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Deconstruct real-time collaboration algorithms. Explore Vector Clocks, Operational Transformation matrices, and Bounded Join-Semilattices powering Figma, Notion, and Yjs.
How mathematical join-semilattices eliminate central coordinator servers and enable true local-first P2P synchronization.
Pioneered by Google Docs and Etherpad. Clients send intent operations to a central master server. The server serializes all edits and transforms character index coordinates using transformation functions T(op1, op2).
Used by Figma, Notion, Yjs, and Automerge. Edits attach immutable identifiers. Mutations form a Bounded Join-Semilattice where merge operations (⊔ join) are mathematically guaranteed to converge anywhere.
Why physical wall clocks drift in distributed networks, and how logical vector clocks track causal happens-before relationships.
How Google Docs adjusts character indices of concurrent text operations against a central serialization server.
The mathematical proof of Strong Eventual Consistency using Commutative, Associative, and Idempotent merge functions.
Positive-Negative Counters, Last-Write-Wins registers, and Observed-Removed Sets (OR-Set).
How modern collaborative editors (Yjs, Automerge, Figma) model rich text as linked trees of immutable character nodes with fractional indices.