# Worked examples (/docs/business-validators/examples)



## Collateral for a $20M portfolio [#collateral-for-a-20m-portfolio]

Assume one role carries $20M of outstanding [notional](/docs/resources/glossary#notional). Apply the [verified marginal tiers](/docs/business-validators/parameters):

| Band           | Calculation            | Required collateral |
| -------------- | ---------------------- | ------------------- |
| First $1M      | $1M × 5%               | $50,000             |
| Next $9M       | $9M × 3.5%             | $315,000            |
| Remaining $10M | $10M × 2.5%            | $250,000            |
| Total          | Sum of the three bands | **$615,000**        |

At an **illustrative** [oracle](/docs/resources/glossary#oracle) price of $0.25 per ASSET, the requirement is **2,460,000 ASSET**. This price is an assumption, not a current quote. An operator posting exactly that amount begins at 100% collateral health before reservations or other restrictions.

If price falls to $0.20, the same stake is worth $492,000, or **80%** of the requirement. Under the ordinary health thresholds it becomes degraded. Restoring 100% requires another $123,000, equivalent to **615,000 ASSET** at that price. SV top-up grace can affect the reported state; raw collateral coverage remains 80%.

## One reward epoch [#one-reward-epoch]

Assume an illustrative, fully funded [epoch](/docs/resources/glossary#epoch) slice of **9,000 ASSET**, no carryover or rounding residue, all three role floors active, and no eligibility reductions. Each role has at least three qualifying validators and $5M notional. This is an allocation example, not the promised slice for the current three-hour epoch.

Each role first receives its 20% floor: **1,800 ASSET**. That leaves **3,600 ASSET** to divide by effective weight. Suppose total effective weights are 180,000 for TV, 90,000 for SV, and 90,000 for IV:

| Role | Floor | Share of remaining pool | Total     |
| ---- | ----- | ----------------------- | --------- |
| TV   | 1,800 | 1,800 (50%)             | **3,600** |
| SV   | 1,800 | 900 (25%)               | **2,700** |
| IV   | 1,800 | 900 (25%)               | **2,700** |

Within TV, consider an operator with $100,000 posted stake value, weighted stake age **A = 12 months**, **N = 50** distinct assets served, and **n = 1** counted offence in the trailing 12 months:

* Age multiplier: `A / (A + 12) = 0.5`.
* Experience multiplier: `1 + 2N / (N + 50) = 2`.
* Reputation multiplier: `max(0.5, 1 − 0.1n) = 0.9`.
* Weight before eligibility gates: `100,000 × 0.5 × 2 × 0.9 = 90,000`.

Assuming this operator is eligible and the two other TV weights are 45,000 each, its share is **50% × 3,600 = 1,800 ASSET**. Treasury-backed positions can split an account's accrual further. Actual calculation uses fixed-point arithmetic, snapshots, eligibility gates, and funding checks; read [Rewards](/docs/business-validators/rewards).

## One Brier evaluation [#one-brier-evaluation]

Assume **100 eligible assets**, all predicted at **10%** probability of default, and **30** observed defaults within the defined outcome horizon. Each asset has an in-scope scheduled payment, and the evaluation time has arrived.

1. Observed score: `(30 × 0.9² + 70 × 0.1²) / 100 = 0.25`.
2. Expected score: `0.1 × 0.9 = 0.09`.
3. Implemented standard error: `sqrt(0.09 × (1 − 0.09) / 100) ≈ 0.028618`.
4. With multiplier 2, the threshold is `0.09 + 2 × 0.028618 ≈ 0.147236`.

Because **0.25 exceeds 0.147236**, the evaluation reports a breach and enters the provisional penalty process. This uses the protocol's implemented standard-error formula. It is not a claim that every statistical calibration method uses that formula.

A sample below the configured minimum of 30 would be skipped rather than counted as successful calibration. Assets without an in-scope payment are excluded. See [Scoring Validator](/docs/business-validators/scoring) for outcome timing and [Penalties and disputes](/docs/business-validators/mechanisms) for what follows a breach.