Physics — Core Framework

The Synergy Standard Model

A geometric framework that derives the fundamental constants of physics — the speed of light, the fine-structure constant, particle masses, and 165+ others — from nothing but a square with side length 1.

6 equations. 0 free parameters. 0 empirical inputs. Run the math yourself.

6
Core Equations
0
Free Parameters
0
Empirical Inputs
165+
Constants Derived
118
Element Masses
81
Theorists Converged

What Is the SSM?

The Synergy Standard Model (SSM) is a mathematical framework that starts with the simplest possible geometric object — a unit square — and derives the fundamental constants of physics from it. No measurements. No curve-fitting. No free parameters.

It produces numbers like:

ConstantSSM OutputCODATA ValueDifference
Speed of light (c)299,792,457.55 m/s299,792,458 m/s0.45 m/s
Fine-structure (1/α)137.03599921137.035999177within 2σ
Proton/electron ratio1836.181836.15267~0.0015%
Electron mass9.10903 × 10¹¹ kg9.10938 × 10¹¹ kgΔ 3.6 × 10³&sup5;
The question is simple: does the math produce the right numbers? If it does, how is that possible from a square?

The Four Axioms

Everything in the SSM derives from four axioms. Nothing else enters at any point.

A0

The Unit Square

A square with side length 1 in Euclidean space. The starting object. The only geometric input to the entire framework.

A1

Euclidean Geometry

The normal rules: distance, angles, midpoints, diagonals. No curved spacetime. No extra dimensions. Just a flat square.

A2

Fibonacci Seed

The first four Fibonacci numbers: 1, 1, 2, 3. These seed the polygon coupling structure inside the square (pentagon, hexagon).

A3

No Empirical Input

No measured value may enter at any step. If a derivation requires a measured number, it fails. This axiom is the constraint that forces everything.

The No-Choice Principle At every step in the derivation, there is exactly one valid next step. Every alternative either violates an axiom, produces a contradiction, or is geometrically impossible. This is proven exhaustively in the No-Choice Proof — which tests every possible value at each step and shows why only one survives.

The 11-Step Derivation

From axioms to the speed of light in 11 forced steps. Each step has exactly one outcome.

Quadrian Ratio

Draw a line from a corner of the unit square to the midpoint of the opposite side. Length = √(1.25) = 1.11803... This is the Quadrian Ratio q.

Golden Ratio

Add ½ to the Quadrian Ratio: q + 0.5 = 1.61803... = φ, the golden ratio. Forced — only possible addition from the square's geometry.

Polygon Coupling

Multiply by (15 + √2). The 15 comes from pentagon-hexagon structure (A2), √2 from the diagonal (A1). Result: θx = 26.5651°

Angular Complement

Take the complement: 90° − θx = 63.4349° = θy. The 90° is forced — it's the corner angle of a square (A0).

Double Angle

θz = 2 × θy = 126.8698°. The 2 is forced by the unit square's bilateral symmetry.

Arena Bounce

The square has 8 compass directions. A path bouncing through 7 legs: θu = θz × 7 = 888.089°

Angular Potential

Sum the angular potentials: PNp = θu + θy = 951.524°

Speed of Light

Plug into the speed equation: cy = 107(30 − 1/(103 − PNp)) − 2PNp/√5
= 299,792,457.55 m/s

Second Speed

The x-axis speed: cx = 299,792,458.45 m/s. Average of cx and cy = exactly 299,792,458.00.

Fine-Structure Constant

The Feyn-Wolfgang coupling: 1/α = 137.03599921. Derived from the same angular structure. Within 2σ of CODATA 2022.

Mass Ratio

Proton-to-electron mass ratio: mp/me = 1836.18. Derived from the Mass Index equation using the same geometry. ~0.0015% from measured value.

The Six Equations

1
Speed of Light — Qs(n)
$$c_y = 10^7\!\left(30 - \frac{1}{10^3 - P_{Np}}\right) - \frac{2\,P_{Np}}{\sqrt{5}}$$
$$q = \sqrt{1^2 + 0.5^2} \;\to\; \Phi = q + 0.5 \;\to\; \theta_x = \Phi(15+\sqrt{2}) \;\to\; \theta_y = 90 - \theta_x$$
cy = 299,792,457.553 m/s   Δ 0.447 m/s from CODATA
Derives the speed of light from angular potentials within the unit square. Every constant in the chain traces back to A0–A3. No measured value enters.
2
Fine-Structure Constant — Fw(n)
$$\alpha = F_w(n) = \frac{1}{F(n)\cdot\bigl(F(n)+1\bigr)}$$
$$F(n) = n + (\sqrt{m_x} - 1), \quad m_x = \sqrt{2} + \frac{1}{\sqrt{15^2 + \frac{1}{\sqrt{(n{+}5) \cdot 20 - \frac{1}{20}}}}}$$
1/α = 137.03599921   CODATA 2022: 137.035999177(21) — within 2σ
The constant that governs electromagnetism. Every number traced: √2 = unit square diagonal (A1+A2), 15 = polygon coupling (A0–A3), 20 = 2×U (Step 7), 5 = pentagon (A3).
3
Mass Index — Mi(n)
$$M_i(n) = \frac{2240}{\sqrt{\sqrt{2} + \dfrac{100}{n}}} \;\to\; 1352$$
Proton/electron ratio ≈ 1836.18   ~0.0015% from CODATA
Produces the mass index that generates the proton-to-electron mass ratio. The 2240 and 100 are geometrically forced from the arena structure.
4
Particle Masses — Ma(n)
$$M_a(n) = n \times 1352 \times \sqrt{F + \varphi - 1} \times \frac{1}{c_y^{\,4}}$$
$$F = 30 \;\text{(angular limit)} \quad \varphi = \tfrac{\sqrt{5}}{2} - \tfrac{1}{2} \quad c_y = \text{Qs}(n)$$
me = 9.10903 × 10¹¹ kg   Δ 3.6 × 10³&sup5; kg
Computes particle masses (electron, proton, neutron) from the geometry. The 1352 is the mass index from Mi(n). F=30 is the angular boundary of the square arena.
5
Pi as Gradient — Syπ(n)
$$\text{Sy}\pi(n) = \frac{3{,}940{,}245{,}000{,}000}{2{,}217{,}131\,n + 1{,}253{,}859{,}750{,}000}$$
$$\text{Sy}\pi(162) = 3.14159268\ldots \quad P_x(\pi) = 162.0055\ldots \quad \text{Sy}\pi(P_x(\pi)) = \pi$$
Round-trip exact to machine precision   Δ 3.07 × 10&sup8;
Treats π not as a fixed constant but as a position-dependent gradient function. The SSM position of π is at n=162, connecting to the 162/163 architecture of the framework.
6
Element Masses — El(e,p,n)
$$\text{El}(e,p,n) = \bigl(m_p p + m_n n + m_e e\bigr)\bigl(1 - \alpha\bigr)$$
$$m_p = M_a(1836.18\ldots) \quad m_n = M_a(1838.18\ldots) \quad m_e = M_a(1)$$
H = 1.661×10²&sup7;   He = 6.647×10²&sup7;   C = 1.994×10²&sup6;   U = 3.955×10²&sup5; kg
Computes the mass of all 118 elements from the particle masses and fine-structure constant. Hydrogen to Uranium — same six equations, same unit square.

Verify It Yourself

You don't need a physics degree. You need a browser. Click Run below to compute the speed of light from a unit square — live, in your browser, right now.

// The entire derivation of the speed of light from a unit square
const q  = Math.sqrt(1**2 + 0.5**2);          // Quadrian ratio = √1.25
const φ  = q + 0.5;                        // Golden ratio = 1.618...
const θx = φ * (15 + Math.sqrt(2));      // Polygon coupling angle
const θy = 90 - θx;                       // Angular complement (90° = square corner)
const θu = (θy * 2) * 7;                  // Arena bounce (7 legs, 8 compass dirs)
const P  = θu + θy;                        // Angular potential sum
const cy = (1e7 * (30 - 1/(1e3 - P))) - (2*P / Math.sqrt(5));

console.log("SSM speed of light =", cy, "m/s");
console.log("CODATA value       =", 299792458, "m/s");
console.log("Difference         =", Math.abs(cy - 299792458).toFixed(3), "m/s");
Click "Run" to compute the speed of light from a unit square.
No Belief Required If the output is ~299,792,457.55 m/s, the math works. Every number in the code above traces back to the unit square. There is no point in this chain where a measured physical value enters. The code IS the proof — run it.

What Makes This Different?

PropertyCERN Standard ModelSynergy Standard Model
Free parameters19 (measured, plugged in by hand)0 (all derived)
Empirical inputsRequires experimental dataNone — pure geometry
Starting objectQuantum field theory + gauge groupsA unit square [0,1]²
Constants explained“We don't know why they have these values”Geometric consequences of the axioms
VerificationRequires particle acceleratorRequires a JavaScript console
Element massesMeasured experimentallyComputed for all 118 elements
FalsifiabilityYes (experimental)Yes (computational — 60 seconds)

The SSM doesn't claim to replace quantum mechanics or general relativity. It makes a narrower, more testable claim: the fundamental constants are not random — they are geometric consequences of the simplest possible starting object.

The Framework Stack

The SSM is the physics layer of the larger FairMind DNA architecture:

Physics

SSM

Structure of reality. Constants, masses, forces — all from geometry.

Value

VDM

Value of that structure. Economics, fairness, measurement — VALUE = a + b + c + d.

Cognition

The Duat

Consciousness as reflective information dynamics. 108 Truth Violations.

Forecasting

DFM

Reality in motion. Real-time forecasting from physics, not training data.

Explore the SSM

⚛ Constants Dashboard 🧪 Periodic Table 🔒 No-Choice Proof 🌀 Syπ Explorer 🔷 Quadrian Arena 🫧 Bubble Core 💡 Two Speeds of Light 🔢 Number Explorer ⚖ Measurement Units ∞ Interphasic Calculator 🔀 81 Theorist Convergences ⚙ Source Code & Implementations 📄 Full Documentation
🇨🇦 © 2015– Wesley Long & Daisy Hope. All rights reserved.  |  Core: CC BY-SA 4.0  |  Code: MIT