# Numerical data dictionary

The three CSV configurations contain **79 recorded synthetic numerical observations**: 40 critical-crossover rows, 35 compact-port rows, and 4 compensation rows. Each file has its own schema. Values are exported directly from the original JSON reports using Python's round-trippable numerical representation.

No personal data or empirical measurements are present. Parameter choices are small deterministic sweeps selected for verification. They do not define a representative distribution of physical systems. Blank fields mean a diagnostic is absent or inapplicable, rather than zero.

## `critical_crossover`

Source: `research/results/critical.json`, `cases[*].rows[*]`.

| Column | Meaning |
| --- | --- |
| `factor_kind` | `diagonal` or `mixed`; the complete coupling matrices are in the source report |
| `tau` | Positive critical ratio, 10, 40, 160, or 640 |
| `n` | Spatial frequency index, 4, 8, 16, 32, or 64 |
| `rho` | Penalty strength, equal to `tau*n**2` |
| `relative_response_error` | Relative matrix error between the full-model and effective inlet responses, as defined in `research/code/verify_critical.py` |
| `Y11_real` … `Y22_imag` | Real and imaginary entries of the full 2×2 compressed inlet response |
| `response_eigenvalue_1`, `response_eigenvalue_2` | Ordered eigenvalues of that response |
| `raw_hermitian_error` | Hermitian-symmetry diagnostic before symmetrization |
| `exact_transfer_cells` | Transfer cells for the exact constant-transfer method, when present |
| `cell_transfer_symplectic_defect` | Exact-transfer symplectic diagnostic, when present |
| `period_subcells`, `total_riccati_cells` | Resolution for periodic short-cell/Riccati composition, when present |
| `maximum_cell_symplectic_defect` | Maximum short-cell diagnostic for the periodic method, when present |

The limiting potential and limiting response are in the source report for each case. No convergence rate is proved from these rows.

## `compact_ports`

Source: `research/results/nexus_uniform.json`, `rows[*]`.

| Column | Meaning |
| --- | --- |
| `case_index` | Zero-based row position in the original JSON report |
| `kind` | `balanced` difference port or `anchored` sum port |
| `epsilon` | Positive twist strength |
| `lambda_finite` | Finite port penalty strength; blank for an exact hard constraint |
| `hard_constraint` | Boolean indicating exact `LP=0` enforcement |
| `check` | `main` parameter run, or a separate mesh/endpoint refinement label |
| `cells`, `xmax` | FEM mesh cell count and truncated right endpoint |
| `capacity`, `impedance` | Minimized capacity and its reciprocal for the measured inlet |
| `scaled_capacity` | `capacity/epsilon` for the documented model with exponent one |
| `port_value` | Computed scalar compact-port value |
| `derivative_energy` | Axial derivative contribution to the quadratic energy |
| `local_leakage_energy` | Local bright leakage contribution |
| `nonlocal_port_energy` | Added finite-rank penalty energy |
| `relative_stationarity_residual` | Recorded FEM stationarity diagnostic |
| `predicted_scaled_capacity` | Leading theorem prediction when stored for the run |
| `relative_error_to_limit` | Relative error to that prediction when stored |

Refinement runs are retained and labeled. They should not be counted as independent evidence or additional parameter samples. A hard constraint has no finite penalty value; its constraint residual is separately reported in the original JSON.

## `critical_compensation`

Source: `research/results/critical.json`, `finite_critical_compensation_design.rows[*]`.

`tau`, `n`, `rho`, the response entries, eigenvalues, and solver metrics have the meanings above. `relative_response_error` compares with the prescribed target response. `effective_potential_identity_error` checks the algebraic compensation identity and is constant across the four rows because the target and factor are fixed.

The design uses `tau=40` and the complex Hermitian target with real part `[[1.1,0.25],[0.25,0.8]]` and imaginary part `[[0,0.12],[-0.12,0]]`. The full factor and reference response are preserved in the original report.

## Loading locally

```python
import csv
from pathlib import Path

with Path('data/critical_crossover.csv').open(newline='', encoding='utf-8') as f:
    rows = list(csv.DictReader(f))
print(len(rows))  # 40
```

CSV readers choose their own types; use the dictionary above when interpreting nullable fields and Boolean flags. The original JSON reports are authoritative for nested matrices, auxiliary refinements, and exact diagnostic definitions.