# Scientific table schemas

All six tables are synthetic or theoretical. Total rows: 1,342.

## `phase_scan`

Synthetic complex reflection and noisy quadratures across drive detuning. [801 rows](research/physics/phase_scan.csv); split `train`.

| Column | Storage type |
| --- | --- |
| `omega_over_Omega0` | `float64` |
| `S_plus_real` | `float64` |
| `S_plus_imag` | `float64` |
| `S_minus_real` | `float64` |
| `S_minus_imag` | `float64` |
| `absolute_contrast` | `float64` |
| `noisy_plus_real` | `float64` |
| `noisy_plus_imag` | `float64` |
| `noisy_minus_real` | `float64` |
| `noisy_minus_imag` | `float64` |
## `raw_control_records`

Four synthetic calibration settings, before and after reflection inversion. [4 rows](research/physics/raw_control_records.csv); split `train`.

| Column | Storage type |
| --- | --- |
| `setting` | `integer` |
| `t_real` | `float64` |
| `t_imag` | `float64` |
| `S_exact_real` | `float64` |
| `S_exact_imag` | `float64` |
| `S_measured_real` | `float64` |
| `S_measured_imag` | `float64` |
| `F_exact_real` | `float64` |
| `F_exact_imag` | `float64` |
| `F_measured_real` | `float64` |
| `F_measured_imag` | `float64` |
## `withheld_controls`

Synthetic held-out controls with exact, noisy, and deliberate-drift errors. [20 rows](research/physics/withheld_controls.csv); split `test`.

| Column | Storage type |
| --- | --- |
| `index` | `integer` |
| `t_real` | `float64` |
| `t_imag` | `float64` |
| `F_true_real` | `float64` |
| `F_true_imag` | `float64` |
| `exact_prediction_error` | `float64` |
| `noisy_prediction_error` | `float64` |
| `deliberate_drift_error` | `float64` |
## `memory_phase`

Two-pole theoretical memory intensity for opposite relational phases. [501 rows](research/data/memory_phase.csv); split `train`.

| Column | Storage type |
| --- | --- |
| `time_times_Omega0` | `float64` |
| `plus` | `float64` |
| `minus` | `float64` |
## `rank_profiles`

Exact theoretical self-adjoint versus dissipative rank profiles. [8 rows](research/data/rank_profiles.csv); split `train`.

| Column | Storage type |
| --- | --- |
| `nodes` | `integer` |
| `seven_state_Hermitian` | `integer` |
| `one_damped_state` | `integer` |
## `damping_kernel_spectrum`

Numerical kernel eigenvalues before and after a known-linewidth correction. [8 rows](research/data/damping_kernel_spectrum.csv); split `train`.

| Column | Storage type |
| --- | --- |
| `index` | `integer` |
| `uncorrected_eigenvalue` | `float64` |
| `known_shift_eigenvalue` | `float64` |

## Interpretation

- `phase_scan`: detuning is normalized by Omega0; reflection quadratures and absolute contrast are dimensionless. Noisy columns contain simulated averaged readout noise.
- `raw_control_records`: `t_*` gives the normalized complex control; `S_*` is dimensionless reflection; `F_*` is inverse root response normalized by Omega0. Noise is added to reflection before inversion.
- `withheld_controls`: normalized inverse-response prediction errors; deliberate drift is a synthetic 0.025 Omega0 hidden-detuning change.
- `memory_phase`: dimensionless time and normalized two-pole memory intensities for phases +pi/2 and -pi/2. See the source plot/formula for intensity normalization.
- `rank_profiles`: theoretical exact ranks, not noisy rank estimates. Each node count is a distinct sampling-set size.
- `damping_kernel_spectrum`: eigenvalues of dimensionless normalized kernels, in descending algebraic order. Tiny signed values near zero can be rounding artifacts; the plotted absolute spectrum is not additional physical spectral mass.

No values are missing. CSV complex quantities are always separated into real/imaginary fields. The authoritative generation formulas and seed are in `research/src/make_data.py`; device-specific calibration is required before experimental comparison.