ParityKernelRegistrationTemplates

Abstract

Dependent signatures type the coordinate-record law and the step-indexed path functionals of parity kernels.

Definition 1.1 (Coordinate-record signature).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/ParityKernelRegistrationTemplates.subcoordinateRecordSignature

Formalization. D5/S3/ConceptDynamics/InformationEscape/ParityKernelRegistrationTemplates.subcoordinateRecordSignature (✓ std3).

Source. Repository-derived.

Commentary.

Parameters are a dimension d, a real profile on the sign hypercube of dimension d, a set of coordinates and a natural horizon T. States are sequences of T + 1 sign vectors. The sole role is Unit with one real output; the anchor type is Empty. Reg/D5/S3/Estimation/TimeArrow/ParityKernelSubcoordinates uses it with the coordinate-record law as the actual readout. The definition is an operand for that source-bound registration, not a theorem or a registration proof.

Definition 1.2 (Profile-pair step signature).

Lean statement: D5/S3/ConceptDynamics/InformationEscape/ParityKernelRegistrationTemplates.profilePairStepSignature

Formalization. D5/S3/ConceptDynamics/InformationEscape/ParityKernelRegistrationTemplates.profilePairStepSignature (✓ std3).

Source. Repository-derived.

Commentary.

Parameters are a dimension d and two real profiles on the sign hypercube. States are path lengths s. The sole role is Unit with one real output; the anchor type is Empty. Reg/D5/S3/Estimation/TimeArrow/ParityPathLikelihoodProducts uses it with the uniform-reference inner products of path likelihoods as actual readouts. The definition is an operand for those source-bound registrations, not a theorem or a registration proof.

References

• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/ParityKernelRegistrationTemplates.profilePairStepSignature
• Truth anchor: D5/S3/ConceptDynamics/InformationEscape/ParityKernelRegistrationTemplates.subcoordinateRecordSignature
• Dependency: D5/S3/ConceptDynamics/InformationEscape/DependentFamily