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.

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.