IndisputableMonolith.Constants.BoltzmannConstant
This module defines the RS Boltzmann analog k_R as ln(φ), the fundamental cost per ledger bit that replaces k_B in RS-native thermodynamics. Workers on holographic bounds, black-hole saturation, or consciousness bandwidth cite it when converting recognition events into energy scales. The module supplies the core definition plus supporting lemmas on positivity, bounds, and equivalence to J-bit cost.
claim$k_R := \ln(\phi)$, the recognition cost per ledger bit in RS-native units, with $\phi$ the golden-ratio fixed point.
background
The module lives in the Constants domain and imports the base Constants module whose sole content is the RS time quantum $\tau_0 = 1$ tick. It introduces the ledger-bit cost that appears in every subsequent bandwidth calculation. The definition is labeled C-006 and is stated directly as $k_R = \ln(\phi)$.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The definition supplies the per-bit recognition cost required by the holographic arguments in RecognitionBandwidth, BlackHoleBandwidth, and ConsciousnessBandwidth. It implements the ledger cost that converts the eight-tick octave and phi-ladder into thermodynamic statements.
scope and limits
- Does not derive numerical agreement with classical $k_B$.
- Does not prove uniqueness of the cost function beyond the supplied definition.
- Does not address temperature scales outside unit-$T$ thermal energy.