docs/DATA_DICTIONARY.md

# Reference-data dictionary

The rows are generated mathematical examples and formula tables. They contain no sampled
population, physical measurements, or GPU benchmark. `train` is a Hub split convention,
with no held-out counterpart.

The eight CSV files keep their upstream bytes. Their fields contain exact integer counts
and categorical labels except `t` and `amplitude` in `detuning_amplitudes`, which are
numerical evaluation fields. The two CSV projections retain each complete original
object as `record_json`.

| Configuration | Rows | Fields |
|---|---:|---|
| `arc_blind_family` | 15 | `p`, `channels`, `state_dimension`, `length_J`, `length_K`, `length_gap`, `minimal_protocols_J`, `minimal_protocols_K`, `protocol_gap` |
| `branch_hilbert_functions` | 56 | `channels`, `degree`, `hilbert_function` |
| `detuning_amplitudes` | 123 | `composition`, `t`, `amplitude`, `predicted_order` |
| `full_state_rank_strata` | 45 | `channels`, `blocks`, `stratum`, `rank`, `state_dimension` |
| `root_budget_profiles` | 1200 | `root_order`, `degree`, `blocks`, `exponent` |
| `root_jet_visibility` | 42 | `channels`, `root_order`, `blocks`, `jet_order`, `rank`, `dimension` |
| `v3_component_and_budget_counts` | 25 | `m`, `edge_parameters`, `star_components`, `triangle_components`, `twin_components`, `total_components`, `minimum_calibration_constraints`, `remaining_scale_classes` |
| `v3_exact_rank_strata` | 27 | `m`, `stratum`, `state_dimension`, `rank`, `nullity` |
| `v3_components_m6` | 41 | `record_json`, `channels`, `component_id`, `kind`, `dimension`, `labels_zero_based_json`, `equation_count` |
| `v3_visibility_certificates` | 9 | `record_json`, `channels`, `stratum`, `blocks`, `visible`, `normalized_response_exact`, `motif_json` |

## Semantics

**arc_blind_family.** Exact counts for J_p=(a^p,b^p) and K_p=(a,b)^p. Equal arc-order profiles can coexist with different analytic ideal membership. Source: `data/arc_blind_family.csv`.

**branch_hilbert_functions.** Degree-by-degree Hilbert values for the known second-deficit elliptic m-fold branch curve. Source: `data/branch_hilbert_functions.csv`.

**detuning_amplitudes.** Numerical evaluations for named detuning compositions. This CSV contains floating amplitude values rather than exact rational certificates. Source: `data/detuning_amplitudes.csv`.

**full_state_rank_strata.** Retained second-deficit full-state rank values on the specified symbolic strata. Source: `data/full_state_rank_strata.csv`.

**root_budget_profiles.** Exact root-of-unity detuning exponents indexed by root order, degree, and block budget. Source: `data/root_budget_profiles.csv`.

**root_jet_visibility.** Exact parameter-jet visibility counts for the stated root-order and block choices. Source: `data/root_jet_visibility.csv`.

**v3_component_and_budget_counts.** Formula-derived component counts and sharp selected-twin budgets for m=6 through m=30. Source: `data/v3_component_and_budget_counts.csv`.

**v3_exact_rank_strata.** Exact ranks and nullities for nine named third-deficit examples at m=6,7,8. Source: `data/v3_exact_rank_strata.csv`.

**v3_components_m6.** All 41 component records. record_json preserves each original equation matrix and label list. Source: `hub_data/v3_components_m6.csv`.

**v3_visibility_certificates.** Nine certificate records. record_json preserves original motifs, exact responses, and component memberships. Source: `hub_data/v3_visibility_certificates.csv`.


## Component equations and indexing

Each row of `linear_equations_ascending_edges` in `data/v3_components_m6.json` is a
homogeneous linear equation in logarithmic $\theta$ coordinates. Ascending edge order is
$(0,1),(0,2),\ldots,(0,5),(1,2),\ldots,(4,5)$. Labels are zero-based.
Dimension equals 15 minus the equation matrix rank.

```python
import json
original_component = json.loads(components[0]["record_json"])
equations = original_component["linear_equations_ascending_edges"]
```

## Certificate semantics

`visible: false` records invisible-component membership. `visible: true` carries a
supported nonzero motif. The exact normalized response must be multiplied by the recorded
invertible crossing unit to compare it with a raw ordered-word response.
The API's `full_partition(m)` supplies the completed protocol.

## Regeneration

- `scripts/generate_data.py` generates the retained tables and certificates.
- `scripts/generate_v3_data.py` generates version-3 counts, ranks, arrangement, and certificates.
- `hub_tools/prepare_viewer_data.py` regenerates the two lossless CSV projections.
- `data_catalog.json` records paths, counts, fields, hashes, and provenance.

After changing raw JSON, regenerate the viewer projections and then release checksums.
A mathematical-data change should be documented as such.