module module high

`IndisputableMonolith.Papers.GCIC.BekensteinFromLedger`

The module assembles definitions deriving the Bekenstein bound from the RS ledger once D equals 3. Cosmologists and quantum gravity researchers cite it to connect Recognition Science constants to surface-scaling entropy limits. It proceeds via boundary exponents, cube isoperimetric ratios, and the equality G hbar equals one in RS units.

claimWith $D=3$ forced by the RS chain, the Bekenstein bound takes the form $S_A = A/4$ in units where $G_{rs} hbar_{rs}=1$, using boundary dimension $d=D-1=2$ and cube surface-to-volume ratios.

background

Recognition Science reaches T8 where three spatial dimensions are forced. The Cost module supplies the J-cost function satisfying the Recognition Composition Law. The Constants module sets the RS-native time quantum tau_0 to one tick along with G_rs = phi^5 / pi and hbar_rs = phi^{-5}. This module defines boundary_dimension as D minus one, boundary_exponent, cube_volume_surface, cube_sv_ratio, cube_isoperimetric, and the product G_hbar_product_eq_one to prepare the ledger-based entropy bound.

proof idea

This is a definition module, no proofs. It structures the argument through sequential definitions of geometric ratios, boundary scaling, and constant equalities that support the Bekenstein derivation.

why it matters in Recognition Science

The module supplies the ledger derivation of the Bekenstein bound imported by BrainHolography, which concludes that brain information access scales with surface area. It directly implements the T8 step (D equals 3) in the GCIC chain and closes the link from RS constants to holographic scaling.

scope and limits

Does not derive the bound for non-cubic geometries.
Does not include quantum corrections or loop effects.
Does not compute explicit numerical entropy values.
Does not address time-dependent ledger evolution.

used by (1)

From the project-wide theorem graph. These declarations reference this one in their body.

IndisputableMonolith.Papers.GCIC.BrainHolography module_import

depends on (2)

Lean names referenced from this declaration's body.

IndisputableMonolith.Constants module_import
IndisputableMonolith.Cost module_import

declarations in this module (17)

def D L42
theorem boundary_dimension L45
theorem boundary_exponent L49
theorem cube_volume_surface L53
theorem cube_sv_ratio L61
theorem cube_isoperimetric L67
def G_rs L79
def hbar_rs L82
theorem G_hbar_product_eq_one L86
theorem G_rs_pos L93
theorem hbar_rs_pos L98
def info_per_voxel L105
theorem bekenstein_hawking_from_rs L114
theorem bekenstein_positive L121
theorem info_scales_subvolume L135
theorem sv_ratio_decreasing L145
theorem area_not_volume_certificate L159