Unified frameworks: C.O.R.E. kernel logic, toroidal mandala geometry, reversible computation, and finite group theory
The NUMO Field operates on digits 0-9 through four fundamental operators that generate all reversible transitions. This minimal kernel (C.O.R.E. = Cauldron Operator Rotational Engine) underlies the entire system.
Core identity states
Central cavity—void to spark transition via C-operator
Inversion band
Equatorial twist where δ and μ coincide
Polarity rails
Vertical stabilizers anchoring orientation
Circulation ring
4-cycle loop: 2→5→6→9→2
Pairs: n + δ(n) = 11. Represents balanced opposition.
(0↔0), (1↔1), (2↔9), (3↔8), (4↔7), (5↔6)
Left-right symmetry across polarity axis.
(2↔5), (3↔8), fixed: 0,1,4,6,7,9
Radial transition between interior states.
(0↔1), fixed: 2-9
Circulation on engine layer: 2→5→6→9→2
L⁴ = identity, fixed: 0,1,3,4,7,8
All operators are strictly reversible. δ, μ, C are self-inverse (f² = identity). L has inverse L⁻¹ = L³. No information is ever lost—every state transition can be undone.