black_hole_maximal
plain-language theorem explainer
Black holes saturate the maximum entropy allowed by their boundary area under the Recognition Science ledger projection. Quantum gravity researchers would cite this when invoking the holographic principle or Bekenstein bound. The equality follows immediately by reflexivity from the shared definition of black hole entropy and maximal information.
Claim. For any positive real number $A$, the black hole entropy $S_{BH}(A)$ equals the maximal information content $I_{max}(A)$.
background
The module derives the holographic bound from ledger projection: ledger entries are fundamentally two-dimensional surfaces, volume is reconstructed from boundary data, and information is limited to one bit per Planck area. Entropy of a configuration equals its total defect, so zero defect yields minimum entropy. The active edge count per tick is fixed at $A=1$, enforcing the phi-power balance at $D=3$ spatial dimensions.
proof idea
The proof is a one-line reflexivity that equates the two sides by their common definition.
why it matters
This result shows black holes are maximally entropic objects, saturating the bound that emerges from the two-dimensional ledger structure. It completes the QG-006 target stated in the module documentation for the paper on holography from ledger structure. It aligns with the forcing chain landmarks of eight-tick octave and $D=3$.
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