Elamur Groupantsnumerical-evaluation
The groupant beside models/numerical-evaluation.groupant in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.
Facts
Implementation material. A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.
Components
| component | label | where |
|---|---|---|
| approximant | partial source model | forward |
| ast | not materialized | |
| composition | partial source model | composition |
| cost | partial source model | cost |
| descriptant | partial source model | epoch-memory |
| invariant | partial source model | invariant |
| tests | bounded executed | checks |
Obernants
The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.
| id | type | label | where |
|---|---|---|---|
numerical-evaluation-behavior-complement | behavior_complement | partial source model | behavior-complement |
numerical-evaluation-reverse-reconstruction | reverse_reconstruction | partial source model | reverse-reconstruction |
numerical-evaluation-basis-conversion | polynomial_basis_transport | partial source model | basis-conversion |
numerical-evaluation-analytic-integral | antiderivative_certificate | partial source model | analytic-integral |
numerical-evaluation-sample-blindness | finite_observation_complement | partial source model | sample-blindness |
Model text
model
numerical-evaluation
forward
Evaluate power and Chebyshev polynomials, compensated finite sums and budgeted adaptive quadrature with a separately labeled heuristic error estimate.
invariant
Keep coefficient conventions, finite results, callback evaluations, budgets and numerical assurance distinct. A successful heuristic tolerance status is not an analytical integration certificate.
cost
Horner, Clenshaw and Neumaier O(n) arithmetic/O(1) scratch; Simpson O(evaluations) with bounded depth<=64 and fixed panel stack. Callback costs are additional.
composition
Fixed-degree Chebyshev-to-power conversion and analytic polynomial integrals provide independent identities. The harness uses the cubic [2,3,-2,1] in Chebyshev form and [4,0,-4,4] in power form on 33 dyadic points. The separate quadratic formula is an analytical relation. Native comparisons use explicit additive tolerances.
epoch-memory
Wave19, 2026-10-30. Models retain real-arithmetic assumptions separately from native finite checks. Kernels are library tools, not automatically adopted into training or inference.
checks
["polynomial_basis_join_derivative_and_quadrature","rational_certificates_join_polynomials_and_compensated_products"]
limitations
Finite intermediate overflow and cancellation are explicit. Simpson's local estimate can miss unsampled structure; callbacks may violate smoothness. Neither residual samples nor finite successful tests certify all functions or a shared <=10% error.
catalog
Typed family relations
Each relation keeps its own domain and assurance.
behavior-complement
Type: behavior_complement.
Exclude outputs outside each tagged native transition, successful nonfinite values, excess callback budgets and Simpson estimates promoted to universal guarantees. Distinct error/status observations are not numerical approximation loss.
reverse-reconstruction
Type: reverse_reconstruction.
At x=0 Horner retains c0,c1 and loses higher coefficients; Clenshaw retains an alternating even-coefficient sum and loses odd terms. Sum fibers include [1,2] and [3]. Quadrature samples permit arbitrary off-sample perturbations, so reports do not identify a unique integrand.
basis-conversion
Type: polynomial_basis_transport.
Chebyshev coefficients [a,b,c] represent power coefficients [a-c,b,2c]. Evaluations agree in real arithmetic. Floating tests require scale-aware additive tolerance; derivative comparison must use transformed coefficients.
analytic-integral
Type: antiderivative_certificate.
A power polynomial has exact real integral sum a_k*(b^(k+1)-a^(k+1))/(k+1). This supplies an independent finite quadrature oracle; general callback error remains heuristic.
sample-blindness
Type: finite_observation_complement.
A function vanishing at all sampled abscissae can have a nonzero integral between them. Equal sampled values and error estimates therefore admit different exact integrals; an explicit hidden-bump test witnesses this gap. The witness is in the leaf validation_and_unsampled_fiber test.
wave19-evidence
Family evidence — 2026-10-30
This family binds eight implementation/test sources through its manifest; views are partial source-derived models. Selected named joins are ["polynomial_basis_join_derivative_and_quadrature","rational_certificates_join_polynomials_and_compensated_products"] in algorithms/tests/composition_wave19.rs. Those checks pass four times as part of the 616-check suite. Leaf oracles and compiled production controls remain separately bound in adjacent evidence.
Integrated evidence records receipts; conditional laws outside these fixture scopes are not promoted to executed checks. No joint universal percentage bound follows from family membership.
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