IndisputableMonolith.Chemistry.MaillardTemperatureLadder
This module defines the Maillard temperature ladder in Recognition Science native units. It sets the reference temperature to the dimensionless value 1 calibrated to 140°C and supplies the temperature at each rung on the phi-ladder together with lemmas for positivity, strict increase, and adjacent ratios. Researchers applying the RS framework to chemical onset thresholds would cite these constructions. The module is purely definitional.
claimReference Maillard onset temperature $T_0 = 1$ (RS-native dimensionless, calibrated to 140°C). Temperature at rung $r$ is given by $T(r)$, satisfying $T(r) > 0$, $T(r+1)/T(r)$ constant, and $T$ strictly increasing.
background
The module sits in the chemistry domain and imports Constants, which defines the fundamental RS time quantum as τ₀ = 1 tick. It introduces the reference Maillard onset temperature as the dimensionless value 1, calibrated to the physical temperature of 140°C. The module then defines tempAtRung and establishes lemmas such as tempAtRung_pos, tempAtRung_succ_ratio, tempAtRung_strictly_increasing, and temp_adjacent_ratio to characterize the ladder.
proof idea
This is a definition module, no proofs. The module consists of a sequence of definitions for the reference temperature and rung-dependent temperatures, followed by theorems that prove basic properties of these functions.
why it matters in Recognition Science
This module feeds MaillardTemperatureCert and maillardTemperatureCert. It applies the phi-ladder (from T5 J-uniqueness and T6 phi fixed point in the forcing chain) to temperature scales for chemical processes, providing a calibrated link between RS-native units and experimental Maillard reaction temperatures.
scope and limits
- Does not derive the reference temperature from fundamental RS equations.
- Does not include specific chemical species or reaction pathways.
- Does not extend to non-Maillard chemical reactions or other temperature scales.