Seeing the element tensor.

The familiar projection.

The Mendeleev table freezes charge to zero, freezes the nucleus to its ground state, integrates over the neutron axis (which is why isotopes don't appear), and displays Z against valence shell structure. The f-block tear at the bottom is the projection failing — orbital angular momentum ℓ=3 refuses to flatten onto the (n, valence-count) plane, so we cut it off and float it. Click any element to read out what this projection left behind. Measured AME2020 binding energies are used where available; the rest come from the predictive engine in section III.

The nuclear binding surface.

Rotate this. Two horizontal axes: Z (protons) and N (neutrons). The vertical axis is binding energy per nucleon. The chemists' periodic table is this surface projected onto the Z edge with N marginalized out. Iron sits near the peak. The ridges along closed neutron and proton shells are shell effects — extra binding where quantum numbers align — derived here from the AME2020 measurements themselves, not from a smooth liquid-drop approximation. The cliffs at the edges are the drip lines. Most of the interesting physics lives on this face.

Known physics is enough.

The semi-empirical mass formula (Bethe and von Weizsäcker, 1935) predicts nuclear binding from five macroscopic effects: bulk binding, surface tension, Coulomb repulsion, isospin asymmetry, and nucleon pairing. Adding a sixth term — the microscopic Strutinsky shell correction — closes the gap between the smooth liquid drop and the real measured surface. The shell correction comes from filling Nilsson single-particle levels up to Z or N and computing the fluctuation of the sharp energy sum against a properly smoothed Fermi background. Ninety years of physics, precomputed into a lookup table, recomputes in microseconds.

This is where to look.

Every cell below is a (Z, N) pair the engine predicts is bound. Color is binding per nucleon, using measured AME2020 values where available and the shell-corrected model elsewhere. The dashed lines are the nuclear magic numbers. The bright patch near Z=114, N=184 is the island of stability, and it isn't drawn in by hand — it's the engine's own output once empirical shell corrections and predicted superheavy closures are added to the liquid drop. Every superheavy synthesis program in the world — Dubna, Riken, GSI, Berkeley — is aiming at features visible on this map. Cross-reference the 3D landscape, the predictor, and section I's detail panel and you can ask, for any point, what measurement we have, what the engine predicts, and how far you are from a closed shell.

Other indices, other projections.

The nuclear sector is half the tensor. The other half is electronic: the quantum numbers (n, ℓ, m_ℓ, m_s) that describe how electrons occupy states around a given Z. Slide Z and watch the orbitals fill in Madelung order — rows are the principal quantum number n, columns are the angular momentum ℓ, each box holds 2(2ℓ+1) electrons. Noble gases are the closures where a shell finishes. The f-block exists because ℓ=3 orbitals enter at n=4. Past Z≈100 the relativistic parameter (αZ)² approaches unity and the Madelung order begins to fail: g-orbitals predicted to arrive no earlier than period 8 start contending with the classical d and f assignments. The bar at the bottom tracks where the current element sits on that regime axis.

Strip electrons, see the core.

The classical table assumes neutral atoms — charge q = 0 frozen. This face releases that constraint. Pick an element and slide the charge state from 0 toward Z−1 (hydrogen-like). As outer electrons peel away, the remaining electrons feel less screening and the orbital binding energies explode. This face uses the Dirac-Sommerfeld formula — not the non-relativistic Rydberg — so orbital energies depend on (n, j) rather than just (n, ℓ), and you can see the fine-structure splitting that creates the Kα₁/Kα₂ doublet. For uranium, 2p₁/₂ and 2p₃/₂ sit about 5 keV apart (the L₂-L₃ splitting); the Kα doublet is what you actually measure in an X-ray fluorescence experiment. Plasma physicists, fusion engineers, and X-ray astronomers all work on this face — the atoms in the solar corona, a tokamak edge, or an accretion disk around a black hole are highly ionized and live nowhere near the neutral column of Mendeleev's chart. Slater screening gives Zeff; Dirac-Sommerfeld gives the relativistic binding. Inner-shell binding for heavy atoms is accurate to ~10% — good enough to see the physics, not a replacement for multi-configuration Dirac-Fock.

Shape of the nucleus.

Most nuclei aren't round. The closed-shell ones are — Pb-208, Sn-132, Ca-40 sit at β₂ ≈ 0 — but between magic numbers, the single-particle level scheme favors a stretched (prolate) or squashed (oblate) shape because some Nilsson orbitals are lowered by the deformation and the nucleus pays the liquid-drop surface cost to reach them. The rare earths and actinides are the paradigmatic examples: U-238 is a football, deformed by β₂ ≈ 0.28. The gain in binding is typically 5–10 MeV. The seventh face shows where on the chart this matters: the heat map of |β₂_eq| has the two characteristic deformation islands (rare earths Z≈60-70, actinides Z≈90-100) flanking the spherical Pb plateau, and the predicted superheavy island at Z=114, N=184 returns to spherical because the shell correction there is strong enough at β₂=0 to beat any deformation gain.

Caveat: first-order Nilsson with quadrupole splitting captures the magnitude of equilibrium deformation but misses the prolate/oblate asymmetry — and produces no double-hump structure, so the literal fission barrier of an actinide isn't accessible from this approximation. The 1D plot shows the deformation potential energy curve symmetrized to |β₂|; the equilibrium dot is the Nilsson minimum; the descent past it is the LDM cost taking over, not a real fission saddle. To get fission barriers properly you need a deformed Woods-Saxon or Möller-Nix calculation with multiple deformation degrees of freedom (β₂, β₄, γ at minimum). What's here is honest about what it can do.