Proper classes (in the project's sense: circular self-embedding structures) have their mathematical home in terminal coalgebras νF ≅ F(νF).
Part C: Generation
Bisimulation serves as the identity criterion; in the finite case it is decidable via Paige–Tarjan partition refinement.
5 is the least integer admitting, on one element set, two mutually irreducible directed Hamiltonian cycles (steps 1 and 2); hence the "five" of the Five Phases is fixed by number theory.
Restraint = generation²: on ℤ₅ the overcoming map is the square of the generating map.
For the logistic map, all period-2ᵏ orbits appear below the accumulation point r∞≈3.570; period 5 appears only beyond it.
Sharkovskii's theorem (external anchor): periods of continuous interval maps obey the Sharkovskii ordering.
Nuclear-hexagram basin spectrum: the nuclear map is the only irreversible inter-hexagram relation; the basin spectrum of the 64 hexagrams under its iteration (three attractor basins) is exhaustively determined.
The Feigenbaum accumulation point r∞≈3.570 can be read as a dynamical realization of the Axiom-of-Foundation boundary.
Period-doubling 2ᵏ corresponds to the nested yin-yang trigram system; period 5 corresponds to the Five Phases.
There is a unique hexagram–object assignment (e.g. one hexagram = one specific codon).