Basics of a Geometry-Independent HBMB Holographic Principle: From Horizon Bits to Bulk Wavefunctions–Part I

In this work we formulate a geometry-independent holographic principle within the Holographic Bit-Mode Balance (HBMB) framework, interpreting the Bekenstein-Hawking entropy as a physical resolution bound. Our starting point is that for a horizon/screen of radius R, the bit capacity S(R)=A(R)/(4l_P^2) is not merely an information-theoretic upper limit, but directly constrains the maximal number of independent bulk eigenmodes that can be represented. Accordingly, wavefunction-like bulk field data admit a finite eigenmode synthesis: screen-encoded mode amplitudes (coefficients) reconstruct a complex field psi in a geometry-dependent eigenbasis within a chosen local domain (patch) associated with the screen. The main claim is that this "holographic Nyquist" logic is not AdS-specific. In local cosmological (dS) patches, flat-space domains, and AdS regions, the same capacity argument yields a physical cutoff, lmax(R) approx sqrt{S(R)}-1, which controls reconstruction accuracy. We provide a unified toy-model protocol for numerical reconstruction of target fields and show that the reconstruction error decreases systematically as the Bekenstein-cutoff bound is approached. Finally, we discuss the "nested horizons" picture in which local horizons (black holes, local cosmological horizons, microscopic effective horizons) are interpreted as overlapping subcodes of a universe-scale master-horizon code, rather than as mutually independent entropy budgets. We also note that an "edge-physics" intuition is compatible with the code-subspace viewpoint: screen boundary data can be regarded as operational coordinates of an edge-mode algebra, rather than a purely mathematical choice of basis.