Elamur Groupantscertified-approximation
The groupant beside models/certified-approximation.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 |
|---|---|---|---|
certified-approximation-behavior-complement | behavior_complement | partial source model | behavior-complement |
certified-approximation-reverse-reconstruction | reverse_reconstruction | partial source model | reverse-reconstruction |
certified-approximation-subset-embedding | objective_embedding | partial source model | subset-embedding |
certified-approximation-absolute-transport | lipschitz_error_transport | partial source model | absolute-transport |
certified-approximation-cancellation | normalization_countermodel | partial source model | cancellation |
Model text
model
certified-approximation
forward
Compute bounded-loss feasible objectives, exact rational interpolation and quantized integer dot observations with distinct certificates.
invariant
Feasibility, objective loss, conditional interpolation error and dot absolute/L1 error remain separately typed. Unsupported percentages and resource/arithmetic errors are categorical.
cost
Knapsack value scaling O(n^3/epsilon); trimmed subset list O(nLlog L), L=O(n*log(target)/epsilon) in the mathematical model. Interpolation validates O(n) then searches O(log n); dot O(n). Work and allocation limits apply.
composition
Embedding subset values as equal knapsack weights/profits preserves the exact optimum. The two approximate outputs may differ while satisfying their own loss bounds. Conditional absolute interpolation error transports through a known Lipschitz map; dot L1 normalization does not imply relative scalar error under cancellation.
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
["fptas_objectives_join_exhaustive_subset_fibers","rational_certificates_join_polynomials_and_compensated_products"]
limitations
Curvature bound is a caller premise, not inferred from knots. Overflow, work limits and allocation failures do not count as small approximation errors. Integer certificates do not provide a shared parent percentage or universal speed gain.
catalog
Typed family relations
Each relation keeps its own domain and assurance.
behavior-complement
Type: behavior_complement.
Exclude infeasible or over-optimal FPTAS outputs, violated declared loss bounds, extrapolated interpolation, and true dot errors outside the absolute certificate. Exclude promotion of caller curvature to checked fact and promotion of L1-normalized dot error to cancellation-relative error.
reverse-reconstruction
Type: reverse_reconstruction.
Objective certificates admit many item lists and optimal subsets. One interpolated ordinate admits many functions through the supplied knots; dot values admit sign/permutation and cancellation fibers. Reconstruct only constraints retained by the certificate, not unique original inputs.
subset-embedding
Type: objective_embedding.
On representable inputs, each subset value v becomes a knapsack item of weight v and profit v with capacity target. Exact optima coincide. Each accepted epsilon result lies between (1-epsilon)*OPT and OPT; results need not coincide.
absolute-transport
Type: lipschitz_error_transport.
If interpolation error <=e and downstream real map is L-Lipschitz on the reached interval, downstream discrepancy <=L*e. Any independent downstream error adds separately; floating conversion and missing curvature premises require extra treatment.
cancellation
Type: normalization_countermodel.
For signed products near cancellation, sum(abs(products)) may be large while abs(sum(products)) is zero or tiny. A <=10% L1-normalized dot certificate supplies an absolute bound, not <=10% relative error of the scalar dot.
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 ["fptas_objectives_join_exhaustive_subset_fibers","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.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/models/certified-approximation.groupant/