UOR Carry Algebra

IRI: https://uor.foundation/carry/
Prefix: carry:
Space: kernel
Comment: Carry chain algebra: generate/propagate/kill event classification, carry profiles, encoding configurations, and encoding quality metrics for d_Δ optimization.

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This is a kernel-space namespace in the Define stage of the PRISM pipeline. It provides the immutable algebraic substrate — ring structure, schema vocabulary, and operation algebra.

Learn more: Pipeline Overview

Class hierarchy

Imports

https://uor.foundation/op/
https://uor.foundation/observable/
https://uor.foundation/partition/

Classes

Name	Subclass Of	Disjoint With	Comment
`CarryChain`	`Thing`		The Boolean function chain c_{k+1} = or(and(x_k, y_k), and(xor(x_k, y_k), c_k)). The carry chain is the algebraic mechanism behind the incompatibility metric d_Δ.
`CarryEvent`	`Thing`		A single carry event at site k. Three kinds: Generate (and(x_k, y_k) = 1), Propagate (xor(x_k, y_k) = 1 and c_k = 1), Kill (neither generate nor propagate).
`CarryProfile`	`Thing`		The complete carry pattern for an addition x + y. Aggregates carry events across all sites into counts and position masks.
`EncodingConfiguration`	`Thing`		A mapping from a finite symbol set S to Z/(2^k)Z where 2^k ≥ \|S\|. Determines how domain values are represented as ring elements.
`EncodingQuality`	`Thing`		The d_Δ quality metric for an encoding over observed data. Measures how well an encoding minimizes carry-induced metric incompatibility.

Properties

Name	Kind	Functional	Domain	Range	Comment
`chainLength`	Datatype	true	`CarryChain`	`nonNegativeInteger`	The number of sites in this carry chain.
`generateMask`	Datatype	true	`CarryChain`	`nonNegativeInteger`	Bit mask of site positions where carry is generated: and(x_k, y_k) = 1.
`propagateMask`	Datatype	true	`CarryChain`	`nonNegativeInteger`	Bit mask of site positions where carry propagates: xor(x_k, y_k) = 1.
`killMask`	Datatype	true	`CarryChain`	`nonNegativeInteger`	Bit mask of site positions where carry is killed: neither generated nor propagated.
`eventKind`	Datatype	true	`CarryEvent`	`nonNegativeInteger`	The kind of carry event: Generate, Propagate, or Kill.
`sitePosition`	Datatype	true	`CarryEvent`	`nonNegativeInteger`	The site index k at which this carry event occurs.
`carryCount`	Datatype	true	`CarryProfile`	`nonNegativeInteger`	The total number of carry events in this profile.
`maxPropagationLength`	Datatype	true	`CarryProfile`	`nonNegativeInteger`	The longest consecutive propagation run in this profile.
`profileChain`	Object	true	`CarryProfile`	`CarryChain`	The carry chain that this profile summarizes.
`symbolSetSize`	Datatype	true	`EncodingConfiguration`	`positiveInteger`	The cardinality of the symbol set S being encoded.
`quantizationBits`	Datatype	true	`EncodingConfiguration`	`positiveInteger`	The number of bits k used for encoding (2^k ≥ \|S\|).
`encodingMap`	Object	true	`EncodingConfiguration`	`TermExpression`	String representation of the mapping from symbols to ring elements.
`meanDelta`	Datatype	true	`EncodingQuality`	`decimal`	The mean d_Δ over observed pairs for this encoding.
`discriminationRatio`	Datatype	true	`EncodingQuality`	`decimal`	The ratio of distinguishable pairs to total pairs under this encoding.
`isOptimalEncoding`	Datatype	true	`EncodingQuality`	`boolean`	Whether this encoding minimizes Σ d_Δ over observed pairs.