IndisputableMonolith.Constants.BoltzmannConstant
The module defines the RS Boltzmann analog k_R as ln(φ), the fundamental cost per ledger bit replacing k_B in native thermodynamics. Bandwidth unification modules for black holes, consciousness, and recognition cite this definition when computing maintenance costs. The module supplies the core definition plus lemmas establishing positivity, bounds, and equivalence to J-bit cost.
claimThe RS Boltzmann analog is the constant \(k_R = \ln \phi\), where \(\phi\) is the golden ratio; it equals the fundamental cost per ledger bit and replaces the classical Boltzmann constant in Recognition Science thermodynamics.
background
The module belongs to the Constants domain and imports the parent Constants module, which supplies the RS time quantum (\tau_0 = 1) tick. Definition C-006 introduces (k_R = \ln \phi) as the cost per ledger bit. Sibling declarations establish that (k_R > 0), (k_R \neq 0), (k_R < 1/2), and (k_R = J)-bit cost, where J denotes the Recognition cost function.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the Boltzmann analog required by the bandwidth unification arguments. It feeds BlackHoleBandwidth (maximal recognition saturation), ConsciousnessBandwidth (holographic constraint on conscious extent), and RecognitionBandwidth (core definitions linking holographic bound, k_R cost, ILG parameters, and 8-tick cadence). It directly implements definition C-006 in the Recognition Science framework.
scope and limits
- Does not derive k_R from classical statistical mechanics.
- Does not supply a numerical conversion to SI units.
- Does not prove thermodynamic identities such as equipartition.
- Does not address fermionic or bosonic statistics.