# Certificate Degradation Rules

Stability margins are quantitative. When certificates are chained, sampled, or coarse-grained, margins generally degrade.

SFT treats this as part of the artifact logic.

## Generic rule (minimum margin)

When a composed claim depends on multiple certificates, the output margin is bounded by the minimum of the input margins.

- `LCM_pi_out <= min_i LCM_pi_i`
- `HMR_P_out <= min_i HMR_P_i`

## Sampling and discretization

If a witness is inferred from samples, additional degradation is recorded as an explicit nonnegative loss term.

- `LCM_pi_out <= LCM_pi_in - eta_sampling`

## Coarse-graining

If the observable is compressed (binning, quantization), the degradation is recorded as an explicit loss term.

- `LCM_pi_out <= LCM_pi_in - eta_quant`

## Audit interface

When degradation is declared, the certificate may include:

- `degradation.rule` (string)
- `degradation.inputs` (list of certificate ids)
- `degradation.checks` (list of numeric inequalities that must hold)

The audit script is required to verify these inequalities.

