K=1 Chronogeometrodynamics

Background. Time has invariably entered physics as a primitive -- an underived input. Framework. Time is modelled as the cost of change, with information time dtᵢnfo: = dPhi/H. Modelling the signed leading quadratic form G associated with dtᵢnfo² as satisfying Axioms R, E, T in the companion Realizability paper gives, under nondegeneracy, Sig (G) = (1, 1), equivalently det G0; K (x) =xT G x=1 is the unit-cost locus. Within the symplectic-dissipative class GA=alpha J-GD of Law II, the unique law is xdot= (JG-D) grad V; at critical damping with normalised eigenvector base, kappaK=4 dc. Thermodynamic content. In the stationary regime near K=1 with Tₑff=Tₜol, the Clausius relation fixes the noise amplitude in terms of the Tolman temperature and the stability boundary dc; combined with S proportional to A, this provides Route A's local thermodynamic bridge to the Jacobson argument, recovering G₌ₔ ₍ₔ=8 pi T₌ₔ ₍ₔ. Route B is thermodynamically independent but limited to spherical symmetry. Gravitational content. For static, spherically symmetric metrics on intervals where f>0, with symplectic eigenvalues sigma₁: = r sqrt (f) and sigma₂: = r, the conjectured field-level analogue sigma₂² Box ln sigmaᵢ=1 (i=1, 2) is algebraically equivalent to the Einstein vacuum equations R₌ₔ ₍ₔ=0. Axiom T forces sigma₁>0, placing sigma₁-degenerate regions, including curvature singularities, outside the domain; the OU variance bound Var (K) <1 gives a Planck-order self-consistency bound. Keywords: Lorentzian signature; Information time; Symplectic-dissipative dynamics; Jacobson argument; Rindler horizon