The Constraint Network dynamical system, defined by three axioms, rigorouslyproves the existence and uniqueness of emergent constants. In prior work, the precise values 1836 and 1837 were derived under the conditionθₜol = 1°. This paper provides a rigorous proof that θₜol = 1° itself isa necessary consequence of the axioms, thereby closing the final link in thederivation chain from the axioms to the fundamental constants. The proofproceeds by exhaustive elimination: the parameter space (0, π) ispartitioned into three mutually exclusive and collectively exhaustiveintervals—θₜol 1°—and it is shown thatonly θₜol = 1° is dynamically viable. The argument is organized into threecomplementary components. The core proof (Section 4) is a dynamicalstability analysis: an upper bound on the accretion rate derived fromphase-space geometry and a lower bound on the sparseification rate derivedfrom escape-cone geometry together exclude all θₜol 1°. Alogical bridge (Section 3) connects this uniqueness result to the numericalvalue Nₛeal = 1836 derived in companion work under θₜol = 1°. Anumber-theoretic consistency verification (Section 5) confirms that thediscrete orbital parameters obtained in companion work are internallycoherent with θₜol = 1°. These three components are not three independentproofs; their logical relationship is sequential and complementary. Withθₜol = 1° rigorously established, the emergent constant Nₛeal is uniquelydetermined as 1836. The complete derivation chain—axioms → unique θₜol →unique Nₛeal—is thus closed without adjustable parameters.
Menggang Yu (Tue,) studied this question.