Proofs as Probabilities

Many proofs are not deterministic. Location signals, sensor readings, and human attestations are often best modeled as probabilistic evidence with a confidence score. Local Protocol uses these signals only through protocol-defined, bounded interfaces so they can improve incentives without becoming an unbounded attack surface.

See: Proofs in Local Protocol

Confidence-weighted evidence

Model a proof attachment as evidence with confidence , where means “strong evidence” and means “no evidence”.

The protocol does not need to agree on a universal meaning of . It only requires:

a deterministic rule for how affects ledger-level policy inputs (weights, seed eligibility/weight, caps/bonds),
and objective verification hooks where possible (e.g., by sampling proofs in audits or requiring stronger bonds for high-impact claims).

How probabilistic proofs affect the graph

Probabilistic proofs are consumed in two primary places:

Edge weights (service proofs): adjust proof_factor (and sometimes quality) in:

Seed mass (identity/service baselines): affect seed eligibility and/or seed weight in the market-relative teleport distribution used by diffusion.

Because diffusion follows outgoing edges proportional to weights and restarts from , confidence-weighted evidence influences incentives by changing where influence can flow.

Dampening over distance and time

Even strong evidence should not create permanent or global privilege.

Distance dampening: in a restarted random walk, influence along length- paths is damped by roughly .
Time decay: implementations can apply deterministic decay schedules to proof-derived boosts (edge-weight multipliers and/or seed weights) so old evidence fades unless refreshed.

Practical guidance (protocol-level)

Bounded impact: clamp proof-derived multipliers and seed weights (caps prevent “proof = unlimited reward”).
Risk coupling: require stronger bonds for claims that rely heavily on proof multipliers, and reduce future capacity via penalties when audits fail.
Market-relative context: evaluate proof effects within a market context; bootstrapping mechanisms (seeds + vaults) can vary across markets while keeping the algorithm fixed.

See: Market Bootstrapping

Next Steps

Next, see an example of probabilistic evidence in action:

Location Proofs