Tuesday, September 29, 2026

Five-Phase track (五行轨)

The two-relation, five-element track; the minimal closed rotor carrying generation (step 1) and restraint (step 2) as irreducible relations

Formal technical name
minimal bi-Hamiltonian rotor on ℤ₅

Related claims

Tier under review: an upstream claim has changed and the tier of this claim is being reviewed.
SGC-0013 Theorem Proof in manuscript

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.

Tier under review: an upstream claim has changed and the tier of this claim is being reviewed.
SGC-0014 Theorem Proof in manuscript

Restraint = generation²: on ℤ₅ the overcoming map is the square of the generating map.

Tier under review: an upstream claim has changed and the tier of this claim is being reviewed.
SGC-0015 Theorem Proof in manuscript

5 ∤ 2ᵏ: the Five-Phase track cannot be reduced to a binary (yin-yang track) representation.