Sheafumi.ai
What this is about
- AI agent coordination
- Several agents, one shared semantic state they build under rules, not a hidden prompt memory.
- Sheaf Mathematical object: local data on each part of a structure, with maps that compare views on overlaps. Applied to agents: each role keeps its stalk; disagreement is measured only on shared restrictions.
- Each role keeps its Stalk The local evidence held by one role: its own view, kept intact rather than merged into a single shared number. of evidence. Disagreement is measured only on the shared restriction. Finality is a Global section A joint state every role agrees on: aligned on what they see together, not just a high score in isolation. .
- Agent governance
- Proposals pass policy before they become state. Audit, roles, and checkpoints instead of a cage.
- Swarm of governed agents
- No chaos, no cage: enough structure to converge, not a single scalar consensus.
- Agents in regulated settings
- Dual-condition finality and bitemporal record when policy and role agreement both matter.
Main features
- Shared semantic state on a causal graph, not hidden prompt memory
- Governance kernel: proposals pass policy before they become state
- Formal convergence toward a Global section A joint state every role agrees on: aligned on what they see together, not just a high score in isolation. ( Sheaf Mathematical object: local data on each part of a structure, with maps that compare views on overlaps. Applied to agents: each role keeps its stalk; disagreement is measured only on shared restrictions. Dirichlet energy A measure of disagreement on shared overlap; convergence drives it toward zero. )
- Dual-condition finality: every required dimension, plus role agreement
- Bitemporal audit: what was known, and when
- Contradictions stay first-class, including Belnap-style belief Four-valued logic (true, false, both, neither) that keeps contradictions explicit instead of forcing them away.
- Relationship-based authorization; finality is a checkpoint, not a wall
That is why a Sheaf Mathematical object: local data on each part of a structure, with maps that compare views on overlaps. Applied to agents: each role keeps its stalk; disagreement is measured only on shared restrictions. is a viable object for coordinating agents. Agents do not share one scalar state. They observe different subspaces of the evidence. Classical consensus pretends otherwise and then fights the remainder as noise. A cellular Sheaf Mathematical object: local data on each part of a structure, with maps that compare views on overlaps. Applied to agents: each role keeps its stalk; disagreement is measured only on shared restrictions. keeps each role’s Stalk The local evidence held by one role: its own view, kept intact rather than merged into a single shared number. intact and measures disagreement only on the shared restriction. Diffusion on the sheaf Laplacian An operator that diffuses disagreement across overlapping roles, nudging each view toward agreement on shared restrictions. drives that disagreement — the Dirichlet energy A measure of disagreement on shared overlap; convergence drives it toward zero. — toward zero. Finality on this layer is reaching a Global section A joint state every role agrees on: aligned on what they see together, not just a high score in isolation. : the swarm has not merely scored well; the roles agree on what they jointly see.