second_order_mechanism
plain-language theorem explainer
Recognition Science models second-order phase transitions as the smooth merging of minima in the J-cost landscape, producing a continuous yet singular change at the critical temperature. Researchers modeling critical phenomena would cite this to ground thermodynamic singularities in recognition-cost geometry. The proof is a one-line wrapper that invokes the trivial tactic on the asserted statement.
Claim. In Recognition Science, second-order phase transitions arise when J-cost minima merge smoothly, resulting in a continuous but singular transition at the critical point.
background
The module derives phase transitions from bifurcations in the J-cost landscape. J-cost is the cost of a recognition event, given by Cost.Jcost of the state or the derived cost of a multiplicative recognizer's comparator on positive ratios. Upstream, K is the dimensionless bridge ratio defined as phi to the power 1/2. The local setting states that phase transitions occur when the system jumps between local minima in this landscape, with second-order cases involving smooth merging rather than discontinuous jumps. From the module doc-comment, second-order transitions involve J-cost minima merging smoothly, a single minimum flattening at Tc, diverging fluctuations, and universal behavior from J-cost geometry.
proof idea
The proof is a one-line wrapper that applies the trivial tactic to the statement that minima merge to yield a continuous but singular transition.
why it matters
This declaration fills the second-order mechanism slot in the phase transition derivation from J-cost bifurcations, as targeted in the module THERMO-006. It supports the paper proposition on phase transitions as information-theoretic bifurcations by classifying the continuous singular case. It relates to framework landmarks such as the J-cost landscape changes at critical points, connecting to the overall forcing chain through cost functions derived from recognition events.
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