G-Set

a G-Set (grow-only set) is the simplest CRDT. elements can be added and never removed. the merge function is set union

definition

state: a set S

update: add(e) → S' = S ∪ {e}

merge: merge(S₁, S₂) = S₁ ∪ S₂

query: lookup(e) = e ∈ S

algebraic structure

the G-Set forms a join-semilattice under set inclusion (⊆). the join is set union (∪). union is commutative, associative, and idempotent — the three properties that guarantee convergence regardless of update order

role in cyber

BBG uses G-Sets for content sync. each particle is identified by a CID (content identifier). when a node encounters a new CID, it adds it to the local G-Set. merge with any other node is union — CIDs that appear on either side appear in the result. deduplication is automatic because set union ignores duplicates

the grow-only constraint is a natural fit for content-addressed data: a CID, once created, is immutable and permanent. there is no meaningful "remove" for content that is addressed by its own hash

see CRDT for the family of convergent data structures. see particle for the content objects identified by CID