Datasets:
Formats:
csv
Languages:
English
Size:
1K - 10K
Tags:
mathematics
inverse-problems
observability
noncommutative-algebra
symbolic-computation
calibration-rigidity
| # Exact reference API | |
| Install the included `src/noulith/` package with `python -m pip install -e .`. | |
| The functions below are existing upstream entry points. | |
| | Function in `noulith.third` | Meaning / boundary | | |
| |---|---| | |
| | `all_components(m)` | Star, triangle, and twin descriptors; theorem domain m>=6 | | |
| | `component_equations(m, component)` | Exact integer matrix in ascending logarithmic edge order | | |
| | `intersection_dimension(m, components)` | Dimension computed from stacked exact equations | | |
| | `component_membership(m, q)` | Components containing a coefficient point under the implemented relations | | |
| | `certify_scalar(m, q)` | Exact rational certificate, m>=6 and abs(q+1)<1/20 | | |
| | `predicted_rank(m, q)` | Third-deficit rank from classification conditions | | |
| | `direct_block_rank(m, q, r)` | Independent all-subset calculation; exponential in m | | |
| | `optimal_calibration_subfamily(m)` | Attaining selection of twin outlier pairs, m>=6 | | |
| | `calibration_classes(m, selected_twins)` | Equivalence classes of edge scales constrained by the selected twin subspaces | | |
| | `example_point(m, kind, permutation=None)` | Nearby rational example point | | |
| | `q_from_exponents(exponents, base=Rational(1001,1000))` | Rational coefficients from directed antisymmetric integer exponents | | |
| Named examples: `origin`, `star`, `triangle`, `twin`, `uniform_star`, `star_twin`, | |
| `edge`, `double_star`, `generic`. | |
| ## Verify a raw witness | |
| ```python | |
| from noulith.algebra import TwistedAlgebra | |
| from noulith.third import example_point, certify_scalar | |
| m = 6 | |
| q = example_point(m, "generic") | |
| certificate = certify_scalar(m, q) | |
| assert certificate.visible | |
| blocks = certificate.full_partition(m) | |
| algebra = TwistedAlgebra(m, q) | |
| raw = algebra.isolated_response(blocks) | |
| assert len(blocks) == m - 3 | |
| assert raw == algebra.isolated_unit(blocks) * certificate.normalized_response | |
| assert raw != 0 | |
| ``` | |
| This checks the actual sparse algebra, including its crossing factor. It should not be | |
| replaced by a rounded near-zero test. | |
| ## Scope | |
| The local analytic theorem and strict real-rational implementation neighborhood are | |
| distinct. Passing an arbitrary dictionary to a low-level routine does not extend a theorem. | |
| A selected calibration pair represents an entire twin-subspace constraint, not a detector | |
| sample. Do not apply the third-deficit theorem at m=5 or the generic core formula at r=0. | |