Ricci-Flow Closure in Quantum Measurement Units (QMU): Aether Geometry as Curvature Diffusion with Ledger Monotones

Ricci-Flow Closure in Quantum Measurement Units (QMU): Aether Geometry as Curvature Diffusion with Ledger Monotones Summary. Ricci flow provides a canonical geometric coarse-graining rule that evolves a metric by curvature diffusion while admitting entropy-like monotone functionals. This preprint embeds Ricci flow into the Aether Physics Model (APM) using a Quantum Measurement Units (QMU) normalization anchored to the quantum length $\lambda_C$ and the quantum cycle frequency $F_q$. Geometry is rendered dimensionless via $\widehat g$ (scaled by $\lambda_C$), and the flow parameter is expressed in forward QMU cycles $\tau_q$. Core proposal. The paper introduces a QMU-normalized Ricci--DeTurck flow for the dimensionless metric $\widehat g$, coupled to an APM ledger-closure defect field\[\Phi := \ln\!\left(\frac{A_u\cdot \mathrm{curl}}{{F_q}^2{\lambda_C}^2}\right),\]so that ledger closure corresponds to $\Phi\equiv 0$. Closure is treated as a constraint manifold in configuration space, and closure restoration is required operationally along admissible smoothing trajectories. Ledger-augmented Perelman diagnostic. Motivated by Perelman's entropy functionals, the paper defines an APM-augmented functional\[\mathcal{W}_{\mathrm{APM}}(\widehat g,f,\tau_q)=\int_M\left[\tau_q\left(\widehat R + \|\widehat\nabla f\|^2 + \beta\,\Phi^2\right)+ f - n\right]\,(4\pi\tau_q)^{-n/2}\,e^{-f}\,d\widehat V,\]and frames monotonicity as an evolution design constraint rather than a theorem: admissible couplings are those that admit trajectories with $\mathcal{W}_{\mathrm{APM}}$ nondecreasing and $\Phi\to 0$. The conjugate heat evolution for $f$ is extended by an added potential term $\beta\Phi^2$, matching Perelman's coupling structure while incorporating the ledger penalty as an internal variational term. QMU ``temperature-potential'' anchor. The composite\[\Theta := {F_q}^2{\lambda_C}^2\]is identified as a QMU temperature-potential unit for geometric smoothing, consistent with the heat-like character of Ricci flow and Perelman's statistical/entropy analogy. Ledger One becomes\[A_u\cdot \mathrm{curl}=\Theta,\]so Ricci smoothing is interpreted as relaxation toward a ledger-closed temperature-potential state. Implementable algorithm and falsification gate. A discretized log-scale stepper is provided (Steps A--C): (A) Ricci--DeTurck metric update, (B) multiplicative descent/projection driving $\Phi\to 0$ by updating $(A_u,\mathrm{curl})$, and (C) a monotone/closure acceptance rule:\[\mathcal{W}_{\mathrm{APM}}^{(k+1)}\ge \mathcal{W}_{\mathrm{APM}}^{(k)}\quad\text{and}\quad|\Phi^{(k+1)}|\le|\Phi^{(k)}|.\]Failure of this gate operationally rejects the chosen coupling or parameterization. A toy constant-curvature ansatz is included as a minimal closure stress-test before fully general $\widehat g$ deployments. Physics alignment and experiments. The work situates Ricci flow as geometric renormalization (nonlinear sigma-model RG) and aligns it with APM log-window operator methodology. Two laboratory-accessible proxy programs are proposed (wavefront-geometry relaxation and magneto-elastic relaxation). In these proxies, $A_u$ and $\mathrm{curl}$ are inferred via calibrated ledger proxies (surrogate observables forming a ledger chain), and the closure test is applied to the inferred pair. What is new here. A QMU-normalized Ricci--DeTurck flow formulation anchored to $(\lambda_C,F_q)$. A ledger-closure defect field $\Phi$ and an operational closure criterion. A Perelman-type functional augmented by a ledger penalty, with explicit coupling guidance and a falsifiable acceptance gate. A QMU temperature-potential interpretation $\Theta={F_q}^2{\lambda_C}^2$ tied directly to Ledger One $A_u\cdot\mathrm{curl}=\Theta$. An implementable discrete stepper (including a flowchart) and two proxy experiment programs.