Datasets:
Formats:
csv
Languages:
English
Size:
1K - 10K
Tags:
mathematics
inverse-problems
observability
noncommutative-algebra
symbolic-computation
calibration-rigidity
| # 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. | |