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PathCurrentRegistrationTemplates

Abstract

A dependent signature types one real statistic of a whole path in a signed state space with a peak.

Definition 1.1 (Signed-peak path signature).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/PathCurrentRegistrationTemplates.signedPeakPathSignature

Formalization. D5/S3/ConceptDynamics/InformationEscape/PathCurrentRegistrationTemplates.signedPeakPathSignature (✓ std3).

Source. Repository-derived.

Commentary.

Parameters are an arbitrary state type X, a real sign function on X, a peak state, two real profile values, a real normalizer and a natural horizon. States are whole paths N -> X. The sole role is Unit, and its output is one real number; the anchor type is Empty. Reg/D5/S3/Estimation/TimeArrow/SinglePeakPathCurrent uses this signature with the forward-versus-reversed log-likelihood of the single-peak parity kernel as the actual readout. The definition is an operand for that source-bound registration, not a theorem or a registration proof.

References