DATA_DICTIONARY.md

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

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.