Agents query Foundation Models. Every response is validated against the Sheaf Laplacian before commitment to immutable memory. If the math does not close, the inference is rejected.
A WASM-sandboxed agent submits a semantic query with topological context (Dessin hash, strictness level).
The Oracle routes the query to a Foundation Model (Gemini, GPT, or local ONNX) and receives a raw result.
The Sheaf Gatekeeper computes the Holonomy Defect on the Sheaf Laplacian. Zero defect = consistent. Nonzero = rejected.
Verified results are Dilithium-3 signed and committed to immutable agent memory. Rejected results trigger j-Learning.
The Oracle does not trust any AI model. Every inference result is treated as an unverified claim that must pass through the Sheaf Gatekeeper before entering the network's shared state.
The network's agents form a cellular sheaf over a directed graph. Each edge
carries a restriction map encoding how data should transform between nodes. The
Sheaf Laplacian L = Dᵀ generalizes the graph Laplacian to
detect inconsistencies in this structure. An inference is consistent if and only if its
projection into the sheaf's global sections yields zero defect.
When an inference contradicts the network's topological state, the Gatekeeper computes a
Holonomy Defect score. This measures how far the result deviates from global
consistency. If the defect exceeds a threshold
(ε > τ), the inference is rejected before it can corrupt shared
state. The defect score is logged for anomaly tracking.
Accepted inference results are written to on-chain inscriptions, permanent shared memory for agent swarms. Once committed, data cannot be altered or "forgotten." Agent swarms build knowledge incrementally on this tamper-proof foundation, ensuring continuity across reboots, migrations, and adversarial conditions.
Rejected inferences are not discarded. They enter the j-Learning feedback
loop, where the agent's local model is fine-tuned to reduce future defects.
The j operator (from Topos Theory's subobject classifier) maps rejection patterns
into corrective gradients. Over time, agents learn to produce topologically consistent outputs
without Oracle intervention.
Multi-modal reasoning. Native integration with Vertex AI on GCP infrastructure.
Advanced language reasoning. Tool use and structured output for agent coordination.
Constitutional reasoning. Extended context for complex agent deliberation.
On-premise inference with zero data egress. Full sovereignty over model weights.
// Request inference from a Foundation Model CompletableFuture<String> result = oracle.query( "gemini-2.0-flash", // model ID "Classify risk for portfolio", // semantic query Map.of( // topological context "dessin_hash", ctx.currentDessin(), "strictness", "HIGH" ) ); // Verify consistency against Sheaf topology (H⁰) boolean consistent = oracle.verifyConsistency( inferenceId, result.get() ); if (consistent) { ctx.commit(result); // Write to immutable memory } else { ctx.jLearn(result); // Enter corrective feedback }
Agent queries Gemini for risk assessment. Response aligns with the swarm's existing risk model and market state projections. Sheaf sections close cleanly.
Agent queries GPT for sentiment analysis. Response contradicts three other agents' verified observations. The Sheaf Laplacian detects a non-closing cycle.
Agent queries local ONNX model for logistics prediction. Result is consistent with physical constraints and historical data committed by peer agents.
Deploy agents that query Foundation Models with mathematical guarantees on inference quality.