The Exponential Fitted to Rates: Arrhenius's Rate Law, Priced

In 1889 Svante Arrhenius gave chemical kinetics its working law: the rate constant of a reaction moves with temperature as k = A exp(−Ea/RT). I credit that paper at full strength: before it, the steep temperature dependence of reaction rates was a scattered empirical fact, and Arrhenius gave it one portable two-parameter form that organises rates across chemistry to this day. The activation energy the form introduced became the standard measure of a reaction's temperature sensitivity, the Arrhenius plot became the field's everyday extraction device, and the exponential factor itself survives inside both successor mechanisms, collision theory and transition-state theory, at their own addresses. Nothing in this paper falsifies the formula or disputes a single rate it organises. What I price is the standing of the form and its pair in 1889. The exponential was imported, not derived: van 't Hoff's relation governs how an equilibrium constant moves with temperature, and the scholarly record states the transfer plainly — that relation suggested such a formula for the rates of both forward and reverse reactions. The "active molecule" picture Arrhenius supplied is an interpretation of the form, not a derivation of it. And both parameters — the prefactor A and the activation energy Ea — are fitted per reaction from the very rates the formula then organises. My bench prices what that intake carries, on declared inputs only. From two declared rate inputs, T1 = 300 K with k1 = 1.000000 and T2 = 310 K with k2 = 2.000000, in declared arbitrary units, the pair extracts exactly: Ea = 53,597.260791 J/mol and A = 2,147,483,647.999903, which is 2^31 in closed form on these inputs — with residuals of exactly zero at 0 degrees of freedom, exact by construction, not by test. Spent through the form, the same extracted Ea returns a rate ratio per 10 K of 2.211952 at 280 K and 1.481515 at 400 K, against the doubling rule of thumb's flat 2: the rule is a local accident of (Ea, T), not a return of the form. And the pair is fragile in exact proportion to its determinacy: the sensitivity is dEa/d ln k2 = 77,324.502349 J/mol, so a single input rate moving +10 per cent reprices Ea by +13.750352 per cent and the prefactor A by a factor of 19.194342. Grade for this census entry, printed at full size: **REASON FOUND / STILL TURNING** — explicitly not a kill and not a falsification. The program headline stands unmoved: **vacuum catastrophe NOT SOLVED / PARTIAL, producing-count 0.**