Cosmology Inflation Reheat Temperature Inflation Reheat Cert

The reheating certificate

Inflation is the brief, exponential expansion of the universe in its first instant, and reheating is the moment when the energy driving that expansion decays into the hot soup of particles that becomes ordinary matter. The Recognition Science framework's declaration InflationReheatCert certifies, in its machine-checked library of formal theorems, that the reheating temperature in the framework's native units is exactly φ^(−39/2), roughly 10^(−12). Here φ is the golden ratio, about 1.618, and the exponent places the temperature on the framework's ladder of scales between the 19th and 20th rungs.

The number comes from a chain of prior results. The framework derives, from its core cost function, an inflationary epoch with N_e = 44 e-folds, meaning the universe expands by a factor of e^44 during inflation. The same cost function yields the inflaton potential, the energy field driving the expansion. Combining these gives the reheating temperature formula T_reh = φ^(5/2) · φ^(−22) = φ^(−39/2), a value that emerges from the framework's constants rather than being fitted to observation.

The structural claim is the interesting one. The framework's ladder of scales places the reheating temperature just below the rung it associates with abiogenesis, the origin of life, at φ^19. This proximity is flagged as a structural coincidence whose implications remain open. The declaration itself establishes only the temperature value and its position on the ladder; it does not assert a causal link between reheating and life's origin.

What the declaration does not claim is equally precise. It does not claim that this temperature matches any measured cosmological value; it is a prediction from the framework's internal logic, not an empirical result. It does not claim that reheating itself is understood; the framework derives a temperature scale, not the full particle physics of decay. And it does not claim that the proximity to the abiogenesis rung is anything more than a coincidence awaiting interpretation.

structure InflationReheatCert where base : CanonicalCert

structure InflationReheatCert where base : CanonicalCert

What this page does not claim

The reheating temperature is not claimed to match any measured cosmological value. The framework does not claim to model the particle decay process of reheating itself. The proximity of the reheating temperature to the abiogenesis rung is not claimed to be causal.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Cosmology/InflationReheatTemperature.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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