referenceTemp
The reference Maillard onset temperature is fixed at the dimensionless value 1 in RS-native units, calibrated to 140°C at rung zero on the phi-ladder. Chemists scaling browning thresholds for sugar-amine reactions would cite this base when computing temperatures at higher rungs via multiplication by powers of phi. The definition is a direct constant assignment with no lemmas or computation.
claimLet $T_0 = 1$ be the reference Maillard onset temperature in dimensionless RS units, calibrated to 140°C at rung zero.
background
The MaillardTemperatureLadder module extends the J-cost wrapper to an explicit temperature ladder on the phi-ladder, with rung 0 anchored at the empirical Maillard onset of 140°C. Temperatures at rung k are obtained by scaling the reference by phi^k, consistent with the self-similar fixed point and eight-tick octave of the Recognition framework. Upstream results include the temperature definition from BoltzmannDistribution, which identifies temperature as the inverse of the Lagrange multiplier beta, together with multiple rung assignments that label integer levels across sectors such as fermions and ore classes.
proof idea
The definition is a direct constant assignment of the value 1, serving as the zero-rung anchor for the scaling performed in the sibling tempAtRung.
why it matters in Recognition Science
This definition supplies the base case for tempAtRung, which computes Maillard temperatures at arbitrary rungs, and for the positivity theorem tempAtRung_pos. It anchors the chemistry application of the phi-ladder, aligning with the framework's T6 self-similar fixed point and T7 eight-tick octave while providing a structural prediction for reaction thresholds. No open scaffolding questions are addressed.
scope and limits
- Does not convert the dimensionless 1 into physical units such as Kelvin or Celsius.
- Does not incorporate explicit J-cost derivatives for the Maillard reaction itself.
- Does not apply to chemical processes outside the Maillard browning ladder.
Lean usage
theorem tempAtRung_zero : tempAtRung 0 = referenceTemp := by unfold tempAtRung; rflformal statement (Lean)
34def referenceTemp : ℝ := 1
proof body
Definition body.
35
36/-- Maillard reaction temperature at φ-ladder rung `k`. -/