The Information Lattice Model: Entropic Permeability, Emergent Gravity, and the Holographic Structure of the Brane–Bulk Interface

We introduce the Information Lattice Model (ILM), a theoretical framework in the braneworld tradition in which the brane–bulk system is represented as a stratified informational graph whose inter-layer link capacity is governed by a permeability function \mathrm{\Pi}\left(y\right)=1+\varepsilonexp\left(-\lambda\left|y\right|/\ell_{Pl}\right). The dimensionless parameter \varepsilon is identified with the ratio of bulk-to-brane entanglement entropy flux via the Ryu–Takayanagi formula, connecting the model to the Bekenstein–Hawking entropy bound and the AdS/CFT correspondence. This identification is presented as a conceptual proposal ahead of full formal derivation, in the tradition of framework papers from Kaluza–Klein to Verlinde’s entropic gravity. The permeability function modifies the Randall–Sundrum warp factor, introducing an additional entropic dilution of the effective gravitational coupling beyond geometric warping alone. Within this framework, the ILM suggests a unified phenomenological perspective on the hierarchy problem, the black hole information paradox, and the possible role of sub-brane entropic degrees of freedom as an effective dark matter component. The model also predicts frequency-dependent corrections to gravitational-wave propagation arising from bulk-mediated entropic coupling. The model generates two testable predictions. The primary prediction is a positive correlation between the dimensionless radiated energy excess \mathrm{\Delta A} and total merger mass M_{total} in binary black hole systems, arising from the mass dependence of the integrated horizon permeability. Under a quadratic area-law scaling, \mathrm{\Delta A} may approach \sim10-3 for M_{total}\sim{10}^6\thinsp M_\odot events accessible to LISA, while the sign and slope of the \mathrm{\Delta A}–M_{total} correlation is independently falsifiable via stacked regression analysis of the GWTC-3 catalogue; a full Bayesian treatment will be presented in future work. The secondary prediction is a non-linear deviation in quantum decoherence rates near lattice saturation, potentially testable with ion traps, superconducting qubits, and Bose–Einstein condensates.