A semantic functorial network over distributed compute.

Collider-Data-Systems builds mo:os — a categorical hypergraph rewriting kernel where all components, hardware and programs alike, are considered categorically. The session is the centerpiece for human and AI inference; its relations both make it findable (observing surfaces like Drive, Gmail, Calendar, GitHub) and capable of writing the programs that pull the levers (emitting envelopes through leaves).

Together they form a federation: each kernel owns a sovereign log, the router cascades reads across shards, and twin kernels per-host carry replication via twin_link edges.

The kernel state is a hypergraph that grows by four rewrites:

ADD    — create a node with typed properties
LINK   — create a relation (hyperedge) between two nodes via a typed port pair
MUTATE — change one property value on one existing node
UNLINK — remove a relation

state(t) = fold(log[0..t]). Log is truth; state is derived.

Above that, an operad declares the legal types and ports. Above the operad, sessions inhabit kernels (5-facet tuples: scope, purpose, host, owner, occupant) and emit envelopes that have to pass two gates before fold:

• §M11 liveness — every envelope must have a live session context (explicit or inferable via has-occupant)
• §M12 admin-capability — admin-scope rewrites walk WF02 governs from actor through superadmin

The result is a categorical substrate where:

• Sessions are program-authoring layers (where derivations happen)
• Channels are cooperads upstream of ingestion (Gmail, Drive, GitHub, etc.)
• Leaves are partially-applied morphisms: any structure that surfaces values back to a session's open arguments
• Time runs on multiple clocks (kernel sweep, T-day calendar, custom event-driven), each generalized via keeps-time-with LINKs
• Causation is distinct from temporal succession (causes vs scheduled-after), expressed as its own WF

• @Collider-Data-Systems/sam — owns kernels, delegates, and most sessions
• @Collider-Data-Systems/moos — multimodal curation lane

Active work surfaces on Project mo:os — round-by-round iterations with custom HG-aware fields (Agent ID, HG URN, Phase, Owner Role, Collider Category, Branch Role).

mo:os is being built toward an MVP gate sequence (G1–G6) targeting May 2026. The substrate doctrine, ontology, and round-by-round reasoning live in a private workspace; the public face is the two repos above plus their READMEs.

If you're a category theorist, hypergraph-rewriting researcher, or distributed-systems engineer interested in the substrate, the kernel README is the entry point.

Reach out via repository issues or the maintainer's GitHub profile. Solo-builder cadence — responses arrive in rounds rather than in real time.