lmm 0.1.3

A language agnostic framework for emulating reality.
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๐Ÿ‘๏ธ LMM ๐Ÿฆ€

LMM

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LMM is a pureโ€‘Rust framework that represents higherโ€‘dimensional realities through symbolic mathematics and physics simulation, inspired by the Pharaonic model of intelligence: compress the world into durable, universal equations.

๐ŸŽฌ Demo

The following is a proof-of-concept demonstration of the predictive engine generating coherent English sentences. It is powered purely by deterministic mathematical equations and structural Subject-Verb-Object loops, utilizing the standard Linux system dictionary (/usr/share/dict/words) as its vocabulary fallback to function.

This engine supports a complete suite of text-generation CLI commands, including summarize, sentence, paragraph, and essay, enabling sophisticated multi-paragraph construction driven entirely by mathematics.

๐Ÿง  Framework Overview

LMM bridges multimodal perception and actionable scientific discovery through five tightly integrated layers:

Layer Modules Purpose
Perception perception.rs, tensor.rs Raw bytes โ†’ normalised tensors
Symbolic equation.rs, symbolic.rs, discovery.rs GP symbolic regression, differentiation, simplification
Physics physics.rs, simulation.rs ODE models + Euler / RK4 / RK45 / leapfrog integrators
Causal causal.rs SCM graphs, do-calculus interventions, counterfactuals
Cognition consciousness.rs, world.rs, operator.rs Full perceive โ†’ encode โ†’ predict โ†’ act loop

โš™๏ธ Architecture

flowchart TD
    A["Raw Input\n(bytes / sensors)"]
    B["MultiModalPerception\nโ”€โ”€โ–บ Tensor"]
    C["Consciousness Loop\nperceive โ†’ encode โ†’ predict\nevaluate โ†’ plan (lookahead)"]
    D["WorldModel\n(RK4 physics)"]
    E["SymbolicRegression\n(GP equation search)"]
    F["CausalGraph\nintervention / counterfactual"]
    G["Expression AST\ndifferentiate / simplify"]

    A --> B --> C
    C --> D
    C --> E
    E --> G
    G --> F
    D --> F

๐Ÿ”ฌ Key Capabilities

  • ๐Ÿงฌ Genetic Programming: real population-based symbolic regression that seeds templates (linear, quadratic, periodic) and enforces variable-containing equations.
  • ๐Ÿ“ Symbolic Calculus: automatic differentiation (chain rule, product rule), constant folding simplification.
  • ๐ŸŒ€ Physics Suite: Harmonic, Lorenz, Pendulum, SIR epidemic, N-body gravity: all implement Simulatable.
  • ๐Ÿ”ข Field Calculus: N-D gradient, Laplacian, divergence, 3-D curl (central differences).
  • ๐Ÿ”— Causal Reasoning: structural causal models, do(X=v) interventions, counterfactual queries.
  • ๐Ÿงฉ Neural Operators: circular convolution with SGD kernel learning, Fourier spectral operators.
  • ๐Ÿ”ค Text โ†” Equation: encode any text into a symbolic equation; decode it back exactly (lossless via residuals).
  • ๐Ÿ”ฎ Symbolic Prediction: LMM-native text continuation via sliding-window GP regression and vocabulary anchoring.

๐Ÿ“ฆ Installation

From Source

git clone https://github.com/wiseaidotdev/lmm
cd lmm
cargo build --release

The binary is at ./target/release/lmm.

Via Cargo

cargo install lmm --all-features

[!NOTE] Requires Rust 1.86+. Install via rustup.

๐Ÿš€ CLI Usage

  โ–„โ–„โ–„      โ–„โ–„โ–„     โ–„โ–„โ–„   โ–„โ–„โ–„     โ–„โ–„โ–„
 โ–€โ–ˆโ–ˆโ–€       โ–ˆโ–ˆโ–ˆโ–„ โ–„โ–ˆโ–ˆโ–ˆ     โ–ˆโ–ˆโ–ˆโ–„ โ–„โ–ˆโ–ˆโ–ˆ
  โ–ˆโ–ˆ        โ–ˆโ–ˆ โ–€โ–ˆโ–€ โ–ˆโ–ˆ     โ–ˆโ–ˆ โ–€โ–ˆโ–€ โ–ˆโ–ˆ
  โ–ˆโ–ˆ        โ–ˆโ–ˆ     โ–ˆโ–ˆ     โ–ˆโ–ˆ     โ–ˆโ–ˆ
  โ–ˆโ–ˆ        โ–ˆโ–ˆ     โ–ˆโ–ˆ     โ–ˆโ–ˆ     โ–ˆโ–ˆ
 โ–ˆโ–ˆโ–ˆโ–ˆโ–ˆโ–ˆโ–ˆโ–ˆ โ–€โ–ˆโ–ˆโ–€     โ–€โ–ˆโ–ˆโ–„ โ–€โ–ˆโ–ˆโ–€     โ–€โ–ˆโ–ˆโ–„

Large Mathematical Model ยท Equation-Based Intelligence

The `lmm` CLI enables interaction with the Large Mathematical Model (LMM).
It provides advanced equation discovery, physics simulation, causal
inference, and unified sequence processing features.

Usage: lmm <COMMAND>
Commands:
  simulate       Simulate continuous logical pathways
  discover       Discover governing equations from data
  consciousness  Evaluate conscious state coherence
  physics        Run harmonic and chaotic physical models
  causal         Perform causal interventions and counterfactuals
  field          Compute tensor field gradients and divergences
  encode         Encode continuous truth into discrete text
  decode         Decode text back into dynamic equations
  predict        Predict next sequence based on pattern logic
  summarize      Extract key meaning via GP scoring
  sentence       Generate a single structural sentence
  paragraph      Generate a cohesive paragraph from a seed
  essay          Structure a full essay with intro and conclusion
  help           Print this message or the help of the given subcommand(s)

Options:
  -h, --help     Print help
  -V, --version  Print version

๐Ÿ“– Subcommand Reference

1. simulate: Harmonic Oscillator

Runs a harmonic oscillator using the RK4 integrator.

lmm simulate --step 0.01 --steps 200

Simulated 200 steps with step_size=0.01
Final state: [-0.41614683639502004, -0.9092974268937748]
Flag Default Description
-s, --step 0.01 Integration step size (ฮ”t)
-t, --steps 100 Number of integration steps

2. physics: Physics Model Simulation

Simulate one of four built-in physics models.

# Lorenz chaotic attractor (ฯƒ=10, ฯ=28, ฮฒ=8/3)
lmm physics --model lorenz --steps 500 --step-size 0.01

# Nonlinear pendulum
lmm physics --model pendulum --steps 300 --step-size 0.005

# SIR epidemic model
lmm physics --model sir --steps 1000 --step-size 0.5

# Damped harmonic oscillator (default)
lmm physics --model harmonic --steps 200

Lorenz example:

Lorenz: 500 steps. Final xyz: [-8.900269690476492, -7.413716837503834, 29.311877708359006]

SIR example:

SIR: 1000 steps. Final [S,I,R]: [58.797367656865795, 7.649993277129408e-15, 941.2026323431321]
Flag Default Description
-m, --model harmonic Model: lorenz, pendulum, sir, harmonic
-s, --steps 200 Number of integration steps
-z, --step-size 0.01 Step size ฮ”t

3. discover: Symbolic Regression

Runs Genetic Programming (GP) to discover a symbolic equation from data.

lmm discover --iterations 200

Discovered equation: (x + (1.002465056833142 + x))

The engine fits data points (i*0.5, 2*i*0.5 + 1) by default and finds the underlying linear law. Increase --iterations for more complex datasets.

Flag Default Description
-d, --data-path synthetic Data source (synthetic = built-in linear data)
-i, --iterations 100 Number of GP evolution iterations

4. consciousness: Perceive โ†’ Predict โ†’ Act Loop

Runs one tick of the full consciousness loop: raw bytes โ†’ perception tensor โ†’ world model prediction โ†’ action plan.

lmm consciousness --lookahead 5

Consciousness ticked. New state: [0.0019607843137254832, -0.24901960784313726, -0.37450980392156863, 0.5]
Mean prediction error: 0
Flag Default Description
-l, --lookahead 3 Multi-step lookahead horizon depth

5. causal: Causal Graph + do-Calculus

Builds a 3-node Structural Causal Model (x โ†’ y โ†’ z) and applies an intervention do(node = value), printing before/after values.

# Intervene on x: set x = 10, observe how y and z change
lmm causal --intervene-node x --intervene-value 10.0

Before intervention: x=Some(3.0), y=Some(6.0), z=Some(7.0)
After do(x=10): x=Some(10.0), y=Some(20.0), z=Some(21.0)

The SCM is:

  • y = 2 * x
  • z = y + 1
Flag Default Description
-n, --intervene-node x Name of the node to intervene on
-v, --intervene-value 1.0 Value to set the node to (do-calculus)

6. field: Scalar Field Calculus

Computes differential operators on a 1-D scalar field f(i) = iยฒ.

# Gradient: should approach 2i (central differences)
lmm field --size 8 --operation gradient

# Laplacian: should be โ‰ˆ 2 everywhere (second derivative of xยฒ)
lmm field --size 8 --operation laplacian

Gradient of xยฒ: [1.0, 2.0, 4.0, 6.0, 8.0, 10.0, 12.0, 13.0]

Laplacian of xยฒ: [0.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 0.0]
Flag Default Description
-s, --size 10 Number of field points
-o, --operation gradient Operation: gradient or laplacian

7. encode: Text โ†’ Symbolic Equation

This is the flagship demonstration of LMM's power. Any text is treated as a sequence of byte values indexed by position. The GP engine discovers a symbolic equation f(x) โ‰ˆ byte[x]. Integer residuals (byte[x] โˆ’ round(f(x))) are stored alongside the equation, guaranteeing lossless round-trip recovery.

lmm encode --text "The Pharaohs encoded reality in mathematics." \
           --iterations 150 --depth 5

โ”โ”โ” LMM ENCODER โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”
Input text  : "The Pharaohs encoded reality in mathematics."
Characters  : 44
Running GP symbolic regression (150 iterations, depth 5)...

Equation: (95.09620435614187 - cos(x))
Length: 44 chars
MSE: 646.3067
Max residual: 64

โ”โ”โ” ENCODED DATA โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”
{"eq":"(95.09620435614187 - cos(x))","len":44,"mse":646.306722,"res":[-10,9,5,-64,-16,9,3,20,2,15,8,20,-62,7,15,3,15,5,7,6,-63,18,5,1,13,11,22,26,-64,9,15,-62,15,2,20,8,6,15,3,21,9,3,20,-49]}

โ”โ”โ” VERIFY ROUND-TRIP โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”
Decoded text: "The Pharaohs encoded reality in mathematics."
Round-trip  : โœ… PERFECT

To decode later, run:
  lmm decode --equation "(95.09620435614187 - cos(x))" --length 44 --residuals "-10,9,5,-64,-16,9,3,20,2,15,8,20,-62,7,15,3,15,5,7,6,-63,18,5,1,13,11,22,26,-64,9,15,-62,15,2,20,8,6,15,3,21,9,3,20,-49"

[!NOTE] GP is stochastic: the discovered equation and residual values will differ across runs. The round-trip recovery is always โœ… PERFECT because the integer residuals correct for any approximation error.

# Encode from a file
lmm encode --input ./my_message.txt --iterations 200 --depth 5
Flag Default Description
-i, --input - Path to a text file to encode (- = use --text)
-t, --text Hello, LMM! Inline text (used when --input is -)
--iterations 80 GP evolution iterations
--depth 4 Maximum expression tree depth

8. decode: Symbolic Equation โ†’ Text

Reconstructs the original text from the equation and residuals printed by encode.

lmm decode \
  --equation "(95.09620435614187 - cos(x))" \
  --length 44 \
  --residuals "-10,9,5,-64,-16,9,3,20,2,15,8,20,-62,7,15,3,15,5,7,6,-63,18,5,1,13,11,22,26,-64,9,15,-62,15,2,20,8,6,15,3,21,9,3,20,-49"

โ”โ”โ” LMM DECODER โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”
Equation : (95.09620435614187 - cos(x))
Length   : 44

โ”โ”โ” DECODED TEXT โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”
The Pharaohs encoded reality in mathematics.
Flag Required Description
-e, --equation โœ… Equation string (from encode output)
-l, --length โœ… Number of characters to recover
-r, --residuals โœ… Comma-separated residuals. Use --residuals="-3,1,..." for negative values

[!IMPORTANT] Use --residuals="-3,..." (with =) or quote the argument when residuals contain negative values to prevent the shell from treating them as flags.

9. predict: Symbolic Text Continuation

The predict command acts as LMM's continuation engine. Unlike neural network LLMs that use massive statistical models, LMM strings together coherent English output using Pure Mathematics.

It does this by operating on three distinct, deterministic signals:

  • GP Trajectory Equation: f(pos) โ†’ word_byte_tone (discovers long-range subject themes)
  • GP Rhythm Equation: g(pos) โ†’ word_length (discovers alternating phonetic cadence)
  • Dictionary Grammar Engine: Maps mathematical values to a curated pool of English nouns, verbs, adjectives with system dictionary fallback (/usr/share/dict), while flowing through cyclic Subject-Verb-Object (SVO) POS grammar loops.
lmm predict --text "Wise AI built the first LMM" --window 10 --predict-length 80

Loaded 63746 dictionary words
โ”โ”โ” LMM PREDICTOR โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”
Input text  : "Wise AI built the first LMM"
Window used : 6 words
Trajectory  : (99.77577741824268 + ((x + 3.4804258799212793) + 1.7728570078579993))
Rhythm      : (cos(exp(x)) + 3.851491814600415)

โ”โ”โ” PREDICTED CONTINUATION โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”โ”
Wise AI built the first LMM in the true law often long time and a open path of an old scope is the solid order

[!NOTE] Text is parsed completely via pure equations over a carefully constructed English vocabulary pool, mapping geometric relationships and POS states into elegant and mysterious sentences.

Flag Default Description
-i, --input - Path to a text file (- = use --text)
-t, --text The Pharaohs encoded reality in Inline text seed
-w, --window 32 Context window in words
-p, --predict-length 16 Approximate character budget for continuation
--iterations 80 GP evolution iterations for the prediction model
--depth 4 Maximum expression tree depth

10. summarize: Key Sentence Extraction

Summarize distills a large body of text down to its most mathematically significant sentences. It scores each sentence by tracking tone deviations, length variances, and relative position.

lmm summarize --text "The ancient Egyptians built the pyramids using advanced mathematical knowledge. Their understanding of geometry was extraordinary for the time. Modern engineers still struggle to replicate their precision. Mathematics was their sacred language of cosmic alignment." --sentences 2

โ•”โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•—
โ•‘  โœ‚๏ธ  Summarize ยท Key Sentence Extraction             โ•‘
โ•šโ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•

  ๐Ÿ“ Input : 264 chars
  ๐Ÿ“Š Extracting 2 key sentences via GP scoring...

-- Summary -----------------------------------
  1. The ancient Egyptians built the pyramids using advanced mathematical knowledge.
  2. Mathematics was their sacred language of cosmic alignment.
Flag Default Description
-t, --text ... Input text to summarize
-n, --sentences 2 Number of key sentences to extract

11. sentence: Single Sentence Generation

Generates a single, structurally elegant sentence inspired by a seed text, using rotating Subject-Verb-Object (SVO) sequence patterns parsed from math tones.

lmm sentence --text "Mathematics is the language of the universe"

โ•”โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•—
โ•‘  โœ๏ธ  Sentence ยท Single Sentence Generation           โ•‘
โ•šโ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•

  ๐ŸŒฑ Seed : "Mathematics is the language of the universe"

-- Generated Sentence ------------------------
  Analysis enables the dynamic meaning of the universe.

12. paragraph: Cohesive Paragraph Generation

Chains multiple logically coherent sentences together, seeding subsequent sentence structures using extracted keywords from the original seed.

lmm paragraph --text "Equations reveal hidden truths about nature" --sentences 6

โ•”โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•—
โ•‘  ๐Ÿ“„  Paragraph ยท Generate a Paragraph                โ•‘
โ•šโ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•

  ๐ŸŒฑ Seed      : "Equations reveal hidden truths about nature"
  ๐Ÿ“Š Sentences : 6

-- Generated Paragraph -----------------------

  Simulation manifests the continuous symmetry of the truths. The symmetric wavelength connects infinity. Entropy remains the invariant truths underlying knowledge. The entropy of truths connects infinity. In essence, the symmetric integration encodes boundaries. Dimension describes precise reality beneath truths.
Flag Default Description
-t, --text ... Seed topic for paragraph generation
-n, --sentences 4 Number of sentences in the paragraph

13. essay: Full Essay Blueprint

Generates a fully structured essay, complete with an introduction, mathematical body paragraphs based on derived sub-topics, and a cohesive conclusion.

lmm essay --text 'Symmetry and the deeper patterns of physics' --paragraphs 2 --sentences 15

โ•”โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•—
โ•‘  ๐Ÿ“–  Essay ยท Generate a Full Essay                   โ•‘
โ•šโ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•

  ๐ŸŒฑ Topic      : "Symmetry and the deeper patterns of physics"
  ๐Ÿ“Š Paragraphs : 2 (15 sentences each)

-- Essay -------------------------------------

  โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•
  ๐Ÿ“–  Symmetry And The Deeper Patterns Of Physics
  โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•โ•

-- Introduction ------------------------------

  Analysis illuminates the probabilistic motion of the truth. The deterministic probability reflects knowledge. Algebra holds the infinite truth of motion. The frequency of truth shapes chaos. At its core, the axiomatic probability transforms perception. Physics unveils bounded infinity beyond truth. Recursion connects the bounded balance of the truth. The dynamic wavelength unveils infinity. Wavelength remains the bounded truth through reality. The dimension of truth produces identity. At its core, the discrete frequency governs existence. Frequency produces invariant perception pervading truth. Structure unveils the invariant existence of the truth. The coherent integration produces existence. Integration remains the mathematical truth governing complexity.


-- Body ยท ยง1 ---------------------------------

  At its core, the discrete computation governs truth. Computation manifests invariant harmony pervading symmetry. Topology enables the invariant truth of the symmetry. The coherent transformation manifests change. Transformation remains the mathematical symmetry governing time. The physics of symmetry encodes order. In this framework, the continuous calculus generates nature. Geometry enables axiomatic space across symmetry. Gradient determines the axiomatic time of the symmetry. The structural divergence illuminates matter. Physics remains the probabilistic symmetry beneath meaning. The mathematics of symmetry expresses truth. At its core, the deterministic recursion captures matter. Entropy unveils abstract balance of symmetry. Divergence connects the abstract limits of the symmetry.


-- Body ยท ยง2 ---------------------------------

  The recursive transformation manifests energy. Transformation remains the continuous symmetry within limits. The calculus of symmetry enables meaning. At its core, the axiomatic analysis transforms knowledge. Gradient illuminates probabilistic motion inside symmetry. Pattern illuminates the probabilistic truth of the symmetry. The fundamental physics expresses matter. Physics remains the deterministic symmetry underlying harmony. The algebra of symmetry unveils energy. In this framework, the abstract recursion captures causality. Entropy describes bounded truth beyond symmetry. Divergence connects the bounded unity of the symmetry. The dynamic logic unveils truth. Resonance remains the bounded symmetry through knowledge. The entropy of symmetry produces knowledge.


-- Conclusion --------------------------------

  Gradient unveils the invariant limits of the symmetry. The invariant computation compresses balance. Divergence is the bounded symmetry of identity. The pattern of symmetry defines matter. Fundamentally, the continuous gradient generates truth. Logic determines axiomatic harmony across symmetry. Recursion determines the axiomatic infinity of the symmetry. The structural entropy illuminates infinity. Entropy are the probabilistic symmetry beneath space. The dimension of symmetry expresses reality. Moreover, the deterministic frequency defines existence. Frequency connects abstract perception of symmetry. Structure encodes the abstract chaos of the symmetry. The elegant integration encodes existence. Integration are the dynamic symmetry within meaning.
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-t, --text ... Topic or title seed for the essay
-n, --paragraphs 2 Number of body paragraphs to generate
-s, --sentences 3 Number of sentences per paragraph

๐Ÿ”ฌ Architecture Deep Dive

Genetic Programming Symbolic Regression

flowchart TD
    A["Seeded population\n(linear/quadratic/periodic templates + random)"]
    B["Evaluate fitness\nMDL = nยทln(MSE) + complexityยทln(2)"]
    C["Tournament selection (k=5)"]
    D["Crossover & mutation"]
    E["Reject constant collapse\n(inject fresh random expr 70% of the time)"]
    F{Iterations done?}
    G["Best variable-containing expression (simplified)"]

    A --> B --> C --> D --> E --> F
    F -- No --> B
    F -- Yes --> G

Multi-Signal Prediction Engine

flowchart TD
    In["Context Window\n(Recent Tokens)"]

    In -->|Train| M["2nd-Order Markov Chain\nTransition probabilities"]
    In -->|GP Fit| T["Word-ID Trajectory GP\nf(pos) โ‰ˆ word_id"]
    In -->|GP Fit| R["Word-Length Rhythm GP\ng(pos) โ‰ˆ length"]

    In --> S["Suffix Pattern Matcher"]

    S -- "Match Found" --> Out["Exact Phrase Continuation"]
    S -- "No Match" --> Score["Composite Scorer"]

    M --> Score
    T --> Score
    R --> Score

    Score -->|Lowest Score| W["Select Best Word from Vocab"]
    W -->|Update Recency| Out

RK45 Adaptive Integrator

All Butcher-tableau coefficients are named package-level constants:

const RK45_A41: f64 = 1932.0 / 2197.0;
const RK45_A42: f64 = -7200.0 / 2197.0;
const RK45_A43: f64 = 7296.0 / 2197.0;
const RK45_B5_1: f64 = 16.0 / 135.0;
// ... etc.

Step size is adapted each iteration using the error estimate:

h_new = 0.9 ยท h ยท (tol / error)^0.2

๐Ÿ“ฐ Whitepaper

LLMs are Usefull. LMMs will Break Reality: the blog post that started this project.

๐Ÿค Contributing

Contributions are welcome! Feel free to open issues or pull requests.

๐Ÿ“ License

This project is licensed under the MIT License: see the LICENSE file for details.