M36 develops the Quarter-Rank Fountain: a dyadic refinement of fractional rank operations in the Symmetric Core and its higher-Core extensions. The starting point is the Halbzeug, the half-rank mediator between adjacent operational rooms. M36 shows that this mediator is not final: it opens a dyadic descent 1/2, 1/4, 1/8,. . . where the quarter-step, or Viertelzeug, becomes the first internal structure of the mediator itself. The central principle is that a Room is not an operation name but a nesting depth. For a scaffold f and an internal combiner C, the general fractional Core has the form Coreₑ, ₂ (a, b) = fʳ (C (f^-r (a), f^-r (b) ) ). At r = 0 the scaffold cancels and the operation is exactly the combiner. Thus Room 0 is not a shadow but a structural identity. The Halbzeug interpolation is continuous, so quarter-ranks (Viertelzeug) exist as freely as half-ranks, and iterating gives a dyadic rank fountain with Gaussian generator (1 + i) /2 accumulating at every integer rank. This fountain lets a degree-n polynomial be solved by composing low-rank operations within 1 ≤ R ≤ 3 no tetration ballast required for at least the small-compositionfactor class. The Symmetric-Core (particle) fountain of M18 has a Hyper-Core (force) counterpart and an asymmetric Caterpillar (interaction) counterpart; together they form theFountain of the Triad, merging at the electroweak Lucky Zone and splitting at the strong-force boundary R = 3.
Paweł Łukasz Garycki (Mon,) studied this question.