Combinatorics / CONCEPT
The component correction identity
Let H be a finite family of subsets of an n-element vertex type, m=card(H), and P=binom(n,2). The side predicate is defined for every H. Under DUF and the cap of at most four neighbors per ground pair, each four-edge fiber F(S) with card(S)=4 determines one center/support component, and each counted component has exactly two sides.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES2
PROOF DEPTH4
DOCUMENT LINKS1
Two fibers per component
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- A cone with a linear remainderstructural-affinity · Closed
- Charging saturated link componentsstructural-affinity · Closed
- Exact stars at a marked packetstructural-affinity · Closed
- Fifteen-vertex separation and the fourteen-vertex boundstructural-affinity · Closed
- Ownership at a marked exchangestructural-affinity · Closed
- Reciprocal fibers and actual link componentsstructural-affinity · Closed
- Two incidence counts and the codegree-four boundstructural-affinity · Closed
- Unordered wedges and four-edge common linksstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
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