Horizon Thermodynamics as a Dark-Sector Regulator: Addressing the H₀ and S₈ Tensions with a Derived Coupling

In the context of holographic cosmology, this paper identifies an H0-independent kinematic relation in spatially flat matter+Λ cosmology. The rate at which vacuum energy is swept into the apparent horizon is ṀΛ = (9/4) ΩΛ(1−ΩΛ) c³/G. For concordance values ΩΛ≈0.68, this lies within approximately 2% of the Schwarzschild/Misner–Sharp marginal-surface capacity benchmark c³/(2G). The equality condition has exact roots ΩΛ=1/3 and 2/3. The lower root, equivalently Ωm=2/3, is the familiar onset of cosmic acceleration at q=0 and z≈0.63; the upper root, equivalently Ωm=1/3, is a near-present crossing at q=−1/2 and z≈0.02. The roots therefore delimit a finite super-capacity interval q∈(−1/2,0) that spans nearly the full observed acceleration history to date, without implying that accelerated expansion ends at the upper crossing. Equivalently, S ≡ ṀΛ/[c³/(2G)] = (9/2)ΩmΩΛ = |dq/d ln a|. The continuously processed branch of the horizon flux generates a vacuum-to-cold-dark-matter interaction, Q = β Ieff S Hρcrit, with Ieff=(1−q)/2=1−(3/4)Ωm. The interaction is continuous rather than hard-gated: it is strongly suppressed during radiation and matter domination but is not switched on only inside the super-capacity window. It slows the dilution of matter and moves the observed trajectory toward the distinguished surface Ωm=1/3, q=−1/2. In the optional bound-enforcing future completion this surface is the stable asymptotic attractor; the minimal unregulated continuation instead approaches a de Sitter-like future. When S>1, the horizon is assumed to process the incoming flux at its derived capacity while the fractional excess Δ(S)=Θ(S−1)(1−1/S) is accumulated once per geometric horizon-processing cycle, dXH=Δ d ln a. The operational H0 extension separates three graded ingredients: capacity overflow; shift-protected storage of the accumulated exposure; and a common-gate temporal+ruler endpoint readout. Equal unit endpoint weights under one physical gate fix the gain ratio ηT/ηR=1 independently of the common amplitude. The baseline fixes the remaining common matching gcom=1 in advance, giving ηT=ηR=1 and Amap=2. Thus the model has zero additional continuously fitted parameters, while retaining explicitly graded structural premises and one fixed common-gate matching. Within this protected-memory/common-gate realization and with the local-ladder likelihood included, the zero-exposure limit is disfavoured at more than 4σ; non-ladder data alone do not establish the recipient channel. The preferred realization is operational rather than a homogeneous modification of the bulk metric. The memory is read locally by temporal and ruler calibration registers associated with an irreducible physical comparator. A common photometric zero-point shift cancels between the standardized supernova magnitude and Hubble-flow intercept, so the temporal register is necessarily non-photometric. Universal source-luminosity changes and common detector gains likewise calibrate out. The convention-independent observable is nonclosure of a redundant calibration loop. The specific homogeneous reservoir and bulk-metric realizations implemented in the analysis are disfavoured by their BAO and supernova-shape response, consistently with the separate metric-exclusion argument. The coupling strength is derived from the quantum-information capacity of the horizon. Bekenstein–Hawking pixelation supplies N=A/(4ℓP²) gravitational channels, and Pendry-limited throughput of the two transverse gravitational polarizations gives an aggregate quantum throughput c⁵/(24G). Normalizing this to the Misner–Sharp capacity scale c⁵/(2G) fixes β = 1/12 ≈ 0.0833. The numerical identity 1/12=(1/3)(1/4), involving the Nariai compactness margin and the Bekenstein–Hawking coarse-graining factor, is recorded as a suggestive observation rather than a second derivation. A conformally coupled quintessence realization with exponential-potential slope λ=√(9/2)≈2.12 provides a candidate field-theory embedding compatible with commonly discussed Swampland slope criteria. MCMC analysis using Planck 2018 TT, TE, EE and lensing, DESI DR2 BAO, Pantheon+, DES Y3, and the 2025 JWST+HST SH0ES result yields S8 = 0.775 ± 0.006, consistent with DES Y3 and the fiducial HSC-Y3 cosmic-shear result. The floated coupling diagnostic gives β=0.102±0.043, 0.43σ from 1/12. Its posterior mean lies 2.4 marginalized posterior standard deviations above zero; because zero is the boundary of the adopted nonnegative prior, this is reported as an amplitude diagnostic rather than a boundary-corrected detection significance. The hard-gate exposure has the exact flat matter+Λ closed form XΛhard = (10/27) ln 2 − 2/9 = 0.03449896, independent of H0, Ωm, and all other cosmological parameters within that benchmark. Integrating the interacting background gives X0≈0.0359. With one read by each register, H0,ladder/H0,phys = exp(2X0), which yields H0,ladder=73.58±0.25 km s⁻¹ Mpc⁻¹, 0.09σ from the 2025 SH0ES value 73.49±0.93. The sampled early-time normalization is 67.62±0.23 km s⁻¹ Mpc⁻¹, while the physical z=0 expansion rate is 68.48±0.24 km s⁻¹ Mpc⁻¹. In the native ladder coordinates the predicted shifts are ΔMB = 0.07796 mag, ΔaB = 0.01559, with the normalization-independent common-gate relation ΔMB=5ΔaB. With Amap floated, the chain returns 1.95±0.36, or gcom=0.975±0.18; this is an amplitude-consistency diagnostic because the local-ladder likelihood primarily constrains AmapX0. A minimized Amap=1 fit is disfavoured by Δχ²=4.7 relative to the two-register baseline. The no-SH0ES result is interpreted as a prior-blind posterior push-forward: it shows that the mapped value is not pulled into place by a local H0 prior, but it does not independently validate the endpoint operator or common-gate matching. Using the final proper minima, the complete model achieves Δχ²=−30.0 relative to ΛCDM, with ΔAIC=ΔBIC=−30.0. The likelihood gain decomposes, up to rounding, as SH0ES −20.6, CMB −6.4, supernovae −2.5, BAO −0.9, and DES +0.5. A held-out-DES test gives an additional robustness check: fitting without DES, ΛCDM predicts the unseen DES S8 at 1.55σ, whereas the holographic model predicts it within 0.36σ, S8=0.782±0.008, while retaining H0,ladder=73.40±0.29 km s⁻¹ Mpc⁻¹. The background expansion remains nearly degenerate with ΛCDM, with CPL surrogate (w0,wa)≈(−0.995,−0.023). The observational distinction therefore lies mainly in perturbation growth and calibration transport rather than a strongly modified distance–redshift relation. A direct CLASS transfer-function calculation, with the interaction source active in both synchronous and Newtonian perturbation branches, gives a mild suppression of the linear velocity-defined RSD combination fθσ8. Using the production filter F(k)=[(k/keq)²]/[1+(k/keq)²], keq=0.073 ωcb Mpc⁻¹, and an unweighted diagnostic mean over k=0.02, 0.05, 0.10, and 0.20 h Mpc⁻¹, the holographic-to-ΛCDM suppression is 1.92% at z=0.10, 1.51% at z=0.30, 1.16% at z=0.50, 0.87% at z=0.70, 0.58% at z=1.00, 0.31% at z=1.50, and 0.18% at z=2.00. The scale spread decreases from 1.8% at z=0.1 to approximately 0.1% by z=2. These fixed-parameter transfer-function values supersede both the earlier f=Ωm^0.55 proxy and the Newtonian-gauge negative-control run in which the interaction source was absent. The density-defined growth rate is much more strongly diluted because smooth matter injection enters the continuity equation while the CDM-rest-frame Euler equation remains geodesic. At k=0.10 h Mpc⁻¹ and z=0.1, fδ=0.4422 and fθ=0.6016, so fθ−fδ=0.1594 and 1−fδ/fθ=0.265. The implemented filtered identity closes to |R|≤8.15×10⁻4 over the full validation grid and |R|≤5×10⁻4 for k≥0.05 h Mpc⁻¹, with a ΛCDM control below 1.7×10⁻4. The distinctive perturbation-level prediction is therefore a large density–velocity growth inconsistency, not a large direct suppression of peculiar velocities or a baryon–CDM velocity slip. Further falsifiers include the native relation ΔMB=5ΔaB, calibration-loop nonclosure at pre-registered one-unit and two-unit amplitudes of 0.07796 and 0.15591 mag, the mild scale dependence of the RSD response, and the future behavior of the optional bound-enforcing completion. Register weights for standard sirens, cosmic chronometers, time-delay cosmography, and megamasers must be derived from their estimator chains rather than assigned by method name. Sub-2% standard-siren measurements can distinguish neutral, one-endpoint, and full-gate assignments; in the minimal neutral-siren completion, a result near 73.6 km s⁻¹ Mpc⁻¹ would falsify that topology. Companion papers:Paper II: doi:10.5281/zenodo.21158741Paper III: doi:10.5281/zenodo.21158711 The Zenodo record includes the manuscript, modified CLASS implementation, Cobaya configurations, custom likelihoods, converged chains, minimization outputs, patched perturbation source, per-k RSD validation table, post-processing scripts, and figure-generation tools required to reproduce the reported results.