# Rule Catalog

```{toctree}
:hidden:
:maxdepth: 1

PH-BC-001
PH-BC-002
PH-CON-001
PH-CON-002
PH-CON-003
PH-CON-004
PH-NUM-001
PH-NUM-002
PH-POS-001
PH-POS-002
PH-RES-001
PH-RES-002
PH-RES-003
PH-SYM-001
PH-SYM-002
PH-SYM-003
PH-SYM-004
PH-VAR-002
```

## PH-BC

| Rule | Name | Severity | Input modes |
|------|------|----------|-------------|
| [PH-BC-001](PH-BC-001.md) | Boundary condition violation (relative or absolute mode) | error | adapter+dump |
| [PH-BC-002](PH-BC-002.md) | Boundary flux imbalance (divergence theorem) | warning | adapter+dump |

## PH-CON

| Rule | Name | Severity | Input modes |
|------|------|----------|-------------|
| [PH-CON-001](PH-CON-001.md) | Mass conservation violation | error | adapter+dump |
| [PH-CON-002](PH-CON-002.md) | Energy conservation violation | error | adapter+dump |
| [PH-CON-003](PH-CON-003.md) | Energy dissipation sign violation | warning | adapter+dump |
| [PH-CON-004](PH-CON-004.md) | Per-element conservation hotspot | warning | adapter+dump |

## PH-NUM

| Rule | Name | Severity | Input modes |
|------|------|----------|-------------|
| [PH-NUM-001](PH-NUM-001.md) | Quadrature convergence warning | warning | adapter+dump |
| [PH-NUM-002](PH-NUM-002.md) | Refinement convergence rate below expected | warning | adapter+dump |

## PH-POS

| Rule | Name | Severity | Input modes |
|------|------|----------|-------------|
| [PH-POS-001](PH-POS-001.md) | Positivity violation | error | adapter+dump |
| [PH-POS-002](PH-POS-002.md) | Maximum principle violation | error | adapter+dump |

## PH-RES

| Rule | Name | Severity | Input modes |
|------|------|----------|-------------|
| [PH-RES-001](PH-RES-001.md) | Residual exceeds variationally-correct norm threshold | error | adapter+dump |
| [PH-RES-002](PH-RES-002.md) | FD-vs-AD residual cross-check discrepancy | warning | adapter |
| [PH-RES-003](PH-RES-003.md) | Spectral-vs-FD residual discrepancy on periodic grid | warning | adapter+dump |

## PH-SYM

| Rule | Name | Severity | Input modes |
|------|------|----------|-------------|
| [PH-SYM-001](PH-SYM-001.md) | C4 rotation equivariance violation | warning | adapter+dump |
| [PH-SYM-002](PH-SYM-002.md) | Reflection equivariance violation | warning | adapter+dump |
| [PH-SYM-003](PH-SYM-003.md) | SO(2) Lie derivative equivariance violation | warning | adapter |
| [PH-SYM-004](PH-SYM-004.md) | Translation equivariance violation | warning | adapter+dump |

## PH-VAR

| Rule | Name | Severity | Input modes |
|------|------|----------|-------------|
| [PH-VAR-002](PH-VAR-002.md) | Hyperbolic norm-equivalence conjectural | info | adapter+dump |