Infinite-Dimensional
Wave Theory

Infinite-Dimensional Wave Theory starts from a space with infinitely many ordinary spatial directions, all of the same kind as the three we see, plus time. One field fills that space, and every particle is a stable pattern of it. A pattern is bound in a fixed number of directions, its depth, and is free in all the others. Matter is bound in at most ten.

Within its depth $d$, a pattern sits at a whole-number level $n$. Its mass is the scale shared by that depth times the number of points in a simplex with $n$ points along each edge in $d$ directions:

$m=\mu_d\dbinom{n+d-1}{d}$

With the electron mass as its single measured input, this rule gives the W, Z and Higgs bosons, five quarks, the muon and the tau. Nine of these ten masses fall within one percent of measurement, and the top quark within 2.2 percent.

The electron orbits the nucleus through four spatial directions at a fixed distance, so each shell is a three-sphere. The angular patterns on that shell give capacities of 2, 8, 18 and 32 electrons, and their subshell content matches every one of the seven periods of the periodic table.

The levels connect the families. Each charged lepton’s level is a quark level plus a neutrino level: electron 13 = up 3 + neutrino 10, muon 35 = charm 20 + neutrino 15, and tau 23 = down 1 + neutrino 22.

The depth-five counts fix the neutrino masses at 1.53, 8.90 and 50.4 meV in normal order. Their sum, 60.8 meV, lies below the current cosmological bound.

• Petals, Tubes and Rings: The Structure of the Four-Direction Orbit

  Fedge No · 11 November 2026 · PDF

  Gives the closed form of the four-direction electron orbit and its petal, ring and tube views, with its stability, its link to the Frost circle and its radius-set turning ratio.

• Shell Capacities from Four Spatial Directions

  Fedge No · 11 November 2026 · PDF

  Counts the angular patterns on the three-sphere shell of a four-direction orbit and matches their capacities and subshell content to the seven periods of the periodic table.

• The Generation Law: Each Charged Lepton Is a Quark Plus a Neutrino

  Fedge No · 11 November 2026 · PDF

  Shows that each charged lepton level is the sum of a quark level and a neutrino level, with the simplex geometry and the Vandermonde expansion of the counts.

• Absolute Neutrino Masses from the Depth-Five Simplex Count

  Fedge No · 11 November 2026 · PDF

  Derives the neutrino mass ratio 2002:11628:65780 and splitting ratio 0.03035 from depth-five counts and compares the resulting absolute masses with oscillation, cosmology and beta-decay data.

• Shapes of the Counted Patterns and the Exact Branch at Every Depth

  Updated 10 November 2026

• Shell Counts and the Rydberg Squares from Four Directions

  Updated 10 November 2026

• The Precession Term and the Fine-Structure Beats

  Updated 10 November 2026

• Orbits That Stay Apart and Molecular Shape

  Updated 10 November 2026

• A Neutrino Bound in Two of the Three Observed Directions

  Updated 10 November 2026