holographic_bound
plain-language theorem explainer
The holographic bound states that entropy S of any physical system satisfies S ≤ A/(4 l_P²) for boundary area A > 0. Quantum gravity and black hole thermodynamics researchers cite this when applying the area law for information content. The proof is a one-line term that invokes trivial to affirm the statement.
Claim. For any positive real number $A$, the entropy $S$ of a physical system in a region with boundary area $A$ satisfies $S ≤ A/(4 l_P^2)$.
background
The module sets the local setting as QG-006, deriving the holographic bound from Recognition Science's ledger structure. The core insight is that the ledger is fundamentally two-dimensional, with volume emerging from boundary data and information limited to one bit per Planck area. Entropy is defined upstream as proportional to total defect of a configuration, reaching zero only in the minimum entropy state.
proof idea
The proof is a term-mode one-liner that applies the trivial tactic to discharge the goal directly.
why it matters
This declaration occupies the QG-006 position in the Recognition Science framework, linking the holographic principle to ledger projection as described in the module doc for PRD - Holography from ledger structure. It relates to D = 3 spatial dimensions by emphasizing surface encoding of information over volume. No parent theorems appear in the used-by graph, leaving integration with the forcing chain and phi-ladder open.
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