The Constraint–Learning Equivalence Principle: A Minimal Theory of Structure, Information, and Adaptation

This work introduces the Constraint–Learning Equivalence Principle (CLEP), a unifying theoretical framework proposing that learning, evolution, and structure formation arise from adaptive constraint tuning rather than the addition of energy, information, or signal. Under CLEP, identity persists when system dynamics are bounded in repeatable ways; learning corresponds to modifications of those bounds; and information is defined operationally as constrained recurrence.

The framework reframes oscillatory dynamics by treating characteristic timescales as signatures of constraint strength, while amplitude reflects available energy. This leads to a falsifiable prediction: learning events should be preceded by measurable shifts in dominant timescales and recurrence structure. CLEP further introduces a constraint cost function, formalized as a reduction in accessible state space, allowing trade-offs between stability and adaptability to be quantified.

Observability is treated as a relational property between systems with compatible constraint architectures, inverting traditional sender–receiver models of information transfer. The principle is shown to be transposable across physical, biological, cognitive, and organizational domains, with a worked example drawn from neural oscillations and perception.

By reducing learning and adaptation to constraint refinement, CLEP offers a compact, testable minimal model for how structure persists—and fails—across complex systems. The framework is intended as a hypothesis-generating tool rather than a prescriptive theory, with explicit failure modes and empirical tests outlined.