qptExamples
plain-language theorem explainer
This definition supplies a static list of quantum phase transition examples including Mott insulator-metal and Quantum Hall plateau transitions. Researchers modeling criticality via information cost would reference it when linking condensed-matter phenomena to bifurcations in the J-cost landscape. The definition is a direct enumeration of strings with no computation or lemmas.
Claim. The quantum phase transition examples are the list consisting of Mott insulator-metal, Quantum Hall plateau transitions, heavy fermion systems, and superconductor-insulator.
background
The module derives phase transitions from bifurcations in the J-cost landscape, where J-cost is the non-negative cost of a recognition event given by the derived cost of a multiplicative recognizer comparator. J itself satisfies the Recognition Composition Law J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y) and is realized as (x + x^{-1})/2 - 1. Upstream structures supply the cost function via ObserverForcing.cost and MultiplicativeRecognizerL4.cost, while PhiForcingDerived.of and DAlembert.LedgerFactorization.of calibrate J on positive ratios.
proof idea
The definition is a direct enumeration that constructs the List String by literal insertion of the four example strings. No lemmas or tactics are applied; it is a static constant definition.
why it matters
The definition populates the examples section of the THERMO-006 paper proposition on phase transitions as information-theoretic bifurcations. It supplies concrete instances for the claim that topology changes in the J-cost landscape produce transitions such as Kosterlitz-Thouless or topological insulator cases, without yet feeding any downstream theorem.
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