The Unified Holographic Master Action in Entropic Formulation

The Unified Holographic Master Action in Entropic Formulation Branchwise Entropy Coordinates and a Variationally Coupled Einstein–Scalar/Quantum Boundary Model Dr. Theodor HeutschiIndependent Researcher, Lucerne, SwitzerlandDate: 12 November 2026 AbstractWe investigate whether temporal and radial evolution parameters can be replaced, locally and without altering the underlying physical dynamics, by suitably defined entropy-related coordinates. A signed microscopic coordinate is constructed from changes of reduced von Neumann entropy; its negative values do not imply negative absolute entropy. A distinct radial coordinate is constructed from the monotone holographic c-function of a four-dimensional Einstein–scalar domain wall. We derive its monotonicity from the bulk equations, establish the domain of invertibility, and transform the radial ADM action, Hamiltonian constraints, Hamilton–Jacobi functional and cutoff-flow coefficients. A two-parameter formulation is proposed without identifying timelike and spacelike foliations. For a non-Hermitian two-level model, we derive a positive metric in the unbroken region and the additional connection term required for norm preservation when that metric varies. Exact AdS fixed points, entropy turning points and stationary de Sitter horizons furnish counterexamples to universal global substitution. The resulting construction is a controlled reparametrization with a proposed integrability program, not a demonstrated new theory of quantum gravity. V6 additionally defines a scalar-dependent finite-cutoff quantum boundary interaction, derives its conditional Ward identity and boundary source, and solves an exact two-qubit probe model on a nontrivial domain wall. A coupling-dependent entropy susceptibility and local two-parameter transport flatness are established within the probe assumptions. Neither a globally backreacted solution nor a new fundamental unified theory is claimed. The present V9 extension adds a distinct stationary homogeneous quantum-medium effective model, derives an exact medium-dependent Einstein–scalar domain-wall solution with gravitational backreaction, and establishes a cutoff-independent but coupling-dependent geometric–spectral identity. These results do not solve the original localized boundary impurity, nor do they establish a new fundamental theory; the scope and assumptions are made explicit. The V10 addition integrates an exactly solvable Gaussian boundary quantum effective action, derives its scalar and metric variations and retarded two-point function, and establishes the unit-normal geometric–spectral relation R_ω=4λ² on the backreacted homogeneous benchmark. A conditional equivalence theorem proves that this result is also obtained in ordinary Einstein–scalar effective field theory with the same oscillator coupling; consequently the proposed minimal completion does not yet produce a physically distinguishing prediction. The defect and homogeneous medium are explicitly kept distinct. V11 further defines a nonminimal, symmetry-compatible scalar–Gaussian-mode coupling, derives an exact stationary mean-field backreacted domain-wall benchmark by potential reconstruction, computes the retarded spectral poles, and proves a radial-coordinate- and cutoff-independent conditional spectral–geometry identity. The coupling yields a falsifiable pole shift relative to a specified minimal comparator, but conventional effective field theory with the same operator reproduces the prediction. Therefore no unique fundamental unification or experimental validation is claimed.