MaillardTemperatureCert
plain-language theorem explainer
The MaillardTemperatureCert structure records that the temperature sequence defined by reference temperature times phi to the power k satisfies positivity for every natural number k, the recurrence multiplying by phi at each step, strict increase, and adjacent ratios exactly equal to phi. A chemist or Recognition Science modeler would cite the certificate to validate the predicted Maillard temperature ladder with 140°C at rung zero. The definition is a direct record packaging four lemmas already established for the geometric sequence.
Claim. A Maillard temperature certificate is a record asserting that the sequence $T(k) := T_0 phi^k$ for $k in mathbb{N}$ satisfies $T(k) > 0$, $T(k+1) = phi T(k)$, $T(k) < T(k+1)$, and $T(k+1)/T(k) = phi$ for every $k$, where $T_0$ is the reference temperature at rung zero.
background
The module develops the Maillard reaction temperature on the phi-ladder. The function tempAtRung assigns to each natural-number rung k the value referenceTemp multiplied by phi to the power k. This implements the self-similar scaling forced by J-uniqueness in the forcing chain. The upstream temperature definition from BoltzmannDistribution identifies temperature as the inverse of the Lagrange multiplier beta, supplying the thermodynamic reading for the ladder steps.
proof idea
This declaration is a structure definition whose four fields are universal statements over the naturals. Each field is supplied in the downstream construction by direct appeal to the lemmas tempAtRung_pos, tempAtRung_succ_ratio, tempAtRung_strictly_increasing, and temp_adjacent_ratio. The definition requires no further proof steps beyond the record construction.
why it matters
The certificate supplies the type for the downstream maillardTemperatureCert that instantiates the structure. It completes the explicit temperature-rung ladder in the Chemistry module, extending the Maillard wrapper that applies the canonical band to J-cost. Within the Recognition framework this realizes the phi-ladder scaling for chemical reaction thresholds, predicting Maillard onset, peak, and char boundaries at successive powers of phi. It touches the open question of empirical calibration of the reference temperature against specific sugar-amine pairs.
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