, c) LDA, and then d) Gradient (MetaGGA).*

An acceleration allocation segment determines the order of operation from the underlying math for the Perdew Ladder for DFT.  For DFT, and more generally the mass (1/m) in all equations, . . . in restated order:

- Scale must be net-dimensionless, (d/d_Base)^V/W.  LDA requires particle-edge radius (r_e) base, versus standard force scaled hc at Bohr-Hydrogen(a₀), so converting hc@a₀ via fine α=(r_e/a₀)^1/2.

- That base updates for each Element (based upon a sawtooth step-function for each element (S_N)*r_e: odd (8/7), even (1/2)^1/3, then with outer subshell refinements, refining Okun, Burke’s presentation last year.

- LDA Localization, mass, gets replaced by position-in-field using the known 1/x^3/4, so (r)^4/3, transformation as rescaled above.

- The relative position-in-field inverse, interactive for both particles (1+PiF₁/PiF₂) by 1/x^3/4, refining MetaGGA, gradient for Conservation of Force by acceleration allocation.  So, force per particle become acceleration that allocates by gradient from 2-particle, 2-level (acceleration, velocity) 4x4 matrix.

One integrated segment has all four, importantly the relative position-in-field inverse, interactive for both particles (1+PiF₁/PiF₂) gradient for Conservation of Force by acceleration allocation.  So, force per particle allocates by 2-particle, 2-level (acceleration, velocity) 4x4 matrix.  Critically, then (Σa_n=F).

That math defines order of operation:  1) r_e scaling, 2) sawtooth step-function by Element . . . and eventually outer subshell refined, 3) LDA, 4) position-in-field double gradient, inverse and interactive.  Now, with two steps before today's Perdew Ladder.