Sacred Math Module
Mathematical foundations: golden ratio, Fibonacci, Lucas numbers, fractal geometry, quantum gravity, particle physics, and cosmology.
math
Router and help for all math subcommands.
Aliases: sacred-math
tri math # Show all math subcommands
tri math <subcommand> # Run specific subcommand
Core Commands (Cycle 82)
constants
Display sacred mathematical constants organized in 4 sections.
Aliases: const
tri constants
Example output:
+=======================================================================+
| SACRED MATHEMATICS CONSTANTS |
| phi^2 + 1/phi^2 = 3 = TRINITY |
+=======================================================================+
--- GOLDEN RATIO ---
Golden Ratio (φ)
Value: 1.6180339887498948482
Formula: (1 + √5) / 2
Phi Squared (φ²)
Value: 2.6180339887498948482
Formula: φ² = φ + 1
Inverse Phi Squared (1/φ²)
Value: 0.3819660112501051518
Formula: 1/φ² = φ - 1
Trinity Sum (φ² + 1/φ²)
Value: 3.0
Formula: φ² + 1/φ² = 3
TRINITY IDENTITY — exact equality
--- TRANSCENDENTAL ---
Pi (π) 3.14159265358979323846
Euler's Number 2.71828182845904523536
π × φ × e 13.816890703380645 ≈ TRYTE_MAX (13)
--- GENETIC ALGORITHM ---
Mu (μ) 0.0382 Mutation rate
Chi (χ) 0.0618 Crossover rate
Sigma (σ) 1.618 Selection pressure
Epsilon (ε) 0.333 Elitism rate
--- QUANTUM ---
CHSH Inequality 2.8284271247461903 (2√2)
Fine Structure α⁻¹ 137.036
Berry Phase (β) 2.112
SU3 Constant 0.927
+=======================================================================+
| Trit: -1 0 +1 | Base: 3 | phi = 1.6180339... |
| mu = 0.0382 | chi = 0.0618 | sigma = phi | epsilon = 1/3 |
| Lucas: 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123 |
+=======================================================================+
phi
Compute golden ratio powers phi^n.
Aliases: golden
tri phi [n] # Default: n=10
tri phi 20
Example output:
phi^10 = 122.9918693812442100
fib
Fibonacci number F(n).
Aliases: fibonacci
tri fib [n] # Default: n=10, max safe: n=92
tri fib 20
Example output:
F(20) = 6,765 [4 digits]
Special flags: F(4) = 3 = TRINITY, F(7) = 13 = TRYTE_MAX.
lucas
Lucas number L(n) = phi^n + 1/phi^n.
tri lucas [n] # Default: n=5, max safe: n=86
tri lucas 10
Example output:
L(10) = 123 [3 digits]
* L(10) = 123 (Lucas number L(10))
Highlights L(2) = 3 = TRINITY!.
spiral
Phi-spiral coordinates.
Aliases: phi-spiral
tri spiral [n] # Compute phi-spiral for point n
tri spiral 5
Example output:
+--------------------------------------------------------------+
| phi-SPIRAL |
+--------------------------------------------------------------+
n : 5
angle : 1456.23 deg (25.416018 rad)
radius : 70.00
x : 67.210122
y : 19.565263
+--------------------------------------------------------------+
math-compare
Side-by-side comparison table of phi^n, F(n), L(n).
Aliases: compare
tri math-compare [n] # Default: n=12, max: n=92
tri math-compare 20
Example output:
Sacred Math Comparison Table (0..12)
================================================================
n phi^n F(n) L(n) phi^n+1/phi^n note
--- ----------- -------- -------- ------------- --------
0 1.0000 0 2 2.0000 (L=2, F=0)
2 2.6180 1 3 3.0000 TRINITY
4 6.8541 3 7 7.0000 F=3=TRINITY
12 321.9968 144 322 323.0000 F=144=12^2
Verification & Benchmarking (Cycle 82)
math-verify
Run 38 mathematical correctness checks.
Aliases: trinity-verify
tri math-verify
Checks include:
| Category | Checks | Examples |
|---|---|---|
| Core Identity | 9 | phi^2 + 1/phi^2 = 3, Fibonacci bases, Lucas bases |
| Fractal/Quantum | 10 | Sierpinski dim, Berry phase, SU(3) dim = 8 |
| Holographic/Gravity | 4 | Bekenstein-Hawking S/A = 1/4, Barbero-Immirzi |
| Particle Physics | 15 | Fine structure 1/alpha, proton/electron ratio, E8 dim = 248 |
Example output:
Sacred Math Verification (38 checks)
================================================
[OK] phi^2 + 1/phi^2 = 3.0000 = 3 Trinity
[OK] F(4) = 3 = 3 Fibonacci confirms
[OK] F(7) = 13 = 13 TRYTE_MAX
[OK] Sierpinski dim = 1.5850 = 1.5850 fractal
[OK] S/A = 1/4 (B-H) = 0.2500 Bekenstein-Hawking entropy
[OK] dim(E8) = 248 = 248 exceptional Lie group
...
All 38/38 checks PASSED
math-bench
Benchmark key mathematical operations.
Aliases: sacred-bench
tri math-bench
Example output:
Sacred Math Benchmark
================================================
fibonacci(19) 7.23 us 1.4 Gops/s
lucas(19) 6.89 us 1.5 Gops/s
phiSpiral(100) 12.45 us 804 Mops/s
goldenWrap 2.34 us 4.3 Gops/s
fibonacci(50) 15.67 us 638 Mops/s
All benchmarks: 10000 iterations each
Extended Constants (Cycle 83)
math exotic
Rare mathematical constants (Apery, Catalan, Feigenbaum).
Aliases: rare
tri math exotic
math physical
Fundamental physics constants (fine structure, Planck, speed of light).
Aliases: physics, phys
tri math physical
math chaos
Feigenbaum constants and logistic map bifurcation demo.
Aliases: feigenbaum
tri math chaos
math all
Display the complete catalog of all 145 constants.
tri math all
Advanced Models (Cycle 84)
math golden-function
Pellis 2025 Golden Function: G(x) = phi^x + phi^(-x).
Aliases: gf, pellis
tri math golden-function [n] # Default: n=10
Continuous extension of Lucas numbers. Verifies G(n) = L(n) for integers and computes half-integer extensions.
math nuclear
Nuclear Fibonacci shell stability model.
Aliases: nuc, shell
tri math nuclear
Magic numbers (2, 8, 20, 28, 50, 82, 126) correlated with Fibonacci/Lucas sequences. Island of Stability at Z=126, N=184.
math fractal
Fractal dimensions and self-similar phi structures.
Aliases: frac, hausdorff
tri math fractal
Sierpinski triangle (dim = 1.585), Koch snowflake (1.262), Menger sponge (2.727), golden spiral self-similarity. Includes ASCII Sierpinski rendering.
Quantum Mechanics (Cycle 85)
math quantum
Berry phase and geometric phase calculations.
Aliases: berry
tri math quantum
math su3
SU(3) color symmetry simulation with golden ratio.
Aliases: color, qcd
tri math su3
dim(SU(3)) = 8 = F(6). Gluon coupling, asymptotic freedom.
math planck
Planck units with phi-scaling relationships.
Aliases: units, planck-phi
tri math planck
Planck length, time, mass, temperature, energy. Verifies (l_P*phi)^2 + (l_P/phi)^2 = 3*l_P^2 = TRINITY.
math qutrit
Ternary phase gates and qutrit quantum states.
Aliases: qt, ternary-gate
tri math qutrit
3-level quantum system. Entropy: log_2(3) = 1.585 bits = Sierpinski dimension.
Holographic & Quantum Gravity (Cycle 86)
math holographic
Bekenstein-Hawking entropy and the holographic principle.
Aliases: holo, bekenstein
tri math holographic
S = A/(4*l_P^2). Hawking radiation, Unruh effect, black hole information paradox.
math ads-cft
AdS/CFT correspondence (Maldacena 1997).
Aliases: ads, maldacena
tri math ads-cft
Brown-Henneaux central charge c = 3R/(2G) — the 3 = TRINITY. Ryu-Takayanagi entanglement entropy. Complete AdS/CFT dictionary.
math quantum-gravity
Loop Quantum Gravity, Barbero-Immirzi, Regge calculus.
Aliases: qg, lqg
tri math quantum-gravity
Area quantization, spin foam models, Regge trajectories. Five levels from Trinity identity to LQG area gap.
Particle Physics (Cycle 88)
math particles
Particle mass spectrum with sacred ratio approximations.
Aliases: mass, quarks
tri math particles
Lepton and quark masses. Sacred formulas: m_p/m_e = 6*pi^5, Cabibbo angle = 13 degrees = F(7).
math groups
Exceptional Lie groups and sacred number theory.
Aliases: group-theory, e8, dimensions
tri math groups
SU(2) through E8 (dim = 248). Connections to string theory.
Visualization & Simulation (Cycle 87)
math holo-render
Holographic ASCII renderer.
Aliases: render, holo
tri math holo-render [mode] # ads | spin | penrose | entropy | hawking
math qg-sim
Quantum gravity time-evolution simulation.
Aliases: spin-foam
tri math qg-sim [steps] # Default: 100
math visual
ASCII phi-spiral visualization with holographic annotations.
Aliases: viz, plot
tri math visual [n] # Points: 0-64
math quantum-sim
Qutrit gate simulation.
Aliases: qsim, simulate
tri math quantum-sim [steps]
Cosmology (Cycle 87-90)
math trinity
Complete mathematical proof of phi^2 + 1/phi^2 = 3.
Aliases: identity, proof
tri math trinity
math harmony
Musical ratios and phi in acoustics.
Aliases: music, acoustic
tri math harmony
math cosmos
Cosmological parameters: dark matter, dark energy, Hubble tension.
Aliases: cosmological, hubble
tri math cosmos
math formula
Sacred formula approximator: find V = n*3^k*pi^m*phi^p*e^q for physical constants.
Aliases: sacred-formula, approximate, predict
tri math formula
math universe
Live universe simulation.
Aliases: multiverse, cosmo-sim
tri math universe [mode] # multiverse | brane | inflation | dark-energy | timeline
math string-theory
String theory and Calabi-Yau compactification.
Aliases: strings, calabi-yau
tri math string-theory [mode] # strings | calabi-yau | dualities | landscape
math engine
v3.0 Sacred Computation Engine status.
Aliases: v3, about
tri math engine
Economy Commands
math marketplace
$TRI economic dashboard.
Aliases: market, tri-market
tri math marketplace [mode] # dashboard | staking | proof | economics
math defi
$TRI DeFi protocol.
Aliases: yield, pools
tri math defi [mode] # pools | yield | oracle | governance
math rewards
$TRI staking rewards calculator.
Aliases: tri-rewards, stake
tri math rewards [n]
Complete Command Summary
| Command | Aliases | Cycle | Category |
|---|---|---|---|
tri math | sacred-math | 82 | Router |
tri constants | const | 82 | Core |
tri phi | golden | 82 | Core |
tri fib | fibonacci | 82 | Core |
tri lucas | — | 82 | Core |
tri spiral | phi-spiral | 82 | Core |
tri math-compare | compare | 82 | Core |
tri math-verify | trinity-verify | 82 | Verification |
tri math-bench | sacred-bench | 82 | Benchmark |
tri math exotic | rare | 83 | Extended |
tri math physical | physics, phys | 83 | Extended |
tri math chaos | feigenbaum | 83 | Extended |
tri math all | — | 83 | Extended |
tri math golden-function | gf, pellis | 84 | Advanced |
tri math nuclear | nuc, shell | 84 | Advanced |
tri math fractal | frac, hausdorff | 84 | Advanced |
tri math quantum | berry | 85 | Quantum |
tri math su3 | color, qcd | 85 | Quantum |
tri math planck | units, planck-phi | 85 | Quantum |
tri math qutrit | qt, ternary-gate | 85 | Quantum |
tri math holographic | holo, bekenstein | 86 | Gravity |
tri math ads-cft | ads, maldacena | 86 | Gravity |
tri math quantum-gravity | qg, lqg | 86 | Gravity |
tri math particles | mass, quarks | 88 | Particle |
tri math groups | group-theory, e8 | 88 | Particle |
tri math holo-render | render, holo | 87 | Visual |
tri math qg-sim | spin-foam | 87 | Visual |
tri math visual | viz, plot | 87 | Visual |
tri math quantum-sim | qsim, simulate | 87 | Visual |
tri math trinity | identity, proof | 87 | Deep |
tri math harmony | music, acoustic | 87 | Deep |
tri math cosmos | cosmological, hubble | 87 | Deep |
tri math formula | sacred-formula, predict | 87 | Deep |
tri math universe | multiverse, cosmo-sim | 90 | Simulation |
tri math string-theory | strings, calabi-yau | 90 | Simulation |
tri math engine | v3, about | 87 | Status |
tri math marketplace | market, tri-market | 87 | Economy |
tri math defi | yield, pools | 90 | Economy |
tri math rewards | tri-rewards, stake | 87 | Economy |
tri math gematria | gem, coptic | 96 | Engine |