Slow Passage and Prepared Hysteresis in Adaptive Spectral Carriers
A slow sweep delays switching past the static fold by a preparation-dependent amount. The prepared cycle has a nonzero geometric loop limit, while physical maintenance work grows as the sweep slows.
The operator and dynamical results use the forms, metrics, inputs and readouts stated in each chapter. Numerical checks test those realizations. Recurrence across readouts does not identify a single microscopic mechanism.
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The argument in full
Follow the chapters in order or enter at a particular question. Definitions, mathematics, proofs, constructions and substantive appendices belong to this reading edition.
A Slow Sweep Passes the Stationary Fold
The complete reciprocal source, uninterrupted triangular input and bounded-input energy estimates.
Read chapter →Complete Folds and the Mixed Critical Coordinate
The stationary count, full saddle-node coefficients and a passing-trajectory estimate in the fixed-fold chart.
Read chapter →Preparation Selects the Airy Delay
The two-thirds-power law, its proof by matching and exit bounds, and the difference between local departure and complete arrival.
Read chapter →From Local Exit to a Complete Hysteresis Return
Strict loss gives the outgoing connection; stable tracking gives the prepared return and separates geometric area from physical work.
Read chapter →Four complete cycles test delay, capture and work
Compare event-localized switching with unfit Airy laws, test preparation controls, and separate the geometric loop from the energy ledger.
Read chapter →What the Prepared Return Proves
The limits of the hysteresis result and the complete finite-preparation residual audit.
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