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.

Imports

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

Classes

Name	IRI	Subclass Of	Disjoint With	Comment
CarryChain	`https://uor.foundation/carry/CarryChain`	`http://www.w3.org/2002/07/owl#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	`https://uor.foundation/carry/CarryEvent`	`http://www.w3.org/2002/07/owl#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	`https://uor.foundation/carry/CarryProfile`	`http://www.w3.org/2002/07/owl#Thing`		The complete carry pattern for an addition x + y. Aggregates carry events across all sites into counts and position masks.
EncodingConfiguration	`https://uor.foundation/carry/EncodingConfiguration`	`http://www.w3.org/2002/07/owl#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	`https://uor.foundation/carry/EncodingQuality`	`http://www.w3.org/2002/07/owl#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	`https://uor.foundation/carry/CarryChain`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The number of sites in this carry chain.
generateMask	Datatype	true	`https://uor.foundation/carry/CarryChain`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Bit mask of site positions where carry is generated: and(x_k, y_k) = 1.
propagateMask	Datatype	true	`https://uor.foundation/carry/CarryChain`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Bit mask of site positions where carry propagates: xor(x_k, y_k) = 1.
killMask	Datatype	true	`https://uor.foundation/carry/CarryChain`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Bit mask of site positions where carry is killed: neither generated nor propagated.
eventKind	Datatype	true	`https://uor.foundation/carry/CarryEvent`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The kind of carry event: Generate, Propagate, or Kill.
sitePosition	Datatype	true	`https://uor.foundation/carry/CarryEvent`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The site index k at which this carry event occurs.
carryCount	Datatype	true	`https://uor.foundation/carry/CarryProfile`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The total number of carry events in this profile.
maxPropagationLength	Datatype	true	`https://uor.foundation/carry/CarryProfile`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The longest consecutive propagation run in this profile.
profileChain	Object	true	`https://uor.foundation/carry/CarryProfile`	`https://uor.foundation/carry/CarryChain`	The carry chain that this profile summarizes.
symbolSetSize	Datatype	true	`https://uor.foundation/carry/EncodingConfiguration`	`http://www.w3.org/2001/XMLSchema#positiveInteger`	The cardinality of the symbol set S being encoded.
quantizationBits	Datatype	true	`https://uor.foundation/carry/EncodingConfiguration`	`http://www.w3.org/2001/XMLSchema#positiveInteger`	The number of bits k used for encoding (2^k ≥ \|S\|).
encodingMap	Object	true	`https://uor.foundation/carry/EncodingConfiguration`	`https://uor.foundation/schema/TermExpression`	String representation of the mapping from symbols to ring elements.
meanDelta	Datatype	true	`https://uor.foundation/carry/EncodingQuality`	`http://www.w3.org/2001/XMLSchema#decimal`	The mean d_Δ over observed pairs for this encoding.
discriminationRatio	Datatype	true	`https://uor.foundation/carry/EncodingQuality`	`http://www.w3.org/2001/XMLSchema#decimal`	The ratio of distinguishable pairs to total pairs under this encoding.
isOptimalEncoding	Datatype	true	`https://uor.foundation/carry/EncodingQuality`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether this encoding minimizes Σ d_Δ over observed pairs.