IndisputableMonolith.Papers.GCIC.BekensteinFromLedger
The module derives Bekenstein-type bounds from the RS ledger by forcing D=3 via T8 and defining surface-scaling quantities plus RS constants. Holographic information theorists cite it when linking ledger cost to area-law entropy. It consists of targeted definitions and equalities on top of the imported Cost and Constants modules.
claim$D=3$ (T8), boundary_dimension, boundary_exponent, cube_volume_surface, cube_sv_ratio, cube_isoperimetric, $G_{rs}= rac{\phi^5}{\pi}$, $\hbar_{rs}=\\,\phi^{-5}$, $G_{rs}\hbar_{rs}=1$, info_per_voxel.
background
Recognition Science starts from the single functional equation and extracts all physics via the T0-T8 forcing chain; T8 fixes spatial dimensions at three. The module supplies the ledger-specific objects needed for an area-law bound: boundary_dimension and boundary_exponent control surface scaling, while the cube_* family encodes the isoperimetric relation in three dimensions. Upstream, Constants fixes the RS time quantum $\tau_0=1$ tick and Cost supplies the J-cost functional that underlies all recognition accounting.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
Supplies the dimensional and constant scaffolding for the downstream BrainHolography module, which concludes that every local ledger region encodes global state and that accessible information therefore scales with surface area rather than volume. It directly implements the T8 step of the forcing chain inside the GCIC paper derivation.
scope and limits
- Does not derive the Bekenstein bound without the ledger cost structure.
- Does not treat time as a spatial dimension or consider D≠3.
- Does not compute numerical spectra beyond the supplied RS constants.
- Does not address non-cubic or fractal boundary geometries.
used by (1)
depends on (2)
declarations in this module (17)
-
def
D -
theorem
boundary_dimension -
theorem
boundary_exponent -
theorem
cube_volume_surface -
theorem
cube_sv_ratio -
theorem
cube_isoperimetric -
def
G_rs -
def
hbar_rs -
theorem
G_hbar_product_eq_one -
theorem
G_rs_pos -
theorem
hbar_rs_pos -
def
info_per_voxel -
theorem
bekenstein_hawking_from_rs -
theorem
bekenstein_positive -
theorem
info_scales_subvolume -
theorem
sv_ratio_decreasing -
theorem
area_not_volume_certificate