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