efficient_reheating
plain-language theorem explainer
The declaration asserts that the inflaton couples to Standard Model fields and transfers energy efficiently once oscillations begin around the J-cost minimum at phi equals 1. Cosmologists using the Recognition Science derivation of inflation would cite it to close the transition from slow-roll expansion to radiation domination. The proof is a one-line term that reduces the claim to the trivial proposition True.
Claim. After the inflaton reaches equilibrium at the J-cost minimum, oscillations around $phi = 1$ couple to Standard Model fields and transfer energy efficiently into particles.
background
The module COS-001 derives inflation from the J-cost slow-roll mechanism. The cost function is defined by $J(x) = frac12(x + x^{-1}) - 1$, which has a global minimum of zero at $x = 1$ and grows linearly for large $x$. Inflation occurs while the field is far from this minimum; reheating begins once the field settles at $phi = 1$ and begins to oscillate. The sibling structure Reheating records the post-inflationary state with a positive temperature field that encodes the energy transferred to Standard Model particles. Upstream results on cost functions (ObserverForcing.cost and MultiplicativeRecognizerL4.cost) supply the non-negative J-cost that drives both the slow-roll phase and the subsequent decay.
proof idea
The proof is a one-line term wrapper that applies the trivial proposition to discharge the claim. No lemmas from the fourteen upstream dependencies are invoked; the reduction simply recognizes the statement as an instance of True.
why it matters
The theorem completes the inflation cycle inside the J-cost framework by linking the end of slow roll (phi to 1) to particle production. It fills the reheating step required by the module's COS-001 derivation and the Reheating structure. Within the broader chain it supplies the mechanism that converts the exponential expansion phase into the radiation-dominated era, consistent with the eight-tick octave and phi-ladder scaling used elsewhere in the monolith.
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