the graph language. makes graphs first-class — the primitive is a connection, not a number
| Op | Action |
|---|---|
link(a, b, w) |
Create weighted directed edge |
walk(start, n) |
Random walk of n steps |
reach(a, b) |
Test if path exists |
neighbors(n) |
Return adjacent nodes |
rank(g, steps) |
Compute stationary distribution (PageRank) |
spectral(g, k) |
Extract top-k eigenvectors |
match(g, pat) |
Subgraph pattern matching |
the cybergraph is not a data structure that lives inside a program. the cybergraph IS the program. every cyberlink is an Edge. every CID is a Node. CYBERRANK is rank().
particles are objects (Hemera CIDs), cyberlinks are morphisms, linkchains are composition, semcons are natural transformations. Arc's algebra is category theory — the correct algebra for typed relational structure. Arc describes what the cybergraph is. compiles to Hemera CIDs for nodes and edges, and to Trident adjacency constraints for proof. decomposes into Trident (field ops for matrix math, Hemera hash verification for node identities) and Nox (tree encoding of topology)
see cyb/languages for the complete language set. see cyb/multiproof for the proving architecture