Pe Landscape
Noble gas (Pe ≈ 0)
COHERENT (Pe < 1)
D1 zone (Pe 1–4)
Fluorine (Pe = 4.65)
V* ceiling (5.52)
Hund anomaly
← Paper 99 · Paper 100 · §34 Math Apparatus

The Periodic Table
Is a Pe Map

Mendeleev sorted 63 elements by chemical intuition in 1869. Three quantum parameters discovered 60 years later plug directly into one equation — and reproduce his entire table from scratch.

What Mendeleev Didn't Know He Was Measuring

The periodic table is one of the most successful organizational frameworks in history. Mendeleev arranged elements by chemical valence — how eagerly they grab electrons from other atoms. It worked perfectly. But he had no idea why.

The reason is Pe. The same dimensionless number we use to score how addictive TikTok is — Pe = (Opacity × Responsiveness) / Constraint — also describes every atom's electron-capture tendency. The three quantum-mechanical parameters that explain this weren't discovered until decades after Mendeleev died. They slot into the formula and reproduce his table.

Spearman ρ = 0.881. Mendeleev's 19th-century thermochemical data vs. quantum parameters he never knew existed. The correlation is not a coincidence — it's the same underlying structure.

One Formula. Two Discoveries. 60 Years Apart.

The void framework's Pe formula maps directly onto atomic structure. No tuning, no extra parameters — the three dimensions of the framework correspond exactly to three independently-measured quantum properties.

Pe = Zeff × EA / σ
O = Zeff  (effective nuclear charge — how much pull the nucleus exerts, screened from view by inner electrons)
R = EA   (electron affinity in eV — how eagerly the atom grabs incoming electrons)
α = σ    (Slater shielding constant — inner electrons constraining the engagement)
Pe_atom predicts electron-capture tendency → predicts chemical reactivity → predicts Mendeleev's table
O
Opacity → Zeff

The nuclear charge is hidden

The nucleus pulls on bonding electrons — but the actual charge is screened by inner-shell electrons. The bonding partner can't see the mechanism directly. High Z_eff = high opacity.

F: Z_eff = 5.20  |  Na: Z_eff = 2.51
R
Responsiveness → EA

The atom responds to electrons

Electron affinity is how much energy is released when an atom accepts an electron. High EA = the atom eagerly responds to incoming electrons. This is direct atomic responsiveness.

F: EA = 3.40 eV  |  Na: EA = 0.55 eV
α
Constraint → σ (shielding)

Inner electrons limit engagement

The shielding constant quantifies how much the inner electron cloud constrains the nuclear engagement. More inner electrons = higher σ = more constrained atom = lower Pe.

F: σ = 3.80  |  I: σ = 46.92
Iodine and Fluorine are both halogens — both want to grab electrons. But Iodine has 46 inner electrons constraining it (σ = 46.92), giving Pe = 0.484. Fluorine has almost none (σ = 3.80), giving Pe = 4.654. Same group, 10× Pe difference. The constraint determines the outcome.

Element Explorer

Hover or tap any element to see its Pe score and regime. The periodic table arranged as a Pe landscape — groups 1, 14–18 shown (the main group elements with data). Noble gases (right column) sit at the constraint pole. Halogens (second from right) are the highest Pe. Red elements are Hund anomalies — their half-filled shells suppress EA below the group trendline.

Hover an element above
Select any element to see its Pe score and framework interpretation.
Pe atomic

Fluorine Almost Touches the Ceiling. Nothing Does.

The drift lock-in threshold — where Pe-cascade becomes self-sustaining — is V* = 5.52. Every social media platform that goes viral crosses V*. Every drug that causes addiction crosses V*. Fluorine, the most reactive element in chemistry, has Pe = 4.654. It doesn't cross V*. Nothing in chemistry does.

Pe_max(Fluorine) = 4.654 < V* = 5.52. Margin: 0.87 Pe units. All of chemistry operates in the COHERENT-to-D1 range. There is no chemical Fisher Runaway.

Why? Pauli exclusion. No two electrons can occupy the same quantum state. This is not a law imposed from outside — it's woven into the antisymmetry of fermionic wavefunctions. It is the hardest prohibition in physics: zero exceptions in 13.8 billion years of particle interactions. It constitutively caps Pe. Chemistry cannot go viral. The prohibition prevents it at the level of physical law.

Every other physical, biological, and social system in the framework has a prohibition. Some are laws (enforceable). Some are conventions (breakable). Some are regulatory (slow). Pauli exclusion is in a different category — constitutive. The wavefunction antisymmetry doesn't prevent violation; there's no violation to prevent. The state simply doesn't exist.

Noble Gases: The Constraint Poles

Noble gases have complete outer electron shells. Their electron affinity is effectively zero — they don't accept electrons under normal conditions. EA ≈ 0 → Pe ≈ 0. They sit at the constraint pole of the atomic Pe landscape.

He
Helium
Pe ≈ 0
Ne
Neon
Pe ≈ 0
Ar
Argon
Pe ≈ 0
Kr
Krypton
Pe ≈ 0
Xe
Xenon
Pe ≈ 0
Rn
Radon
Pe ≈ 0

The octet rule — atoms form bonds to reach 8 outer electrons — is the constraint ritual of atomic chemistry. Every bond formed is an atom performing the ritual of approaching a noble-gas configuration. Noble gases already sit at Pe ≈ 0 permanently. They don't need to perform the ritual. That's why they're inert.

One edge case: XeF₂ and KrF₂ form under pressure because fluorine's Pe (4.654) is high enough to force even noble gases to bond. He and Ne don't form compounds at all — their constraint poles are deeper. The framework predicts this: noble gas compound formation requires a bonding partner with Pe high enough to overcome the constraint pole. Only fluorine qualifies.

The Outliers That Prove the Rule

Nitrogen (N) and Phosphorus (P) are in Group 15 — between carbon and oxygen. You'd expect them to have intermediate Pe. Instead, their Pe is anomalously low. Nitrogen (Pe = 0.070) sits far below Oxygen (Pe = 1.831), despite being right next to it on the table.

The reason is Hund's rule. Nitrogen has a half-filled 2p³ shell — three electrons in three orbitals, all with parallel spins. This is unusually stable. Adding a fourth electron would disrupt the symmetry, costing energy. So nitrogen's electron affinity (EA = 0.07 eV) is almost zero, collapsing Pe.

In framework terms: the half-filled shell is a local constraint pole — orbital stability acting as an additional constraint beyond the baseline shielding. The anomaly is not a failure of the formula. It's a prediction: any element with a half-filled p or d shell should show Pe below its group trendline. The simulation confirmed all five pnictogen elements (N, P, As, Sb, Bi) fall below their adjacent chalcogen at the same period. 5 for 5.

0.881
Spearman ρ
Pe vs Pauling EN
n = 16
4.654
Pe_max (Fluorine)
highest in chemistry
below V* = 5.52
0
Pauli violations
in 13.8 billion
years of physics
#19
Structural isomorphism
in §20E apparatus
ρ = 0.881

Why Does This Matter?

The framework was built to explain social media drift and corporate opacity. It turns out the same dimensionless number — Pe — governs chemistry, geophysics, cosmology, biology, and now atomic structure. This isn't a coincidence or a loose analogy. It's evidence of a structural isomorphism: the same abstract constraint architecture recurring across completely independent domains.

The practical implication: when you see drift cascade in a social system, you're seeing the same physics as when fluorine reacts with everything it touches. The difference is that social systems don't have Pauli exclusion. Nobody built a hard prohibition into the wavefunction of social media. That's why it requires external constraint — and why the constraint architecture has to be designed.

Paper 100 — Full Research

Full derivation, kill conditions, 6 predictions, Spearman analysis, MATH-ATOM-01 simulation notebook (n=30 Mulliken EN extension), and iron as the nuclear V* — all in the Zenodo preprint.

Read Paper (Zenodo) Score a Platform → Research Lab ⚗