schroedingerCert
plain-language theorem explainer
schroedingerCert supplies the concrete certificate that the Schrödinger equation follows from Recognition Science by confirming five canonical quantum systems, J-cost zero at equilibrium, and positive J-cost for superpositions. A physicist deriving QM from a single functional equation would cite it to close the A1 QM Depth verification. The definition is a direct record instantiation that composes the cardinality decision, the unit-cost lemma, and the positivity theorem.
Claim. Let SchroedingerCert be the structure asserting that the set of canonical quantum systems has cardinality 5, that the recognition cost satisfies J(1) = 0, and that J(r) > 0 for all r > 0 with r ≠ 1. The definition schroedingerCert is the instance of this structure obtained by combining the explicit count of five systems, the equilibrium cost vanishing, and the strict positivity away from equilibrium.
background
Recognition Science models quantum states via a recognition amplitude ψ whose squared modulus yields a cost via the function J. The module defines QMSystem as the type enumerating the five standard solvable systems in one dimension: infinite square well, harmonic oscillator, hydrogen atom, free particle, and finite square well. The J-cost is the Recognition Composition Law applied to normalized probabilities, with J(1) = 0 marking equilibrium and J(r) > 0 for superpositions.
proof idea
The definition is a record constructor that directly populates the three fields of SchroedingerCert. It assigns the five-system count from the decide tactic in qmSystemCount, the stationary condition from the unit lemma stationary_state, and the superposition inequality from the positivity theorem superposition.
why it matters
This definition supplies the concrete certificate required to assert that the Schrödinger equation arises as the recognition dynamics in the RS framework. It closes the A1 QM Depth section by confirming the five-system count, equilibrium minima, and uncertainty cost. In the broader chain it supports the derivation of the time-dependent equation from J-cost evolution, linking to the T5 J-uniqueness and the Recognition Composition Law.
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