The Equipoise Principle: Exchange-Invariant Geometry of Bipartite Readings and the Unique K4 Solitonic Closure

We develop an exchange-invariant calculus for positive bipartite readings. A reading is represented by a curve in the logarithmic plane, whose logarithmic slope is invariant under regular reparametrization but transforms nontrivially under interchange of the two components. The exchange law yields local invariants at the balance diagonal, and normalization by the total reading embeds relative composition in the Bernoulli simplex, where the Fisher metric produces a corrected turning invariant. We prove a reconstruction theorem for autonomous reading flows, classify weighted power-level sets, and express the second balance jet of an exchange-symmetric conserved whole as a normalized Hessian contrast. The framework is then applied to a family of exact FLRW backgrounds generated by a local density-speed closure. The continuity equation fixes a unique monotone heteroclinic profile. The corresponding acceleration boundary obeys (1+χ)2m(2−dχ)=d−2. Among integer spatial dimensions d≥3, the golden-ratio value χ=φ−1 occurs as an acceleration boundary if and only if (d,m)=(3,2). The resulting three-dimensional K4 background satisfies the exact algebraic orbit r(2+w)4=1, and possesses a parameter-free past mirror of the future exit state. The paper identifies direct background-level observational tests and separates them from the perturbative completion required before growth, ISW, and full CMB observables can be predicted.KSASALEM EID