ssbMechanism
plain-language theorem explainer
In Recognition Science spontaneous symmetry breaking is the selection of one among equivalent J-cost minima, with the choice initially random but subsequently frozen. This definition supplies the descriptive anchor for phase-transition mechanisms in the thermodynamics module. The declaration is a direct string assignment with no computational steps or lemmas applied.
Claim. Spontaneous symmetry breaking is the process in which a system falls into one of several equivalent J-cost minima, where the J-cost of a recognition event is the value of the derived cost function $J(x) = (x + x^{-1})/2 - 1$.
background
The module derives phase transitions from bifurcations in the J-cost landscape, where multiple local minima appear or merge as parameters vary. J-cost itself is defined as the cost of a recognition event via the upstream ObserverForcing.cost, which returns Cost.Jcost e.state, and equivalently via MultiplicativeRecognizerL4.cost as the derivedCost of a comparator on positive ratios. The local setting is the J-cost landscape whose minima correspond to distinct thermodynamic phases, with the upstream LedgerFactorization.of supplying the underlying structure on positive reals under multiplication.
proof idea
One-line definition that directly assigns the string literal describing selection among equivalent J-cost minima.
why it matters
The definition supplies the verbal core for spontaneous symmetry breaking inside the J-cost bifurcation account of phase transitions. It sits inside the THERMO-006 development that treats first-order and second-order transitions as jumps or mergers between minima of the same landscape. No downstream theorems are recorded, leaving the definition as a descriptive interface rather than a proved lemma.
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