LedgerCapacityLimit
plain-language theorem explainer
LedgerCapacityLimit defines the maximum recognition bits storable on a surface of area A as the ratio A over ell0 squared in RS-native units. Researchers deriving black hole entropy from information capacity in the Recognition Science framework cite this quantity to connect horizon area to bit count. The definition is introduced as a direct ratio with no further computation or lemmas.
Claim. $N = A / ell_0^2$, where $A$ is the surface area and $ell_0$ the fundamental RS length unit (voxel size).
background
The module Black Hole Entropy and Recognition Information derives the Bekenstein-Hawking entropy from the ledger capacity limit, with the stated objective to prove that $S_{BH} = A / 4 ell_p^2$ arises from maximum recognition flux. The fundamental length ell0 is the RS-native voxel, defined as ell0 = 1 in natural units or equivalently c * tau0 where tau0^2 = hbar G / (pi c^5) from the Constants Derivation module.
proof idea
This is a one-line definition that directly computes the ratio of the supplied area A to the square of the fundamental length ell0.
why it matters
It supplies the central quantity for the downstream theorems bh_entropy_from_ledger (which equates entropy to ledger capacity) and max_recognition_flux (which characterizes the horizon by maximum flux over the 8-tick cycle). The definition fills the initial step in the module toward showing Bekenstein-Hawking entropy from recognition information, linking to the forcing chain landmarks T7 (eight-tick octave) and T8 (D=3) via normalized capacities in phi-ladder units.
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