---
title: "math-deriv-numerical-check — Mova code model"
description: "Mova code model of math/src/deriv.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/math/src/deriv.rs.groupant/numerical-check.groupant/"
---
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# math-deriv-numerical-check

The groupant beside math/src/deriv.rs 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

- **kind:** groupant_fragment
- **status:** partial source bound model
- **source:** [`math/src/deriv.rs`](https://github.com/ElamurAI/mova-free/blob/main/math/src/deriv.rs)
- **source SHA-256:** `0ea96ef4d7df85aa…`
- **covers:** check_derivative substitutes eight fixed coordinates, central h=1e-5 max(|p|,1). Unsupported/nonfinite skip, >=3 with scaled discrepancy<=1e-5 accepts. Passing is finite agreement, not global identity or nonsingularity; use parent calc approximation subset. (bytes 6714–8091)
- **part of:** [math-deriv](https://md.groupants.elamur.ai/free/en/mova/math/src/deriv.rs.groupant/)
- **repository folder:** [`math/src/deriv.rs.groupant/numerical-check.groupant`](https://github.com/ElamurAI/mova-free/tree/main/math/src/deriv.rs.groupant/numerical-check.groupant)
- **repository commit:** `48f2e6f74146`

> **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 | [approximant](#approximant) |
| **ast** | partial | `../syntax.json` |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | executed bounded checks | [tests](#tests) |

## 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 |
|---|---|---|---|
| `behavior_complement` | behavior_complement | partial source derived model | [behavior_complement](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial source derived model | [reverse_reconstruction](#reverse-reconstruction) |
| `sampling_coordinates` | sampling_coordinates | partial source derived model | [sampling_coordinates](#sampling-coordinates) |
| `metric_zero` | metric_zero | partial source derived model | [metric_zero](#metric-zero) |
| `availability_filter` | availability_filter | partial source derived model | [availability_filter](#availability-filter) |
| `assurance_limit` | assurance_limit | partial source derived model | [assurance_limit](#assurance-limit) |

## Model text


### descriptant

#### math-deriv-numerical-check

check_derivative substitutes eight fixed coordinates, central h=1e-5 max(|p|,1). Unsupported/nonfinite skip, >=3 with scaled discrepancy<=1e-5 accepts. Passing is finite agreement, not global identity or nonsingularity; use parent calc approximation subset.

Epoch 2026-10-31: complete source read, parent AST reused; partial finite evidence only.

### approximant

#### Scoped forward and cost

check_derivative substitutes eight fixed coordinates, central h=1e-5 max(|p|,1). Unsupported/nonfinite skip, >=3 with scaled discrepancy<=1e-5 accepts. Passing is finite agreement, not global identity or nonsingularity; use parent calc approximation subset.

No executable percent surrogate claimed.

### invariant

#### Scoped invariant

check_derivative substitutes eight fixed coordinates, central h=1e-5 max(|p|,1). Unsupported/nonfinite skip, >=3 with scaled discrepancy<=1e-5 accepts. Passing is finite agreement, not global identity or nonsingularity; use parent calc approximation subset.

Source range[6714,8091) bound by manifest digest. Parent domain applies, not arbitrary public states.

### models

## Source-scoped typed relations

### behavior_complement

Fewer than3 finite usable samples excludes ok=true; any used discrepancy>1e-5 also excludes success. Skipped samples do not contribute false evidence of equality.

### reverse_reconstruction

A passing check admits all f,df agreeing to tolerance at reached fixed sample neighborhoods. Functions differing elsewhere or vanishing perturbations at samples share the observation; no unique derivative recovery.

### sampling_coordinates

Points are0.3,0.7,1.1,1.9,2.6,-0.4,-1.3,3.7. At each p choose h=1e-5*max(|p|,1); evaluate f(p+h),f(p-h),df(p) in cloned envs with target replaced by V::R.

### metric_zero

num=(a-b)/(2h), err=|num-dv|/max(|dv|,1). Near zero derivative this is absolute scale1, not relative division by zero. Worst records maximum over used samples.

### availability_filter

Missing calc::approx formula or any nonfinite a,b,dv skips sample. Unsupported unknown-call functions can yield0 usable samples even when symbolic derive returns0 by target absence.

### assurance_limit

Finite differences include cancellation/truncation and float error. Eight fixed coordinates cannot prove symbolic identity or nonsingularity elsewhere; threshold is a diagnostic, not1/2/5/10% executable surrogate assurance.

### tests

#### Evidence

See ../tests.md for actual checks and source mutant; this fragment adds no runtime test.

check_derivative substitutes eight fixed coordinates, central h=1e-5 max(|p|,1). Unsupported/nonfinite skip, >=3 with scaled discrepancy<=1e-5 accepts. Passing is finite agreement, not global identity or nonsingularity; use parent calc approximation subset.