vacuum_jcost_zero
plain-language theorem explainer
Recognition vacuum is the configuration at which the J-cost function vanishes. String theorists working inside the Recognition Science model cite this equality to fix the zero-cost point at unit scale. The argument is an immediate invocation of the J_one lemma.
Claim. $J(1) = 0$, where $J(x) = (x + x^{-1})/2 - 1$ is the recognition cost function.
background
The J-cost function measures recognition penalty on a scale factor and is defined by $J(x) = (x + x^{-1})/2 - 1$. Upstream results establish that $J(x) > 0$ for $x > 0$, $x ≠ 1$, with equality only at the unit point, via the AM-GM inequality. The module StringTheoryFromJCost applies this cost to the moduli space of string vacua and identifies the recognition vacuum with the configuration that achieves global minimum J-cost of zero at scale factor $r = 1$.
proof idea
The declaration is a one-line wrapper that applies the J_one lemma.
why it matters
It supplies the vacuum_zero field inside the stringTheoryCert definition, which certifies the string theory landscape via J-cost selection. This step instantiates the T5 J-uniqueness property at the vacuum point and confirms that the recognition ledger selects the $r = 1$ configuration as the zero-cost state. The sibling stringTheoryCount then enumerates the five canonical superstring theories plus M-theory.
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