A Six-Bit Origin of Physics

Modern physics is extraordinarily successful—and deeply unsatisfying.

The Standard Model predicts experimental results to more decimal places than any theory in history. General Relativity describes gravity with breathtaking accuracy. Yet together they leave us with more than nineteen unexplained numbers: particle masses, mixing angles, coupling constants, and cosmological parameters that must simply be measured and accepted.

Why three generations of matter?
Why the gauge group SU(3)×SU(2)×U(1)?
Why is the cosmological constant so small?
Why does matter dominate over antimatter?

These are not philosophical questions. They are structural gaps in our understanding.

Turning the Logic Upside Down

Most approaches to quantum gravity start with a continuous spacetime and attempt to discretize it later. String theory, loop quantum gravity, and grand unification all follow this path—and all inherit enormous freedom.

The S21 Theory inverts that logic.

Instead of assuming a continuum, it starts with a single discrete postulate:

At the Planck scale, spacetime admits exactly six binary degrees of freedom per cell.

That’s it. No fields, no symmetries, no adjustable constants.

From this minimal assumption—and nothing else—the entire structure of known fundamental physics emerges.

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Why Six Bits?

Six is not chosen. It is forced.

Independent arguments converge on the same answer:

• Phase space: Three spatial dimensions require six degrees of freedom (position + momentum).

• Lorentz symmetry: The Lorentz group has six generators.

• Spinors: Fermionic structure requires six binary distinctions.

• Holography: The Bekenstein bound allows at most ~9 bits per Planck cell; consistency requires fewer.

• Gauge structure: The Standard Model’s rank plus symmetry breaking adds up to six.

Fewer than six bits fail to encode known physics. More than six introduce instabilities.

Six is the unique solution.

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From 64 Possibilities to 21 Real Vacua

Six bits define 64 possible local states. But physics does not permit all of them.

When Lorentz consistency, causality, and minimal propagation are imposed, only 21 configurations survive as stable vacuum states.

They organize themselves uniquely into:

• A connected 20-state manifold (M₂₀)

• One isolated state (σ)

This is not an assumption. It is the unique fixed point of the constraints.

That single topological fact—20 + 1—turns out to explain an astonishing amount.

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Why There Are Three Generations of Matter

The connected vacuum manifold M₂₀ contains exactly three independent topological cycles.

In topology, this number is called the first Betti number.

b₁ = 3

Those three cycles correspond directly to the three generations of fermions.

Not approximately. Not statistically.

Exactly.

A fourth generation would require changing the topology of the vacuum itself—something the theory does not permit. This is a hard, falsifiable prediction.

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Why the Gauge Group Is What It Is

The Standard Model gauge group
SU(3)×SU(2)×U(1)
is often treated as an arbitrary input.

In S21, it isn’t.

When the six bits are decomposed into causal “past” and “future” trigrams, the allowed adjacencies between trigrams form a graph whose structure reproduces:

• An SU(3) hexagon (the gluons)

• Two SU(2) triangles (the weak sector)

• A U(1) connector (hypercharge)

The gauge group is not imposed—it is read directly off the adjacency structure of information itself.

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The Golden Ratio in Neutrino Physics

The 20-state vacuum manifold has icosahedral symmetry, governed by the group A₅.

That symmetry has a fingerprint: the golden ratio.

From the unique A₅-invariant tensor, the theory predicts:

sin²θ₁₂ = (φ − 1)/2 = 0.309017…

In 2025, the JUNO experiment measured:

0.3092 ± 0.0087

That’s a 0.02σ agreement—without any parameters tuned to data.

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Why Matter Exists at All

The universe contains about one excess baryon per billion photons.

In the Standard Model, this is unexplained.

In S21, it follows from topology.

The vacuum manifold contains 10 CP-conjugate channels. The shortest loop capable of carrying a CP-violating phase has length 7.

That single integer determines the matter–antimatter imbalance:

η₍B₎ = (10/9) × (1/21)⁷ ≈ 6.17 × 10⁻¹⁰

Observed value: 6.1 × 10⁻¹⁰
Agreement: ~1%

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Why the Cosmological Constant Is So Small

The same loop length—7—appears again.

Vacuum energy contributions factorize over the 10 CP channels, each suppressed by the minimal CP-odd loop.

The result:

Λ / Mₚₗ⁴ ≈ (1/21)⁹⁰ ≈ 10⁻¹¹⁹

Observed value: ~10⁻¹²⁰.

No fine-tuning. No anthropics. No cancellations.

The cosmological constant and baryon asymmetry come from the same topological invariant.

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Dark Matter: An Isolated State

The 21st vacuum state, σ, is completely isolated.

It has no allowed transitions to visible-sector states.

This makes it:

• Stable

• Non-interacting with gauge forces

• Naturally dark

Its mass follows directly:

mχ ≈ Mₚₗ × (1/21)¹⁰ ≈ 700 TeV

Dark matter is dark not because of a symmetry we impose—but because it lives on a disconnected island in the vacuum.

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What This Theory Claims—and What It Doesn’t

S21 does not claim to be the final word on physics.

It claims something narrower and stronger:

• One discrete postulate

• Zero free parameters

• Concrete, falsifiable predictions

• Agreement with existing data

• Clear failure modes

If a fourth fermion generation is discovered, the theory fails.
If the solar neutrino angle shifts significantly, it fails.
If dark matter is light or gauge-coupled, it fails.

That is how science should work.

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The Takeaway

The surprising lesson of S21 is not that the universe is complicated.

It’s that the universe appears to be severely constrained.

Given six bits of information per Planck cell, the rest seems almost inevitable.

The universe, it turns out, had very little choice.