The Spatial Architecture and Ambient Universe: A Constructive, Computationally Bounded Foundation for Physics

We present a foundational framework for physics built on constructivemathematics and intuitionistic logic rather than on continuousZermelo--Fraenkel set theory. Space is formalised as a coproduct of adiscrete inductive skeleton and a pointless locale; classical integration,differentiation and the Riemannian metric are replaced by aresolution-bound localic accumulator, a resolution gradient, and aminimal-transition-cost metric; and physical evolution is apolynomial-time state automaton minimising a discrete action cost over thelattice. Within this setting we develop a discrete vector calculus inspacetime algebra, a hydrodynamic update rule, a treatment of quantumstates as coinductive choice sequences, and a thermodynamic account ofgravity. Two results distinguish this presentation from its predecessors. First, theframework's saturation bandwidth limit is shown to have been two distinctquantities sharing a name --- a local rate bounded by Margolus--Levitin anda local capacity bounded by Bekenstein --- which removes a conflict oftwenty-six orders of magnitude and recovers the holographic count$2.27\\times10^{122}$ nats as a derived quantity rather than a calibration.Second, the action cost as previously written is unbounded below; we showthat no positive-definite replacement can be Lorentz-invariant, adopt aframe-relative cost, and establish that it is Lorentz-\\emph{equivariant},so the dynamics remains covariant. A mesoscopic realisation of the hydrodynamic sector has been implementedand validated against an external benchmark, reproducing Ghia, Ghia \\& Shin(1982) to $R^2 = +0.9973$. That realisation instantiates the framework'shalting structure without instantiating the Boolean substrate the structureis supposed to arise from, and the distinction is stated wherever it bearson a claim. Within it, two results are reported. The framework's fourcost operators are shown to be a \\emph{gauge} freedom that cannot affectthe flow, so the halting fault is the only component of the update rulewith dynamical content; and the effect of that fault on transport isderived rather than fitted, its amplitude following from the collision ruleby a Chapman--Enskog expansion and the form of the resulting average fromthe geometry of the fault set, with no free parameter. The fault ismeasured to be shear-selective at $5$--$6.5\\sigma$ against a matched randomcontrol. No other sector of theframework has been tested, and every claim in this document carries amarker stating which of axiom, derivation, numerical validation, orconjecture it is.