Datasets:
Formats:
csv
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English
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Tags:
mathematics
homogenization
spectral-theory
variational-methods
matrix-analysis
scientific-computing
| # 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 | |
| ```python | |
| 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. | |