QUANTUM ATOMIC SIMULATOR
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Quantum Atomic Simulator

Anim 1.0×
Hydrogen · 1s¹ · neutral · no emissions
DFT:
1
H 1.008 1s¹
1
H 1.008 1s¹
1
H 1.008 1s¹
Universal Materials System
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Click elements above to add to composition
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Alloy Calculator
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Reflectivity Spectrum
Vision Mode
Quantum Dot Size: 5.0 nm
Keyboard shortcuts.
SpaceExcite the active electron (emission spectrum)
SPrepare coherent superposition (quantum beats)
Delete / BackspaceRemove the focused atom from the scene
Ctrl+BToggle render mode (legacy = full fidelity / fast = cached DOM for macromolecules)
Shift+click (spectrum)Fire an absorption probe photon at the clicked wavelength
Click (spectrum tick)Re-fire that exact emission transition
Click (spectrum gap)Fire the closest valid transition to that wavelength
Drag (scene)Orbit camera · Shift+drag = pan · Ctrl+drag = box-select atoms
ScrollZoom (reveals nucleus → quarks at deep zoom)

Cloud density override. The slider next to "Focus atom (camera)" controls |ψ|² Born sample count per electron. Auto (default, value −1) scales the count down for large molecules to maintain framerate — full quality for ≤5 atoms, halved for 6-12, quartered for 13-24, minimum for macromolecules. This is a visual sampling change only: the underlying |ψ|² probability density is computed identically at any sample count (more samples = sharper picture of the same distribution, like increasing pixel count on the same photograph). Setting a manual value (0-60) forces that exact count regardless of molecule size — useful for high-quality screenshots of large molecules at the cost of performance. The physics (orbital energies, bond forces, electron positions) is completely unaffected.

What this is. A working quantum atom for every element from H (Z=1) to Og (Z=118). Each electron is a ghost particle orbiting on its proper orbital, with the physics layered in:

Configuration (NIST ground states). Aufbau filling order plus the ~17 known anomalies (Cr 3d⁵4s¹, Cu 3d¹⁰4s¹, Pd 4d¹⁰5s⁰, La/Ce/Gd promotions, Pt/Au, the actinides). All three Hund's rules: max-S, max-L, and J = |L−S| or L+S depending on fill. HUD shows the resulting ground-state term symbol (e.g. ⁴F₃/₂ for V).

Wavefunctions. Exact hydrogenic radial functions from generalized Laguerre polynomials up to n=7, with correct radial nodes (n−ℓ−1).

Atomic radii — empirical contraction. Measured atomic radii (Wikipedia empirical column) — critical because they show the lanthanide contraction (Ce 185 → Lu 175 pm) and the actinide contraction (Ac 195 → U 175 pm) properly, which the Clementi calculated column smears out.

Outer-shell Zeff from measured ionization energies. Rather than approximate Zeff via Slater for the outermost electron, we derive it directly from the experimentally measured first IE: Zeff = neff·√(IE/R). This is the Desclaux-equivalent: identical accuracy without typing 900 Dirac-Fock values. Inner shells still use Slater (whose IE isn't directly measurable).

Quantum defects δ_ℓ. Expanded from alkali-only to ~50 elements covering noble gases, alkaline earths, every transition-metal block, lanthanides, actinides. Calibrated against measured IEs so Zeff(outer) comes out near 1.0 for alkalis and 1.5–2 for noble-gas ions — physically correct.

Relativistic shrinkage. Inner s-shells of heavy atoms multiplied by √(1−(Zα/n)²) from the Dirac equation. Why gold is gold.

Spin-orbit splitting + visible spin. Each electron has real j = ℓ±½. ⟨r⟩ of j=ℓ+½ vs j=ℓ−½ split by ~(Zα/n)². Spin-up (↑) electrons show white tick above; spin-down (↓) dark tick below.

Trajectories. Three frequencies in the ratio φ : (1+√2) : (3+√13)/2 — KAM-stable noble means — detuned per electron by δℓ.

Excitation & emission. Hit Excite (or spacebar). Outermost electron jumps to (n+1, ℓ±1) — Δℓ = ±1 dipole selection rule — sits briefly, then decays emitting a photon at the Rydberg-formula wavelength in its real color. Hydrogen 3→2 emits Balmer-α at 656 nm.

Emission spectrum panel. Below the atom is a wavelength axis from 200 nm (deep UV) to 1200 nm (near-IR). Every emission lays down a tick at its λ; repeated transitions grow brighter log-style. The visible 380–780 nm band is shown with its true rainbow gradient; UV strip on the left, IR strip on the right. Click a tick to re-fire that exact transition. Click anywhere else on the strip to fire the closest valid transition to that wavelength.

Ionization & recombination. Hit Ionize and the outermost electron is removed — the atom becomes a cation and the HUD shows e.g. Na⁺ cation. Every remaining electron contracts because there's less mutual screening (lower σ → higher Zeff → smaller ⟨r⟩) — Slater's rules drive this in real time. Strip more electrons to get Na²⁺, Na³⁺, and watch the shells pull in progressively. Recombine brings the last-removed electron back, emitting a UV photon at the ionization-energy wavelength (λ = 1240/IE nm). The recombination photon lands on the spectrum panel as a special "∞ → n,ℓ" line.

Selectable transitions. A Grotrian energy-level diagram sits below the spectrum: five columns (s, p, d, f, g) of horizontal bars, each bar an orbital (n, ℓ) plotted at its real energy En,ℓ = −R·Zeff² / (n−δℓ)². Populated levels are colored by shell with white electron dots showing occupancy. Empty levels are dim. To drive a transition: (1) click an electron in the 3D view — it gets a pulsing white ring. (2) click an empty level on the Grotrian. Cyan = electric-dipole allowed (Δℓ = ±1). Orange = forbidden but firable (Δℓ = 0, ±2 — real "forbidden lines" seen in nebulae). Grey = not above current energy.

Absorption. Shift-click (or right-click) on the spectrum panel at any λ to shoot a probe photon at the atom from offscreen. If λ matches an excitation transition within ±5 nm, the matching electron jumps up — the photon vanishes and a dark Fraunhofer-style notch appears on the spectrum band, labeled below in the photon's color. Miss the line and the photon flies through; the meta text briefly flashes "probe missed." This is the inverse of emission: emission lines show where the atom radiates, absorption lines show where it actually got hit. Try Z=1 → shift-click ~122 nm (deep UV, far left) → Lyman-α absorption. For Na (Z=11), shift-click ~589 nm — the D-line, the same dark notch in sunlight Joseph von Fraunhofer mapped in 1814.

External fields — Zeeman & Stark. Two new sliders apply a magnetic field B (along ẑ) and an electric field E (along x̂). When on, dashed axis arrows appear in the 3D view showing the field directions.

  Zeeman: Each (n,ℓ) splits into (2ℓ+1) m sublevels with energy shifts ΔE = gJ·m·μB·B, where the Landé g-factor is computed from the LS-coupling formula using ℓ and j = ℓ±½ that each electron carries. The Grotrian fans each level into its m-sublevels with small ticks labeled +1, 0, −1, etc. Emitted photons split into three components — π (Δm=0) at the unshifted wavelength, σ⁺ (Δm=+1) blue-shifted, σ⁻ (Δm=−1) red-shifted. In the 3D view, m≠0 electrons start to precess around the z-axis at the Larmor frequency ωL = gJ·m·μB·B/ℏ — opposite m's spin opposite ways.

  Stark: The electric field polarizes the atom along x̂. The orbital cloud shifts off-center toward +x in proportion to E·n²·(1−|m|/ℓ) — the m=0 lobes displace most (they have the largest dipole moment along the field direction). On the spectrum, every line shifts to longer wavelengths (red-shifts) by an amount proportional to E².

  Try: hydrogen, hit Excite repeatedly to populate Balmer-α (656 nm). Now ramp B from 0 → 5 T and watch the line split into three. The famous normal Zeeman triplet. Crank B to 10 T and the spectrum becomes a forest of split lines (Paschen-Back regime).

Multi-atom mode. Hit + Atom to spawn a second atom alongside the first. Up to 8 atoms total, arranged in a ring around the primary. Each atom is fully independent — its own electrons, own ground state, own ionization, own ghost trajectories. The HUD / Grotrian / spectrum panel display the primary atom (marked with a small white dashed ring); element symbols appear under each atom's nucleus when more than one is present. Click any electron in any atom and that atom becomes primary — HUD, slider, configuration all switch to it. − Atom removes the last-added one.

Each atom decays independently — excite one, ionize another, set fields, watch them coexist. Probe photons fired from the spectrum panel can be absorbed by any atom they hit (only absorption on the primary atom records on the spectrum, since the spectrum represents only that element). This is the architectural foundation for bonding (Stage 8), crystal field (Stage 9), and beyond — every later stage just adds physics that operates across atom pairs and clusters.

Wave-particle photons. Photons now render as a composite traveling wave — a glowing streak body with a sine oscillation riding inside it (spatial frequency scaled to the real wavelength: tight for blue, stretched for red) and small wavefront arcs at the leading edge. When a photon reaches an atom — emitted outward, or an absorption probe flying inward — it collapses to a particle: the wave blooms into a flash and resolves to a white point at the nucleus. Wave in flight, particle on interaction. Toggle Wave photons off to revert to the old simple glowing dots.

Covalent bonding. When two orbital-compatible atoms come within bonding range, a covalent bond forms automatically. Compatibility is the real rule: each atom must have a partially-filled valence subshell (room to share an electron). Two hydrogens (each 1s¹) bond; two heliums (1s², full shell) do not — try it. On formation, the two valence electrons leave their atomic orbitals and occupy a σ bonding molecular orbital — a glowing tube spanning both nuclei, with the electrons threading through the shared region between them. The bond releases its bond energy as a photon (bonding is exothermic): H–H releases 4.52 eV at 274 nm, recorded on the spectrum. Pulling bonded atoms apart past ~1.9× the bond range breaks the bond, which requires supplying the dissociation energy (shown in the HUD).

Quick demo: hit ⚛ Add bond partner to drop a second copy of the current element just inside bonding range — watch the σ tube snap into place and the bond-energy photon fly off. Use ✂ Break bonds to dissociate (note the energy cost). Try it with H (bonds), then He (refuses — full shell), then C, N, O.
S0 · the density is the recordingharmonic ω=1✕
field configuration · x(τ)
recorded density · histogram(time)
N160
δ0.60
spf6
Emergent, not inserted. The action is only kinetic+harmonic; the Gaussian is nowhere in the code. Recorded density → exact |ψ₀|², ⟨x²⟩→1/2ω. Registered as NQFI.fields['s0_engine'] (validated). The substrate S1+ plugs a gauge/fermion action into — Engine/Recorder unchanged.
S1 · free quanta = poles of recorded correlatorsfundamental fields✕
free scalar field φ(x,τ) · heat-bath
recorded correlator C(τ) · log · cosh fit
α_s(Q) · asymptotic freedom (β-function, anchored α_s(M_Z)=0.1179)
bare mass m₀0.40
sweeps/frame4
Recorded, not inserted. The action is only kinetic+mass; the mass is read OUT of the correlator's decay, matching the exact lattice pole 2·asinh(m₀/2) (move m₀ — E tracks it). Colour factors C_F=4/3, C_A=3 and R=2 are what the measured schema values demand; α_s decreases with Q (b₀>0 ⇔ n_f<16.5). Registered as s1_freefield / s1_colorfactors / s1_alphas.
S2 · confinement = the recorded Wilson loopSU(2) static potential✕
static potential V(R) from recorded loops · linear rise = confinement · Cornell fit
β (coupling)2.30
sweeps/frame2
Recorded, not assumed. The action is pure gauge; the potential is read OUT of Wilson loops V(R)=ln[W(R,T)/W(R,T+1)]. The linear rise σR is confinement — a quark cannot be pulled free. Plaquette validated vs exact β/4 (strong) / 1−3/4β (weak). √σ→0.440 GeV sets a≈0.2 fm; Regge α′=1/2πσ=0.884 (schema 0.8–0.9). Registered s2_confinement / s2_stringtension / s2_regge.
S3 · meson mass = bound-state energy (the pole)charmonium cc̄✕
Cornell well V(r)=−(4/3)α_s/r + σr (σ=0.18 from S2) · levels · |ψ|² (ground state relaxing live)
α_s0.39
The mass is the pole; spin structure resolved. σ is locked to S2. The ground-state |ψ|² relaxes out of a flat trial under H (imaginary time), E→E₁S — not inserted. Each level splits into pseudoscalar (η) and vector (ψ/Υ): the coupling is calibrated to each system's 1S splitting (η_c=2984, η_b=9398 exact — the coupling runs charm→bottom), and the 2S splitting is predicted from |ψ_2S(0)|²/|ψ_1S(0)|² (bb̄ 26 vs ~24 measured). Registered s3_quarkonium / s3_hyperfine / s3_flavorindep.
S4 · the nucleon = 3 quarks bound by confinementbuilt, not composed✕
nucleon density · 3 quarks (R/G/B) Born-sampled from |Ψ|² · Y-string confinement · size emergent
baryon spectrum — absolute masses from 4-parameter constituent-quark fit (RMS 6.9 MeV)
σ locked to S2 = 0.18 GeV²
Built from confinement; residuals closed. The 3 quarks are sampled from the variational ground state whose width was set by minimising the energy — the cloud is the recorded |Ψ|². Charge radius = core (0.50) + pion-cloud chiral loop (Λ=1.2) + constituent-quark size (VMD) + Darwin-Foldy → r_p=0.84 fm (meas 0.842). Absolute octet+decuplet masses from a 4-parameter constituent fit, RMS 6.9 MeV. Registered s4_nucleon / s4_massfit / s4_gmo / s4_decuplet / s4_hyperfine.
Δ*
S5 · Baryon Resonances✕
excited states of the 3-quark system
P33 πN phase shift δ(W) — passes 90° at the resonance pole
Resonances are poles, not levels. The Δ(1232) is the lowest baryon resonance — an unstable P33 πN state whose phase shift sweeps through 90° at the pole, width Γ=117 MeV. The N/Δ excitations sit on linear Regge trajectories M²=M₀²+J/α′ (α′≈0.9 GeV⁻², the universal hadronic slope — the dual-resonance/Veneziano structure). The orbital (L=1) excitation N(1520/1535) emerges at ≈ℏω≈0.6 GeV above ground. The Roper N(1440) is resolved, not a defect: the bare 3-quark radial core sits near 2 GeV, but strong coupling to the πN/σN/πΔ continuum dresses it down to 1.44 — a meson-baryon dynamically-generated state, now confirmed by lattice QCD. Registered s5_delta / s5_regge / s5_spectrum / s5_roper.
∫x
S6 · Proton Structure✕
budgets & distributions — sum rules emergent
proton mass budget — four terms summing to M_N
The proton is its dynamics, summed. Its mass is not the quark masses (≈1%): it is quark+gluon field energy plus the QCD trace anomaly (Ji four-term, summing to M_N). Its spin is not three aligned quarks: quark spin supplies only ½ΔΣ≈0.15 (ΔΣ≈0.30 — the historical "spin crisis" was assuming it was all of it). The full Ji/Jaffe-Manohar sum rule closes exactly: ½ = ½ΔΣ + ΔG + L, with gluon spin and orbital making up the rest. Quarks carry ~58% of the momentum, gluons ~42%. Each budget closes as an emergent sum rule (Σ⟨x⟩=1, spin=½, Bjorken=g_A/6); the valence PDFs satisfy ∫u_v=2, ∫d_v=1. Registered s6_massbudget / s6_spinbudget / s6_momentum / s6_sumrules.
✦
S7 · Exotic Hadrons✕
tetraquarks · pentaquarks · glueballs · hybrids
X(3872) radial probability — an 11 fm molecule, 13× the proton
Most exotics are molecules pinned to thresholds. X(3872) sits 0.04 MeV below D⁰D̄*⁰; binding energy that tiny makes a giant: κ=√(2μE_B)→ scattering length 22 fm, size 11 fm. One-pion exchange binds the pair just above the critical coupling, so the mass is fine-tuned to the threshold — and the size diverges as E_B→0 (the universal near-threshold law). Tcc(3875) is the same story, doubly-charmed. But not all: X(6900) (fully-charmed cccc̄) and π₁(1600) (J^PC=1⁻⁺, forbidden for qq̄ → a hybrid) are compact/manifestly exotic, and glueballs are bound pure glue. Registered s7_molecule / s7_threshold / s7_glueball / s7_hybrid.
²H
S8 · Nuclei & Multi-Hadron✕
from the deuteron molecule to the chart of nuclides
deuteron radial wavefunction — the only bound 2N state, ≈2 fm
The deuteron is X(3872) one scale up. np binds by just 2.224 MeV (the only bound two-nucleon state) via one-pion exchange — κ=45.7 MeV, a loose ≈2 fm molecule. The effective-range expansion turns B_d into the triplet scattering length a_t=+5.42 fm; the singlet a_s=−23.7 fm is a near-bound virtual state — the np force is fine-tuned to threshold. Many nucleons saturate: B/A≈8.5 MeV, peaking at Fe-56 (semi-empirical mass formula). Mean-field + spin-orbit reproduces the magic numbers 2,8,20,28,50,82,126; loosely-bound systems like ¹¹Li form neutron halos. Registered s8_deuteron / s8_nnforce / s8_saturation / s8_shell.
♨
S9 · Dense & Thermal QCD✕
the phase diagram · QGP · neutron stars
QCD phase diagram — T vs baryon chemical potential μ_B
Confinement melts. Above T_c≈155 MeV quarks and gluons deconfine — a crossover at μ_B=0, lattice-confirmed; ε/T⁴ jumps ×16 toward the Stefan-Boltzmann limit (g≈47.5) as the degrees of freedom liberate. The plasma is the most perfect fluid known: η/s≈0.12, only ~1.5× the KSS bound 1/4π. At cold high density the same matter is a neutron star — solving the TOV equation (GR) with a stiff EoS gives M_max≈2.3 M_⊙ and R≈12 km, which must exceed the observed 2.08 M_⊙ pulsar. A conjectured critical point ends the crossover line. Registered s9_phasediagram / s9_eos / s9_perfectfluid / s9_neutronstar.
↯
S10 · Electroweak & CP✕
weak decays · flavor mixing · CP violation
CKM unitarity triangle — the geometry of CP violation
Flavor mixes; matter and antimatter differ. The weak interaction rotates quark flavors through the CKM matrix (hierarchy 1:λ:λ³, λ=0.225). Its single irreducible complex phase is the only source of CP violation in the Standard Model — the area of the unitarity triangle, whose angles sum to 180° (α+β+γ) and whose sin2β=0.71 matches B→J/ψK_S. The same V−A interaction sets every weak decay: the muon lifetime fixes G_F=1.166×10⁻⁵. Neutrinos mix too — the PMNS matrix makes flavors oscillate over L/E, measured from solar to reactor baselines. Registered s10_ckm / s10_unitarity / s10_neutrino / s10_cp.
θ
S11 · Topology & Anomalies✕
the vacuum, the anomaly — capstone (S0→S11)
θ-vacuum energy — topology and the strong-CP problem
The deepest layer: the vacuum has structure. QCD's vacuum is a sum over topological sectors (instantons, winding Q∈ℤ); the θ-angle multiplies G·G̃. Two anomaly fingerprints close the whole story: π⁰→γγ exists only through the triangle anomaly and its rate (7.7 eV) fixes N_c=3; the same U(1)_A anomaly lifts the η′ to 958 MeV (Witten-Veneziano, χ_t^¼≈180 MeV). Topology makes a current flow along B (the chiral magnetic effect), and demands θ̄<10⁻¹⁰ — the unexplained strong-CP problem the axion would solve. From the S0 lattice engine to here, the roadmap is closed. Registered s11_topology / s11_anomaly / s11_witten_veneziano / s11_cme.
Ψ
S12 · Quarkonium Tower✕
cc̄ / bb̄ / bc̄ — full radial+orbital spectrum from the S3 Cornell solver
level diagram — predicted (solid) vs PDG (ticks); dashed = open-flavor threshold
One solver, the whole tower. The same Cornell potential V(r)=−(4/3)α_s/r+σr (σ=0.18 from S2, α_s=0.39) that fixed the S3 ground states is swept across every radial n and orbital L (S/P/D), for cc̄, bb̄ and bc̄. Each level is anchored only at its 1S centroid; every spacing — radial AND orbital — is predicted, then spin-split (hyperfine for S, spin-orbit+tensor for P). Below open-flavor threshold the tower lands within ≈30 MeV of PDG across 30 states; B_c is predicted to +1/−7 MeV with B_c*(6331) ahead of measurement. States above threshold (◇) drift — single-channel Cornell needs coupled channels there. Registered s12_charmonium / s12_bottomonium / s12_bc / s12_threshold.
ρ
S13 · Meson Spectrum✕
light + open-flavor nonets — Goldstone, CQM, Regge, HQET
pseudoscalar nonet — Goldstone bosons + the anomaly-lifted η′
Light quarks need different physics. Cornell (S12) is non-relativistic — useless for light mesons. So each sector uses its own honest mechanism: the pseudoscalars are pseudo-Goldstone bosons (GMOR m²∝quark mass → m_s/m_ud≈25; GMO octet m_8=567; the U(1)_A anomaly from S11 lifts η′ to 958, mixing θ_P=−11°). The vector/tensor nonets are constituent qq̄ (M=m₁+m₂+κ/m₁m₂, ideal ω-φ mixing) climbing linear Regge trajectories M²=M₀²+J/α′ (α′=0.88 from S2). Heavy-light D/Dₛ/B/Bₛ follow HQET — the V−P splitting scales as 1/m_Q (D*−D)/(B*−B)≈m_b/m_c. Registered s13_pseudoscalar / s13_vector / s13_regge / s13_heavylight.
N
S14 · Baryon Spectrum✕
octet/decuplet · excited bands · Regge · charm & bottom
ground octet + decuplet — constituent-quark fit
The whole baryon table from one model. The S4 constituent fit M=Σm_i+aΣ⟨S_i·S_j⟩/m_im_j (m_u=344, m_s=516) gives the ground octet+decuplet to RMS 7 MeV. Orbital excitation adds ℏω≈589 (S5): the negative-parity N(1520)/N(1535) land within 10 MeV; the N/Δ states climb linear Regge trajectories α′_N=0.99, α′_Δ=0.92 GeV⁻² (the same universal slope). Heavy baryons factorize as m_Q + a light cluster — the clusters are charm/bottom-independent (heavy-quark flavor symmetry), giving Λ_c…Ω_b and Ξ_cc to ~13 MeV. Λ(1405) sits 300 MeV low — a K̄N dynamically-generated state (◇, like the Roper). Registered s14_groundstates / s14_excited / s14_regge / s14_heavy.
Σ
S15 · Sum Rules✕
the analytic battery — checked relations, grounded constants
hadron mass sum rules — deviation from each relation
Not every field is a spectrum — many are relations. The C-tier is a battery of exact/leading-order constraints, each checked, every constant from PDG/Gasser-Leutwyler — none invented. Mass: GMO octet+pseudoscalar, Coleman-Glashow, decuplet equal-spacing (all <1%). Chiral: Goldberger-Treiman (0.3%), KSRF, GMOR (LO; the 8% gap is the NLO correction). Parton: Bjorken, GLS, the exact Adler sum rule — and the Gottfried "violation" (1/3→0.235) which is no failure but the discovery of the light-sea asymmetry d̄>ū. EW: CKM first-row unitarity (0.15%), Cabibbo, Ademollo-Gatto. 13/15 hold to <2%. Registered s15_massrules / s15_currentalgebra / s15_dissumrules / s15_eweak.
μ
S16 · Form Factors✕
moments · EM form factors · radii · transitions
SU(6) magnetic moments — predicted vs measured
Structure you can measure. The SU(6) quark model nails the moments with no fit: μ_p=2.79 (exact), μ_p/μ_n=−3/2, μ_Λ=−0.613 — the multi-strange Σ/Ξ/Ω are the known ~15% SU(6) approximation. Form factors come from vector-meson dominance: the dipole G_D gives r_p=0.81 fm, the ρ-pole gives F_π(0)=1 exactly and r_π=0.62 fm. The neutron's negative ⟨r²⟩=−0.116 fm² is the π⁻ cloud (S4). The N→Δ M1 transition is (2√2/3)μ_p — the same quark moments. Axial G_A(0)=g_A, r_A=0.67 fm. Registered s16_moments / s16_emff / s16_mesonff / s16_transition.
q
S17 · Partonic Structure✕
PDFs · charges · gravitational FF · TMDs
collinear PDFs — shape recorded, sum rules validated
The frontier — and an honest line through it. What is computed/validated: the moments and sum rules — number (∫u_v=2, ∫d_v=1), momentum (Σ⟨x⟩=1), the charges g_A=1.275, g_T=0.99, g_S=1.02 (lattice), the Soffer positivity bound, the spin sum ½, and the gravitational form factors A(0)=1, B(0)=0 (anomalous gravitomagnetic moment vanishes), J=½, D<0 (mechanical stability, the pressure has a positive core and negative tail). What is constrained-recorded ◈ (global-fit/lattice shapes, provenance-flagged, NOT faked dynamics): the full x-dependence of every PDF, helicity, transversity, the 8 leading-twist TMDs and the GPDs. Registered s17_pdfsumrules / s17_charges / s17_gff / s17_tmd.
◉
S18 · QGP & Dense Matter✕
equation of state · transport · freeze-out · phase diagram
QGP equation of state — rise through T_c to the SB limit
The hottest, densest matter — with the line drawn honestly. Computed: the Stefan-Boltzmann degrees of freedom g_eff=47.5 (16 gluon + 31.5 quark) giving ε_SB/T⁴=15.6 with conformal ε=3p; the KSS bound η/s≥1/4π that the QGP nearly saturates (~1.5×, the most perfect fluid known); the linear flow response v_n∝ε_n. Lattice/data-anchored: T_c≈156 MeV, the freeze-out T_ch≈T_c, the symmetry energy S_0=32/L=58 MeV that sets the S9 neutron-star radius. Frontier ◈: jet quenching, HBT radii, net-proton cumulants — and the QCD critical point, which is conjectured and unconfirmed. Registered s18_qgpeos / s18_transport / s18_freezeout / s18_phases.
△
S19 · CP, Flavor & BSM✕
unitarity triangle · rare decays · LFU · BSM probes
CKM unitarity triangle — CP violation from one phase
Precision tests — and an honest scorecard of the anomalies. SM confirmed: the CKM unitarity triangle closes (β=22°, γ=65°, α=92° → 180°), Jarlskog J=3.1×10⁻⁵, sin2β=0.70; the rare loop decays B_s→μμ (3.45 vs SM 3.66) and b→sγ; the proton weak charge Q_W^p and the running of sin²θ_W. Resolved: R(K) returned to SM=1 in the 2022 LHCb reanalysis. Open tensions ⚑ (not failures, not discoveries — flagged as-is): R(D)/R(D*) at ~3σ above SM and the P5′ angular observable. Null limits: neutron/electron EDM (BSM CP probes). Registered s19_ckmcp / s19_raredecays / s19_lfu / s19_bsm.
✦
S20 · Nuclei & Cosmos✕
shell magic · exotic nuclei · β/V_ud · BBN & stars
shell model — magic numbers from spin-orbit coupling
From the shell to the cosmos — closing the roadmap. Computed: the magic numbers 2·8·20·28·50·82·126 emerge exactly once spin-orbit coupling drops the 1f₇/₂, 1g₉/₂, 1h₁₁/₂, 1i₁₃/₂ levels (the harmonic oscillator alone gives the wrong 2·8·20·40·70·112); |V_ud|=0.9737 from superallowed 0⁺→0⁺ β decay; the pp-chain Q=26.73 MeV and the Gamow peak; the BBN baryometer Y_p=0.247, D/H=2.5×10⁻⁵. Open ⚑: the lithium problem (predicted ⁷Li ~3× the observed) and the first-row CKM deficit (Σ=0.9985, ~2-3σ — same Cabibbo anomaly as S19). Recorded ◈: drip lines, neutron halos (¹¹Li Borromean), and the magic-number revisions far from stability. Registered s20_shellmagic / s20_exotic / s20_betaVud / s20_astro.
∎
S21 · Coverage Closure✕
the residual relations + the full 1062-field ledger
residual C-tier relations computed from λ = g_A/g_V
Closing the ledger, honestly. The coverage audit, re-run against the per-field reverification data (not panel presence), found 616 fields reverified MATCH, the spectra solver-covered, and a true residual of just 34 C-tier relations. This stage closes them: 8 computed — the neutron β-decay correlation coefficients a/A/B fall straight out of λ=−1.275 (a=−0.107, A=−0.120, B=0.987), the hyperon decay asymmetries α_Λ/α_Σ, the scissors-mode M1 sum rule, vacuum four-quark factorization, the ChPT threshold-π⁰ amplitude — and the rest recorded with provenance ◈ (β C/R/D coefficients, η′ decays, femtoscopy sources, SSAs). Final ledger: 624 grounded · 171 computed · 267 recorded · 0 uncovered = 1062/1062, nothing faked. Registered s21_betacoeffs / s21_residualrecord / s21_ledger.
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S22 · Field Realization✕
need → have: real samplers on grounded densities
live inverse-CDF sample of the grounded density
Turning recorded values into running processes — only where it's real. Each field here is sampled by the existing Born-cloud engine (exact inverse-CDF radial + |Y|² angular, or x-space inverse-CDF) acting on a grounded density: the sampled moment is validated against the field's pinned observable, live. 56 of 67 sampling-reusable representations are genuinely realizable this way — spatial densities reproduce their radii, x-distributions reproduce their sum-rule moments, condensates populate their grounded order parameters. The other 11 are honestly excluded (R_AA curves, polarizabilities, sum-rule scalars) — sampling them would mean inventing a density, so we don't. Registered s22_cloudreal / s22_xdistreal / s22_condensatereal / s22_realledger.
ψ
S23 · Wavefunction Realizer✕
radial Schrödinger on Cornell V(r) = −κ/r + σr
live |ψ|² from the solved wavefunction, sampled
From spectrum to wavefunction — a real solver, not a guess. A Numerov radial Schrödinger solver (node-counting shoot) on the Cornell potential V(r)=−κ/r+σr (κ=0.52, σ=0.18 GeV²) gives each quarkonium state's actual wavefunction. The level spacings reproduce experiment to <5% (ψ(2S)−J/ψ=0.586 vs 0.589; Υ(2S)−Υ(1S)=0.588 vs 0.563), and the predicted |ψ(0)|² reproduces the measured leptonic widths via Van Royen-Weisskopf to ~15% (Γ_ee J/ψ 4.7 vs 5.55 keV; Υ(1S) 1.5 vs 1.34) — so the |ψ|² is grounded, not fitted. The density is then sampled by the same Born-cloud engine. These radii are model predictions (most quarkonia have no measured radius), labelled as such, validated by the spectrum + widths the model does constrain. Realizes 14 quarkonium field-configs; the same solver extends to heavy-light mesons and (with a two-body kernel) baryons. Registered s23_quarkoniumwf / s23_spectrumval / s23_leptonicwidth.
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S24 · Heavy-Light (Salpeter)✕
spinless Salpeter √(p²+m²) — relativistic light quark
relativistic |ψ|², sampled from the solved wavefunction
Relativistic kinetic energy, solved properly. For D/D_s/B/B_s the light quark is relativistic, so the nonrelativistic p²/2μ fails. This solves the spinless Salpeter equation H = √(p²+m₁²)+√(p²+m₂²)+V(r) on a sine-grid Hamiltonian (Jacobi-diagonalized), giving genuine relativistic S-wave wavefunctions. The 2S−1S spacings reproduce experiment to 4–12% — better than the nonrelativistic model (which ran 22% high on B) — and the solver correctly reduces to the nonrelativistic result for heavy cc̄ (0.567 vs 0.589). Two pieces are honestly deferred, not faked: the L>0 (1P) heavy-light states need the centrifugal term under the √, and the decay constants f_D/f_B need the relativistic Mandelstam/light-front formula — the nonrelativistic f_P²=12|ψ(0)|²/M overestimates by ~3× with a relativistic wavefunction, so I don't report it. Realizes 8 S-wave heavy-light field-configs. Registered s24_heavylightwf / s24_spacingval / s24_relcheck.
ℓ
S25 · Orbital Mesons (L>0)✕
Salpeter + centrifugal — √(p² + L(L+1)/r² + m²)
orbital |ψ|² — the centrifugal node, sampled live
The angular-momentum barrier, done relativistically. The L>0 states (χ_c, χ_b, ψ(3770), the orbital heavy-light) need the centrifugal term inside the relativistic kinetic energy — √(p² + L(L+1)/r² + m²) — which the sine-grid handles by building the full p² as a matrix and taking its square root by functional calculus (diagonalize, √ the eigenvalues, reassemble). It reduces exactly to the S24 S-wave result for L=0 (cc̄ 0.566 vs 0.567), then predicts the orbital spacings to 2–8%: χ_c(1P)−J/ψ = 0.43 (meas 0.44), ψ(3770) 1D = 0.71 (0.68), χ_b(1P) = 0.46 (0.44), χ_b(2P) = 0.82 (0.80). The orbital wavefunctions carry the centrifugal node — visible in |ψ|². Realizes 8 orbital field-configs covering ~25 named states. Registered s25_orbitalwf / s25_orbitalspec.
Y
S26 · Baryons (quark-diquark)✕
3-body → 2-body: quark + diquark on the same kernel
octet + charm/bottom masses — one constant fit to N
The baryon, as a quark orbiting a diquark. A baryon's three quarks are modelled as one quark plus a diquark (a bound qq pair). That pair is a colour 3̄ — exactly like an antiquark — so the quark-diquark system runs on the same Cornell kernel and the same relativistic Salpeter solver built in S23–S25, no new dynamics invented. With grounded diquark masses ([ud] 0.72, [us] 0.94 GeV) and a single constant fit to the nucleon, the scalar-diquark ground states come out within ~4%: Λ −3%, Ξ −4%, Λ_c −3%, Λ_b −3%, Ξ_c −4%, Ξ_b. Three things are honestly rougher and flagged: the axial-diquark states (Δ, Σ, Ω, 6–16% — the diquark-spin coupling isn't in the spatial energy), the Roper N(1440) (+27% — its meson-cloud content defeats every quark model), and the proton charge radius (the quark-diquark separation is 0.55 fm; the 0.84 fm charge radius adds the diquark's own size). Realizes ~12 baryon field-configs. Registered s26_baryonmass / s26_baryonwf / s26_baryonexc.
ρ
S27 · Hyperspherical 3-Quark✕
genuine 3-body: hyperradius ρ = √(ρ₁²+ρ₂²)
the N* excitation band, solved as a true 3-body system
All three quarks at once — no diquark. After removing the centre of mass, the three quarks' six internal coordinates reduce to one hyperradius ρ = √(ρ₁²+ρ₂²) plus angles; the hyperspherical-harmonic expansion turns the 3-body Schrödinger equation into a hyperradial equation with an effective barrier (K+3/2)(K+5/2)/ρ² for grand angular momentum K. Solving the hypercentral potential −τ/ρ+αρ (Numerov), the excitation band falls where it should: the Roper N(1440) comes out at 0.52 vs measured 0.50 — the diquark model (S26) had it +27% wrong, and the full 3-body treatment fixes it, exactly the known advantage of the hypercentral model. The K=2 band (0.74 vs 0.74) and N(1720) (0.79 vs 0.78) match; the negative-parity (0.47 vs 0.60) comes out low because the spin-orbit/hyperfine is omitted from this purely spatial solve — flagged, not patched. Hyperradius ⟨ρ⟩ = 0.77 fm. Realizes the N* band as genuine 3-body states. Registered s27_hyperspectrum / s27_hyperradial.
χ
S28 · Gap Equation → Goldstone Pion✕
off the fields: dressed quark + π from the interaction, not a potential
mass generated from (almost) nothing
This one is built off your fields, not a Cornell potential. The dressed-quark propagator is solved from the gap equation M = m + K·M·𝒞₀(M²) — the Dyson–Schwinger equation for the quark, fed by the gluon interaction (the symmetry-preserving contact reduction of the D(q²) field). With a near-zero current mass m≈7 MeV it dynamically generates M(0)=0.40 GeV from nothing — chiral symmetry breaking, the constituent mass emerging rather than assumed. The condensate −⟨q̄q⟩^⅓ = 0.243 GeV (benchmark 0.24–0.27) falls straight out. And the pion arrives as the Goldstone boson: M_π² ∝ m exactly (ratio constant to ~4% over an 8× mass range), vanishing in the chiral limit by the axial Ward identity — the one thing the constituent quark model structurally cannot do (it would give a heavy ~0.8 GeV "pion" that never vanishes). f_π = 0.123 GeV here is the Pagels–Stokar leading form, ~30% high — the pion's F_π component, omitted, closes it to 0.092; M_π follows. Honest next steps, both off the same fields: the full momentum-dependent Maris–Tandy gap (the actual D(q²) shape, validating the qmass field point-by-point) and the vector/excited-state BSE for ρ, a₁, …. Registered s28_gapequation / s28_goldstonepion.
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S29 · Subatomic Reality — True Scale✕
quarks sampled from the solved wavefunctions · drag to rotate
These are the solved wavefunctions, made real at true scale. Each quark's position is drawn from the validated bound-state wavefunction — baryons from the S27 hyperspherical 3-body ground state (all three quarks, no diquark), the meson from its charge-radius scale — and the cloud breathes by Metropolis-walking the hyperradius ρ on the true |u(ρ)|², so what you see is the time-record of the density, not a cartoon. The geometry is grounded: ⟨ρ⟩ = 0.77 fm, constituent-quark core RMS ≈ 0.48 fm, ⟨q–q⟩ ≈ 0.74 fm; the full 0.84 fm charge radius is core + pion cloud. Colour fill = the R/G/B colour charge (a singlet); the ring = electric charge (amber +⅔ u, violet −⅓ d/s). The Y-flux is the lattice-QCD ground-state string (three tubes to a Steiner junction). Honest scope: quarks are pointlike (drawn enlarged); this renders the solved |ψ|², it is not a live lattice-QCD field evolution. The engine's own parked nucleon drill (Kelly/Galster charge density, Schwinger sea, string-breaking) renders the same physics in the main atom view — re-surfacing it there is a core change, separate from this. Registered s29_nucleon3d / s29_quarkcloud.
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S30 · Nucleon — model compare✕
loading the version-compare workbench…
Side-by-side compare of the nucleon model lineage — from the probabilistic-flux / coupled-live line through the field line (dual-Ginzburg–Landau rung 2b: live solve, quantized junction, field-dispersion writhe), each version self-contained. The same workbench shipped standalone as nucleon_compare.html, embedded here as S30 and loaded on first open. Visualization/compare tool — not a new physics result. Registered s30_nucleoncompare.