion
Asymmetric	F G J L P Q R / f g j l p q r	x² ≠ x, 1	Driver — directional flow

Energy — each letter contributes pos × type_factor where type_factor varies by symmetry class. Words are stable when total energy is positive, finite, and conserved across transforms.

Vectorization — each letter maps to a 4-D vector [pos, type_id, √E, sin(θ)]. Word vectors are the component-wise sum, enabling ML integration and homotopy analysis.

Install

git clone https://github.com/ao3575911/SymPhi-Engine.git
cd SymPhi-Engine
pip install -e .

Runtime requirements: numpy. Optional heavy analysis (regression, pipeline): sympy networkx matplotlib scikit-learn pandas.

pip install numpy                          # core engine only
pip install -r requirements.txt            # full stack

Requires Python ≥ 3.10.

Usage

CLI

python main.py FWEM        # read a word through the implication engine
python main.py hello       # mixed-case works too

Library

from gdk9_core_engine import ImplicationEngine
from gdk9_framework import word_energy, get_symmetry_type, vectorize

engine = ImplicationEngine()

# Decode a word
result = engine.read("AVWM")
print(result["energy"])          # float
print(result["classes"])         # ['idempotent', 'involutive', 'idempotent', 'idempotent']
print(result["vector_sum"])      # numpy array

# Validate conservation
engine.validate_conservation("FWEM")   # True

# Transform
engine.transform("FWEM", morphism="flip")   # "MEWF"

# Lower-level
word_energy("GDK9")           # total energy float
get_symmetry_type("F")        # 'asymmetric'
vectorize("A")                # np.array([1, 0, 1.0, 0.841])

Symbolic cipher

from symbolic_cipher import encrypt, decrypt

ct = encrypt("hello", key="GDK9")
pt = decrypt(ct, key="GDK9")

Module overview

File	Purpose
gdk9_core_engine.py	ImplicationEngine — read, validate, transform
gdk9_framework.py	Symmetry classification, energy, vectorisation
gdk9_framework_extended.py	Extended morphisms and homotopy utilities
symbolic_cipher.py	Energy-keyed symbolic cipher
gdk9_pipeline.py	Full analysis pipeline with metrics
gdk9_pipeline_simple.py	Lightweight pipeline variant
gdk9_regression_engine.py	Energy regression and prediction
gdk9_regression_engine_v31.py	v3.1 regression with expanded ruleset
main.py	CLI entry point

Development

pip install -e ".[dev]"
python -m py_compile gdk9_core_engine.py gdk9_framework.py symbolic_cipher.py

CI runs on Python 3.10, 3.11, 3.12 via GitHub Actions.

License

MIT — © 2025 Adam Grange