bhLaws_eq_4
plain-language theorem explainer
The equality asserts that black hole thermodynamics in Recognition Science comprises exactly four laws, matching the standard thermodynamic count. Researchers deriving entropy and temperature from the phi-ladder and J-cost functional equation would cite this count when confirming the thermodynamic analogy holds in strong-field regimes. The proof is a direct reflexivity step on the upstream definition that fixes the law count at the numeral 4.
Claim. The number of black hole thermodynamic laws equals four, written $4 = 2^2 = 2^{(D-1)}$ where $D$ denotes the configuration dimension for the five canonical quantities (temperature, entropy, mass, angular momentum, charge).
background
The module derives black hole thermodynamics from the Recognition Science functional equation, with entropy given by $S = A/(4G)$ and $G = phi^5/pi$ in RS-native units, yielding $S = A pi/(4 phi^5)$ per unit area. Five canonical quantities are identified with configDim $D=5$, while the four laws are required to satisfy the same counting relation $4=2^2=2^{(D-1)}$ that appears in ordinary thermodynamics. The upstream definition bhLawCount simply sets this count to the natural number 4.
proof idea
The proof is a one-line wrapper that applies reflexivity directly to the definition of the law count.
why it matters
This equality populates the four_laws field inside the bHThermoCert certification structure, which also records the five quantities and the $2^2$ relation. It completes the A4 strong-field depth step in the module, anchoring the black-hole case to the broader forcing chain (T0-T8) and the Recognition Composition Law while keeping the law count independent of the spatial dimension $D=3$. The module reports zero sorrys and zero axioms.
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