IndisputableMonolith.Physics.BlackHoleThermodynamicsFromRS
Module packaging black-hole thermodynamics as RS-native counting statements: four classical laws and a short certificate that the thermodynamic quantity list is closed. Physicists citing the RS derivation of Hawking temperature or area-law entropy would land here. The argument is definitional enumeration plus equality lemmas (four laws = 2 squared), not a dynamical derivation.
claimThe module fixes a finite list of black-hole thermodynamic quantities and asserts that the classical black-hole laws number exactly four, equivalently $2^2$, together with a certificate object recording that count and the quantity roster in RS-native units.
background
Recognition Science works in units with $c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^5/\pi$, and a fundamental tick $\tau_0=1$ from Constants. Black-hole thermodynamics classically comprises four laws (zeroth through third), linking surface gravity to temperature, horizon area to entropy, and the area theorem to the second law.
This module sits in the Physics domain and treats those laws as a discrete roster rather than as continuum GR identities. Sibling definitions introduce a type of thermodynamic quantities, a count of that roster, a law count, and the numerical identities $\mathrm{bhLawCount}=4$ and $4=2^2$. The square-of-two identity is the only structural hint toward the eight-tick octave ($2^3$) and $D=3$ forcing chain, but the module itself does not invoke T7 or T8.
proof idea
Definition module with thin equality lemmas. Quantities and law counts are introduced as inductive or finite enumerations; bhLaws_eq_4 and bhLaws_2sq are definitional or rfl-style equalities. The certificate bundle packages those facts for downstream import. No analytic or geometric proof of the area law appears here.
why it matters in Recognition Science
Supplies the discrete skeleton that later RS physics modules can cite when claiming that black-hole thermodynamics is forced by the same counting that yields the eight-tick period and three spatial dimensions. With no downstream edges recorded yet, it is a leaf packaging layer: it makes the four-law count and the thermodynamic quantity list available as named Lean facts rather than folklore. It does not yet connect to the mass ladder, Berry threshold, or $\alpha$ band.
scope and limits
- Does not derive Hawking temperature or Bekenstein entropy from the J-cost or RCL.
- Does not prove the area theorem or any continuum GR identity.
- Does not link the four laws to T7 eight-tick or T8 dimension forcing.
- Does not fix numerical values of surface gravity or horizon area in RS units.
- Does not address evaporating or charged rotating holes beyond the bare law count.