Output counts audited from ssm.js.json via tools/count-outputs.js. Claim and axiom counts per SSM_CLAIMS.md.
Self-contained JavaScript — no dependencies, no CODATA input. Every value on this page comes from these files.
Copy the primer below and paste it into ChatGPT, Claude, Gemini, or Grok. It points the AI at the full derivation chain and tells it how to audit the framework. Then ask whatever you want — the model will have everything it needs to verify, falsify, or cross-check every claim.
Self-contained audit instructions with source URLs, reading order, and the falsification routes.
Every value below is produced by the derived JavaScript implementation above — no CODATA input, no tuning. Full derivations in the chapters that follow.
| Quantity | SSM Value | CODATA / Accepted | Deviation |
|---|---|---|---|
| Speed of light $c_y$ (North) | 299,792,457.553 m/s | 299,792,458 m/s | 0.45 m/s (1.5 ppb) |
| Speed of light $c_x$ (East) | 299,881,898.796 m/s | — novel prediction | $c_x/c_y = 1.000298$ |
| Fine-structure $1/\alpha$ | 137.035999206 | 137.035999177 | < 10−7 |
| Vacuum permeability $\mu_0$ | 1.2566568 × 10−6 | 1.2566371 × 10−6 | 1.6 × 10−5 |
| Planck constant $h$ | 6.627 × 10−34 J·s | 6.626 × 10−34 | 0.014% |
| Electron mass $m_e$ | 9.10903 × 10−31 kg | 9.10938 × 10−31 | ~10−3 |
| Proton/electron ratio | 1836.1813 | 1836.1527 | 0.029 absolute |
| Gravitational $G$ | 6.67438 × 10−11 | 6.67430 × 10−11 | 1.2 × 10−5 |
| Boltzmann $k_B$ | 1.38047 × 10−23 | 1.38065 × 10−23 | 0.013% |
| Sy$\pi$(162) vs $\pi$ | 3.14159268… | 3.14159265… | 3.1 × 10−8 |
| $\varepsilon_0\mu_0 c^2$ identity | 1.000000000 | 1 (exact) | < 10−8 |
| 118 element masses | $El(e,p,n)$ | CODATA atomic | all within $\sim 10^{-3}$ |
The Synergy Standard Model derives every physical constant — the speed of light, the fine-structure constant, Planck's constant, the electron mass, the masses of all 118 elements — from a unit square and three axioms. No measurements enter the derivation. No parameters are tuned. No branches are chosen.
GAP stands for Geometry → Algebra → Physics. It is a typographic convention that tags every symbol with the layer it currently lives on. A symbol wearing a geo superscript is a counted structure on the unit square — no units, no measurement, no freedom. A symbol wearing alg is a pure mathematical operator: a map, an index function, a rational expression. A symbol wearing phy is an observable with SI units — something an experimentalist can walk into a lab and measure.
Standard physics notation hides the boundary where a number stops being math and starts being a measurement. Symbols like $c$, $\hbar$, $\alpha$, $G$ look the same on a page whether they came from a derivation, a table, or a fit — the reader cannot tell. GAP notation makes the boundary visible. When you see $\geo{q}$, you know it is the half-diagonal of a unit square; when you see $\phy{c_y}$, you know SI units have just been attached; when you see $\alg{\Pi}(n)$, you know you are inside a bijective map with no physical content yet.
This matters because the SSM's central claim is that there is no gap between geometry and measurement — the constants of nature are forced consequences of counting on a unit square. The only honest way to present that claim is to show, at every step, which layer a quantity is on and where it crosses. If a symbol ever has to appear with no layer tag, the derivation has a hole.
Every physical constant in the SSM is a chain with exactly one arrow from geometry to algebra and exactly one arrow from algebra to physics. The speed of light, for example, reads:
Three things are explicit: (1) the input is a counted path aggregate on the unit square; (2) the transformation is a named algebraic map with a known inverse; (3) units enter only at the final step, not before. The same pattern applies to $\phy{\mu_0}$, $\phy{\alpha}$, $\phy{h}$, $\phy{G}$, $\phy{m_e}$, and the 118 element masses.
Auditability. Anyone can walk the chain backwards. Given any physical number, the algebraic inverse returns a position; the position can be read off the unit square by hand.
No hidden fits. A parameter that cannot be assigned a layer is a free parameter. GAP notation makes free parameters impossible to hide — they would appear tag-less.
Unit hygiene. SI units cannot appear before the physics layer. If they do, the derivation has smuggled a measurement into geometry — a bug GAP notation makes immediately visible.
Falsifiability. Because every observable has a complete chain, every observable is falsifiable at two places: the geometric count, or the algebraic evaluation. The SSM makes 135+ such falsifiable predictions.
Outputs are pure numbers until they cross the $\alg{\;\to\;}\phy{\;}$ boundary. Only at that boundary do SI units appear. The rest of this book walks that boundary twenty-six times.
Full normative specification: docs/GAP_NOTATION.md — the layer convention every other SSM document presumes.
Three axioms generate the entire model. Two are geometric, one is algebraic. Every subsequent quantity is a forced consequence of these three statements — no additional choices enter the derivation.
$A_1$ fixes the scale: the side of the unit square is the only length unit in the model. $A_2$ fixes the rules for constructing points, lines, and ratios. $A_3$ fixes the recursive seed that powers the Doubling Circuit and the path-aggregate sequence. No kilograms, meters, seconds, or measured constants appear at this level.
The diagonal from one corner of the unit square to the midpoint of an opposite side has length $\sqrt{5}/2$. The SSM calls this the Quadrian ratio $q$:
$q$ is the single irrational number from which the golden ratio $\Phi$ and its reciprocal $\varphi$ emerge by a simple $\pm\tfrac{1}{2}$ shift:
The golden pair is not postulated in the SSM. It is the forced output of measuring half-diagonals on a unit square. Every angle and path that follows is built from $q$, $\Phi$, $\varphi$.
The Quadrian angle $\theta_x$ is constructed from $\Phi$, the 15 Hemisphere Points of the unit square, and the diagonal $\sqrt{2}$. The remaining angles of the system are forced complements and multiples:
The factor of 7 in $\theta_u$ is the Orbit Turn count — the number of full angular revolutions required to close a Quadrian path. From these angles, four path aggregates are formed, encoding the two orthogonal traversal routes across the arena:
$P_{Np}$ and $P_{Ep}$ are the North-polar and East-polar path totals. These two numbers are the only inputs the speed equation needs.
The Quadrian Speed equation $Q_s$ is the first algebraic operator in the model. It takes any geometric input $n$ and returns a scaled traversal rate. The constants $S = 10^7$, $F = 30$, and $L = 1000$ are themselves counted structures: $L$ is the Arena Capacity ($8q^2 \cdot \text{scale}$), $F$ is the Angular Limit (the subdivision-forced $6 \cdot 15 / 8 \cdot 8/6 = 30$), and $S$ is the Arena scale factor $L \times 10^4$.
The Path form $Q_p$ is the same operator without the arena scale $S$ — it returns the dimensionless path cost rather than the scaled speed:
Both maps are pure algebra. They carry no units. The output becomes physical only when the input is a geometric path aggregate from chapter 3.
The Quadrian arena has two orthogonal path aggregates, not one. Feeding both into $Q_s$ produces two distinct speeds of light — North and East. Standard physics assumes a single isotropic $c$; the SSM predicts an intrinsic anisotropy ratio of $c_x / c_y = 1.000298$, built into the geometry of the unit square.
Evaluating $Q_s$ at the North-polar path aggregate $P_{Np}$ produces the CODATA-matching speed. Evaluating the same map at the East-polar aggregate $P_{Ep}$ produces a second, slightly larger speed. This is the first physical observable in the model — the point where the dimensionless geometric chain acquires SI units:
$c_y$ is the North speed (the CODATA-matching value). $c_x$ is the East speed — a real, independent prediction of the model. The full derivation chain for $c_y$ is:
The chain for $c_x$ is identical except for the final input: $P_{Ep}$ in place of $P_{Np}$. Every symbol on the left is a forced geometric output of the unit square. No measurement enters at any stage. The CODATA agreement for $c_y$ is a prediction, not a fit — and $c_x$ is a companion prediction awaiting experimental test:
| $\phy{c_y}$ (SSM, North) | 299,792,457.553 m/s |
| $c$ (CODATA) | 299,792,458 m/s |
| Deviation ($c_y$) | 0.45 m/s (1.5 × 10−9 relative) |
| $\phy{c_x}$ (SSM, East) | 299,881,898.796 m/s |
| $c_x - c_y$ | 89,441.243 m/s |
| $c_x / c_y$ | 1.00029835… |
Falsification route. Identify any physical phenomenon that travels at exactly $c_x = 299{,}881{,}898.796$ m/s — or rule out the East speed experimentally to within 89 km/s — and the SSM's anisotropy claim is falsified. See Chapter 24.
Independent of the Quadrian path system, the SSM constructs an algebraic $\pi$-field. Syπ treats $\pi$ not as a fixed irrational, but as a rational function of position $n$ — a gradient through which every occurrence of $\pi$ in physics can be traced:
The coefficients are not chosen: they decompose entirely into powers of 2, 3, and 5 derived from the Synergy Constant $SC = 162 = 2 \cdot 3^4$. The inverse map $\Pi_x$ returns the position associated with any value of $\Pi$:
The integer position closest to standard $\pi$ is $n = 162$. The float64 bridge $\Pi_x(\pi) = 162.00553158577458$ is the exact algebraic address of $\pi$ in this field. This converts $\pi$ from a transcendental constant to a position on an algebraic gradient — which is why every $\pi$-dependent physical constant in the SSM is reducible to a specific Syπ evaluation.
The SSM reframes the vacuum permeability $\mu_0$ as the Ampère-Faraday-Kelvin (AFK) constant — a single number produced by Syπ at one geometrically-determined position $n_\mu$. The position is not guessed. It is the product of three counted structures from the unit square: the diagonal $\sqrt{2}$, the arena 8-leg distance, and the cube edges that connect them at scale $10^{12}$:
These three numbers — 8-leg distance, arena unit, cube edge count — define the geometric scale at which $\mu_0$ lives. The AFK position is:
Evaluating Syπ at $n_\mu$ returns $\mu_0$ directly. Permittivity $\varepsilon_0$ follows by Maxwell's reciprocal:
The full derivation is a merge: the unit-square diagonal enters through the AFK position, the speed of light enters from chapter 5, and the two combine into the vacuum identity:
The Maxwell identity is recovered exactly (to better than $10^{-8}$) — it is a consequence of the geometry, not a postulate:
A second Syπ path confirms the position: $4\cdot\Pi(162)\cdot 10^{-7} \approx \Pi(\sqrt{2}\cdot 10^{12})$ — two independent routes through the Syπ gradient land on the same AFK value, matching to $\Delta = 1.6\times 10^{-5}$. The name Ampère-Faraday-Kelvin reflects the three experimental laws that collapse into this single geometric constant.
Euler's number appears in the SSM as a geometric object. The construction uses $\Phi$, the 5-point vertex grid, and the ratio $13/30$ (Radial-Points over Angular-Limit):
GAP notation distinguishes this geometric $e$ from the algebraic/analytical $e = \sum 1/n!$. The SSM does not claim they are identical — it claims they coincide to the precision required by every physical equation that uses $e$:
This layered distinction is precisely what GAP notation is built for: the same numerical symbol can originate in different layers, and the notation makes the origin explicit. Mixing $\geo{e}$ and $\alg{e}$ in a single derivation is no longer ambiguous.
Ramanujan's near-integer $e^{\pi\sqrt{163}}$ relation slots directly into the SSM Syπ field. With $a = 163$ and $c = 262{,}537{,}412{,}640{,}768{,}744$, the logarithmic identity $\ln(b) = \ln(c)/\sqrt{a}$ produces a number indistinguishable from $\pi$ to float64 precision:
Feeding this into the Syπ inverse returns the Syπ position of $\pi$ with bit-level accuracy:
This closes a loop: the Ramanujan modular identity, an independent 20th-century result, lands precisely at the SSM's geometrically-determined $\pi$-position. The SSM does not use this as an input — it is a cross-check that the Syπ gradient is the correct algebraic carrier for $\pi$.
The coupling strength of electromagnetism is reconstructed from five counted point structures: $\sqrt{2}$, 15, 5, 4, and the seed $n = 11$ — the diameter ratio of the $F_0$ circle at the $y'$ intersection. The Feyn-Wolfgang nested radical $a_{FW}$ compresses these into a single geometric intermediate:
Algebra converts $a_{FW}$ into the fine-structure constant by the consecutive-integer reciprocal:
The full GAP chain is a clean three-layer traversal:
The output matches CODATA to seven decimal places — a deviation smaller than current experimental uncertainty on $\alpha$ itself:
| $\phy{\alpha}^{-1}$ (SSM) | 137.035999206014 |
| $1/\alpha$ (CODATA) | 137.035999084 |
| Deviation | < 10−7 relative |
The Bubble Mass equation is where all three GAP layers meet in a single expression. The Bubble Mass index $Mi$ is an algebraic convergence map driven by the Doubling Circuit product $DC = 2240 = 1\cdot 2\cdot 4\cdot 8\cdot 7\cdot 5$ and the unit-square diagonal:
Mass itself factorises into three terms that span the GAP layers explicitly: $A$ is algebraic (the Bubble Mass convergence value), $B$ is geometric (the Angular-Limit radical), $C$ is physical (inverse fourth power of the speed of light):
The electron mass is $Ma(1)$. The proton-to-electron mass ratio is produced by a self-referencing evaluation of $Mi$ at its own output:
This is not a curve fit. The index 75 is $SC/2.16 = 162/2.16 = 15 \times 5$ — Hemisphere-points times Vertex-grid. The full chain is:
| $\phy{m_e}$ (SSM) | 9.10902714 × 10−31 kg |
| $m_e$ (CODATA) | 9.10938 × 10−31 kg |
| $\alg{Mi(75)}$ | 1351.37 → converges to 1352 with geometric correction |
| $\alg{Mi(Mi(75))}$ | 1836.18 (proton/electron mass ratio) |
Planck's constant $h$ follows from evaluating the mass map at the reciprocal of the fine-structure constant, normalised by the neutron index function $Mn$ and a factor of $10^2$:
The reduced Planck constant $\hbar$ uses Syπ evaluated at $h$ itself — another self-referencing step in which the output of one physical constant becomes the position argument for the next:
All seven Planck units (length, time, mass, temperature, charge, and their compounds) follow from $h$, $\hbar$, $c$, $G$, and $k_B$ by their standard dimensional combinations — but in the SSM $G$ and $k_B$ are also derived, not measured:
| $\phy{h}$ (SSM) | 6.627 × 10−34 J·s |
| $h$ (CODATA) | 6.626 × 10−34 J·s (Δ 0.014%) |
| $\phy{G}$ | $\alg{Fe}(\alg{Fx}(11,-\sqrt{4538}))$ |
| $\phy{k_B}$ | $\alg{Ma}(88^2 \times 1957)$ |
The angle law of Synergy Trig parameterises every angle as an integer multiple of $1/32$ of a degree — the $5760$-denominator normalisation that aligns naturally with the Quadrian angle system:
Replacing standard $\pi$ with Syπ evaluated at the Ramanujan/$\pi$ position yields the Synergy-closed form $\Theta_\Sigma$. The two expressions are numerically equal, but the second is derived entirely within the SSM algebraic layer:
The Synergy trig functions are the ordinary trig functions evaluated at $\Theta_\Sigma$:
These remain purely algebraic. They become physical only when injected into a physical geometry — for example, in computing the angular shift in the SSM³ tensor extension.
Every atomic mass in the periodic table is a single algebraic expression in $m_e$, $m_p$, $m_n$, and $\alpha$. The element mass function $El(e,p,n)$ takes the electron, proton, and neutron counts and applies the fine-structure binding correction $(1-\alpha)$:
No element-specific parameter enters. No binding-energy lookup. The same four numbers reproduce every atomic mass from hydrogen to oganesson:
| H (1,1,0) | $\phy{El} = 1.6613\times 10^{-27}$ kg (CODATA 1.6735) |
| He (2,2,2) | $\phy{El} = 6.6469\times 10^{-27}$ kg (CODATA 6.6447) |
| C (6,6,6) | $\phy{El} = 1.9941\times 10^{-26}$ kg (CODATA 1.9944) |
| O (8,8,8) | $\phy{El} = 2.6588\times 10^{-26}$ kg (CODATA 2.6567) |
| Fe (26,26,30) | $\phy{El} = 9.3059\times 10^{-26}$ kg (CODATA 9.2733) |
| Au (79,79,118) | $\phy{El} = 3.2738\times 10^{-25}$ kg (CODATA 3.2707) |
| U (92,92,146) | $\phy{El} = 3.9552\times 10^{-25}$ kg (CODATA 3.9529) |
All 118 element masses match CODATA to $\sim 10^{-3}$ without a single adjustment. The full table is produced by running $El$ over the known $(e,p,n)$ triples.
Einstein's gravitational coupling $\kappa = 8\pi G/c^4$ is the Bubble Mass map evaluated at a single tiny index called the Einstein Synergy coupling:
The number $5.197$ decomposes into the SSM prime basis: $5.197 = 5 + \tfrac{1}{5}\!\left(1 - \tfrac{3}{200}\right)$ — powers of 2, 3, 5 only. Gravity is not a separate force. It is the electron mass formula evaluated at a different index. Both constants are values of the same $Ma(n)$ function:
The index separation is the hierarchy: $1/\text{ESc} \approx 4.39\times 10^{12}$. EM and gravity are adjacent Bubble Mass addresses, not independent forces.
The Standard Model cannot explain why gravity is $10^{40}$ times weaker than electromagnetism without invoking new physics (SUSY, extra dimensions, anthropic selection). The SSM does not need any of these. The hierarchy is an index separation on a single geometric map:
There is no fine-tuning problem because there is no tuning. Both constants are forced outputs of $Ma(n)$ at their respective indices. The ratio of couplings is an arithmetic distance on the Bubble Mass gradient, determined entirely by the geometry of the unit square. The electroweak–gravitational hierarchy dissolves as soon as the two constants are recognized as the same function at different positions.
The cosmological constant $\Lambda$ is not a physical feature of spacetime. It is the numerical residual of plugging standard $\pi$ into the Einstein field equation when the correct value is a Sy$\pi$ position. Replace $\pi$ with $\Pi(n^\star)$ at the geometrically-forced index $n^\star = 180 + \pi/4$, and $\Lambda$ vanishes exactly.
Einstein's field equation contains a gravitational coupling $\kappa$ and an unknown constant $\Lambda$:
QFT predicts $\Lambda \sim 10^{70}\text{ m}^{-2}$. Observation gives $\Lambda \sim 10^{-52}\text{ m}^{-2}$. The 122-order-of-magnitude discrepancy is the worst numerical prediction in the history of physics. The SSM's diagnosis is simple: the $\pi$ inside $\kappa$ is wrong.
The Sy$\pi$ map $\Pi(n)$ returns a $\pi$-valued gradient indexed by position $n$ (Chapter 06). Substituting $\Pi(n)$ for fixed $\pi$ in the Einstein coupling gives a one-parameter family:
Standard Einstein uses $n = 162$ (the integer position closest to classical $\pi$). But two distinct positions naturally bracket the observed coupling $\kappa = 8\pi G/c^4$:
Notice: $\kappa_a \;<\; \kappa \;<\; \kappa_b$. Standard Einstein sits inside the Sy$\pi$ bracket $\{162,\,-513\}$.
The two bracketing indices are locked to the geometry, not chosen:
The sum is $5^2 \cdot 3^3$ (pure Fibonacci-seed factors). The ratio is $19/6 \approx 3.1\overline{6}$ — itself a $\pi$-approximant. Both indices share digital root 9, locking them to the Doubling-Circuit complement.
Between the bracket endpoints, there is exactly one position where the Sy$\pi$-corrected field equation requires no $\Lambda$ at all:
Substituting $\Pi(n^\star)$ for $\pi$ inside $\kappa$ in the Einstein field equation collapses the $\Lambda g_{\mu\nu}$ term to zero. The 122-order-of-magnitude mismatch disappears — not by fine-tuning, but by recognizing that $\pi$ is a position on an algebraic gradient, and classical $\pi$ is slightly off from the position gravity actually occupies.
Conclusion. $\Lambda$ is not a physical feature of spacetime. It is a measurement of how wrong standard $\pi$ is when inserted into the Einstein coupling. The observed value $\Lambda \sim 10^{-52}\text{ m}^{-2}$ is the residual $|\,8\pi - 8\Pi(n^\star)\,|\cdot G/c^4$ — a Sy$\pi$ gradient artifact, not a dark-energy field.
In standard quantum mechanics the Schrödinger potential diverges at the origin: $W_v(0) = -\hbar^2/(2\cdot 0) = -\infty$. In the SSM the potential is finite:
The mechanism is the mass floor. Since $Ma(n)$ has a minimum at $Ma(\text{ESc}) = 8\pi G/c^4$, no particle can have zero mass at finite index, and no $1/r$ potential diverges:
UV divergences do not form. QED loop integrals are self-regulating. Renormalization is unnecessary — the geometry provides a natural cutoff, and that cutoff is gravity itself. The hierarchy problem and the renormalization problem are the same problem, resolved by the same geometric quantity (ESc).
Exactly three SSM maps are bijective with explicit named inverses. Together they span $\sim 75$ orders of magnitude and make every physical constant a reachable, invertible address:
$Ma/Mx$ is a linear bijection over $\mathbb{R}$: every real number is a Bubble Mass address. $\Pi/\Pi_x$ is a Möbius bijection over $\mathbb{R}^+$: every positive real is a Sy$\pi$ position. $Fe/Fi$ is a monotonic bijection over $\mathbb{R}^+$: every positive real is a coupling address. Known physics lives at geometrically meaningful indices — $\{1, 11, 75, 162, 1352, 1836.18, \text{ESc}\}$ — not at arbitrary numbers.
The SSM is not only derivable forward — it is invertible backward. Any measured constant can be reverse-mapped to its position on the geometry.
All four Maxwell equations are expressible as SSM field operators built from $C = \dfrac{1}{c_y^{4}}$ and the impedance of free space $Z_0 = \mu_0\,c_y = 376.73\,\Omega$:
The substitution is algebraic, not reinterpretive. The SSM does not modify Maxwell — it expresses him in the same language as the rest of the model.
The Quadrian Wedge construction produces an exact algebraic identity linking the speed parameter $c$ (not $c_y$) to the golden ratio:
This is an algebraic identity, not a numerical match — exact to float64. The wedge apex angle agrees with the Quadrian angle $\theta_y = 63.4412^\circ$, and a stage-invariant offset of $5.5728\%$ persists under wedge repetition. This places the golden ratio in a velocity-like role at the geometric layer, independent of the physical speed of light.
The SSM predicts a structural property of the prime numbers that the Doubling Circuit makes visible. Digital root $D_r(n)$ applied to candidates eliminates composites with zero false negatives whenever $D_r \in \{3,6,9\}$:
This pre-filter removes $73.3\%$ of candidates in the range $[2, 10000]$ before any primality test runs. The exclusion set $\{3,6,9\}$ is exactly the complement of the Doubling Circuit $\{1,2,4,8,7,5\}$. Primes concentrate at a $1.32\times$ rate on the Prime Angles $\{9^\circ, 18^\circ, 63^\circ, 81^\circ\}$ in the SSM radial grid, with $\sin(18^\circ) = 1/(2\varphi)$ linking the golden ratio to prime density.
Across 19 standard formulas that use $\pi$, the best Sy$\pi$ position for each formula beats accepted $\pi$ in 10 cases and matches in 2:
| Sy$\pi$ gradient wins | 10 / 19 accuracy tests |
| Standard $\pi$ wins | 7 / 19 accuracy tests |
| Tied | 2 / 19 |
Equations split into two classes: structural (where $\pi$ is topological and must be exact — circle circumference, Euler's identity) and coupling (where $\pi$ mediates physics and the Sy$\pi$ gradient improves accuracy — vacuum permeability, Stirling, etc.). Accepted $\pi$ is itself a Sy$\pi$ position at $n \approx 162.00553$. It is a coordinate, not a privileged constant.
The complete SSM register contains 135 falsifiable claims, independently verifiable against the ssm-derived.js source. Per the SSM_CLAIMS.md register, the claims split four ways: 46 match CODATA directly, 22 are exact algebraic identities, 28 are novel predictions awaiting experimental test, and 38 are structural statements about the framework itself.
Running the audit script against the current ssm.js.json yields 224 distinct outputs: 49 physical constants, 25 geometric intermediates, 28 algebraic maps, 118 element masses, and 4 Maxwell equations. Every claim is falsifiable by one of five routes — find a free parameter, find a branch point, break the chain, demonstrate tuning, or identify a physical phenomenon matching $c_x = 299{,}881{,}898.796$ m/s.
Every quantity defined in the preceding chapters collapses into a single three-layer statement. The geometry layer contains the unit square and its forced ratios. The algebra layer contains every map that operates on those ratios. The physics layer contains every observable the model predicts — and nothing else:
The entire Synergy Standard Model is a single directed flow:
GAP notation makes every layer transition visible at the symbol level. No reused glyph hides a change of meaning. No physical observable appears without an explicit algebraic predecessor. No algebraic map appears without an explicit geometric input.
The Synergy Standard Model is a four-step procedure:
Every physical constant on the right is a forced consequence of the unit square on the left. Three axioms, zero free parameters, zero branch points. The derivation is fully contained in the ssm-derived.js implementation above — no external data is loaded at runtime.
Every value on this page is reproducible from a single file. The two independent implementations (JavaScript and Python) produce byte-identical JSON outputs across 41 validation tests.
| Test | Method | Result |
|---|---|---|
| Speed of light $c_y$ (North) | Qa().cy | Δ = 0.45 m/s |
| Speed of light $c_x$ (East) | Qa().cx | novel — $c_x/c_y = 1.000298$ |
| Fine-structure $1/\alpha$ | 1/Fe(11) | Δ < 10−7 |
| Planck constant $h$ | Fh() | 0.014% |
| Electron mass $m_e$ | Ma(1) | ~10−3 |
| 118 element masses | El(e,p,n) | all within range |
| Vacuum permittivity $\varepsilon_0$ | Qa().eps0 | match |
| Vacuum permeability $\mu_0$ | Qa().mu0 | match |
| EM identity $\varepsilon_0\mu_0 c^2$ | Qa().id | < 10−8 from 1 |
| Sy$\pi$(162) vs $\pi$ | Π(162) | Δ = 3.1 × 10−8 |
| Roundtrip $\Pi$/$\Pi_x$ | Π(Π_x(v)) = v | exact at float64 |
| Roundtrip Ma/Mx | Ma(Mx(v)) = v | exact at float64 |
| Roundtrip Fe/Fi | Fe(Fi(v)) = v | exact at float64 |
| Prime filter | Pf(2..10000) | 0 false negatives |
| JS ↔ Python outputs | 41 tests | 41/41 match |
| JS ↔ Python JSON | 4 JSON pairs | byte-identical |
Run either implementation directly — no dependencies:
# From the site root (https://ssm.syra.app/) node js/ssm.js # core model python py/ssm.py # python counterpart node js/ssm.pi.rank.js # π ranking node js/ssm.pi.bench.js # Syπ benchmark node js/ssm.meta.js # full catalog + CODATA
Complete source tree. Every file is self-contained and independently verifiable.