The Chiral Topological Ledger: Holographic Emergence of Dark Matter and Baryogenesis

We formulate a chiral tensor-ledger framework in which a parity-odd primordial tensor sector sources charge asymmetry through the anomalous Ward identity of the active chiral spectrum. A helicity-asymmetric tensor background, h_R ≠ h_L, produces a nonzero expectation value of the gravitational Pontryagin density, ⟨R R̃⟩. This quantity enters the mixed gravitational anomaly and can source a pre-sphaleron B−L asymmetry. Electroweak sphalerons subsequently convert this asymmetry into a baryon asymmetry according to the standard equilibrium conversion factor. For the Standard Model field content without active right-handed neutrinos, the active-spectrum coefficient is C_grav(B−L) = −3; if anomaly-canceling right-handed neutrinos are active during the relevant epoch, the gravitational B−L source cancels. The baryogenesis calculation is therefore reduced to one dynamical input: the helicity-resolved tensor history h_R,L(k, τ). Once this history is specified by a parity-violating tensor completion, the anomaly coefficient, thermal washout rate, and sphaleron conversion determine the surviving baryon yield. We derive the corresponding helicity integral required to reproduce η_B^obs, thereby converting the mechanism into a falsifiable target correlated with parity-odd CMB observables and a helicity-resolved stochastic gravitational-wave background. As a separate infrared application, we show that a late-time macroscopic tensor remnant admits an exact matching target: an auxiliary tensor dielectric with cubic norm potential V(H) = cH^(3/2) integrates out to reproduce the deep-MOND scalar functional. Together, the two branches define a claim-tiered tensor-ledger architecture: the baryogenesis branch is a falsifiable anomaly-source condition, while the infrared branch is an independent matching target for possible late-time tensor response.