The Assurance Algebra

A ledger cannot see the world. Blockchains call this the oracle problem and treat it as a flaw. The Assurance Algebra treats it as a priced, bounded risk.

Every claim carries a formula of the assumptions it rests on. From that formula, any consumer computes, under its own policy, the minimum an attacker must spend or forfeit to make the claim false: the claim’s cost of corruption. An agent relies on a claim only when that cost exceeds what it has at stake, and it reserves the claim’s backing, so that no claim is relied on beyond what slashing can repay. If the claim is proven false, the bonds behind it are slashed and the parties who relied on it are compensated first.

The pieces, each with its own chapter:

A worked example from the architecture paper

An agent must decide whether to pay invoice #1042 for 25,000 USD. The claim invoice payable joins three inputs:

• delivery confirmed by three independent witnesses, each bonded at 20,000 USD;
• the invoice arithmetic, proven by two proof stacks;
• the supplier’s identity credential, from a bank bonding 1,000,000 USD.

The cost of corruption is min(60,000; ∞; 1,000,000) = 60,000 USD: delivery is the weak link. With κ = 2 the agent pays invoices up to 30,000 USD automatically; above that it asks for a fourth witness. If three financiers each wanted to lend 25,000 USD against the same invoice, the first would reserve 50,000 USD of the 60,000 USD backing, and the second would be refused until more evidence was posted.

The same idea, run on the devnet

sion demo invoice runs a smaller version end to end. The invoice rests on the supplier’s dual signature and on either the supplier’s bond or a delivery claim backed by the shipper’s bond:

Pulse  15  supplier issues "Invoice #1042: 10,000 USD payable"  [dual-signature ∧ (bond:supplier ∨ delivery)]
           cost of corruption (standard policy): 50,000 USD, exact
           = 30,000 (supplier's bond) + 20,000 (shipper's bond): a forger must corrupt both routes
           rely on  10000 USD at κ = 2 → ACCEPT: cost of corruption 50,000 covers κ·V = 20,000
           rely on  30000 USD at κ = 2 → REJECT: cost of corruption 50,000 (after detection discount 1000/1000) is below κ·V = 60,000
Pulse  18  financier funds the invoice and reserves 20,000 USD of its backing (κ·V): nobody else can rely on the same bonds beyond what slashing can repay
Pulse  20  buyer challenges the supplier's attestation (deposit 1,000 USD)
Pulse  22  judge upholds: supplier's bond slashed (30,000 USD); the invoice still holds through the delivery route
Pulse  24  buyer challenges the shipper's delivery attestation, under the shipper's own adjudicator
Pulse  26  judge upholds: 2 claims falsified (the delivery, and the invoice resting on it)
           financier compensated 10,000 USD automatically from the slashed bonds (balance 199,999.9988 → 209,999.9988)

Why this matters for AI agents

An agent cannot judge a document’s authenticity the way a person does, but it can evaluate a formula and compare two numbers. The decision rule gives every agent the same machine-checkable trust test. Forged or prompt-injected inputs fail it unless someone puts real money behind them. The MCP tool sion_assess_claim exposes exactly this test (see Connect an AI agent over MCP).

In this implementation

• Built: atoms, formulas over atoms and claims, policy-relative cost of corruption intervals with an exact solver for shared atoms, the decision rule, reservations, bonds with lock periods, challenges, adjudication, slashing with compensation, falsification that propagates to dependent claims, and failure probabilities. Property tests cover the algebra.
• Simplified: the assurance registry is one contended object; every claim, bond and reservation operation touches it.
• Not built: automatic slashing for cryptographically checkable contradictions (every challenge goes to an adjudicator), and an insurance market.