---
title: "kg-cols-integer-codecs — Mova code model"
description: "Mova code model of kg/src/cols.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/kg/src/cols.rs.groupant/integer-codecs.groupant/"
---
Elamur: [Mova](https://md.mova.elamur.ai/free/en/) · [Dictionary](https://md.dictionary.elamur.ai/free/en/) · [Research](https://md.research.elamur.ai/free/en/) · **Groupants**

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# kg-cols-integer-codecs

The groupant beside kg/src/cols.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:** [`kg/src/cols.rs`](https://github.com/ElamurAI/mova-free/blob/main/kg/src/cols.rs)
- **source SHA-256:** `70bf9a9666a17269…`
- **covers:** Private LEB/delta/zigzag/byteplane transformations. (bytes 5309–7619)
- **part of:** [kg-cols](https://md.groupants.elamur.ai/free/en/mova/kg/src/cols.rs.groupant/)
- **repository folder:** [`kg/src/cols.rs.groupant/integer-codecs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/kg/src/cols.rs.groupant/integer-codecs.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` |
| **composition** | partial | [composition](#composition) |
| **cost** | partial | [cost](#cost) |
| **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) |
| `modulo` | modulo | partial source derived model | [modulo](#modulo) |
| `signed_boundary` | signed_boundary | partial source derived model | [signed_boundary](#signed-boundary) |
| `empty_count` | empty_count | partial source derived model | [empty_count](#empty-count) |
| `error_cursor` | error_cursor | partial source derived model | [error_cursor](#error-cursor) |

## Model text


### descriptant

#### kg-cols-integer-codecs

Private LEB/delta/zigzag/byteplane transformations.

##### Modeling epoch — 2026-10-31

Source read before tests and models; retained prospective notes accompany the parent. Current evidence uses bounded invented inputs only. This is partial modeling, not proof or corpus accuracy.

### approximant

#### Forward relation

LEB emits 7-bit groups; delta wraps x-prev; inverse wraps prev+d. Zigzag encodes signed wrapping difference. Planes transpose four little-endian bytes across all values.

##### Executable approximant gap

Exact categorical structure, identifiers, parser decisions and effects have no useful percentage metric established here. No executable surrogate, automatic substitution or 1/2/5/10% guarantee is claimed.

### invariant

#### Invariant and domain

Decode of encoder-produced values and exact count recovers u64/u32 bitpatterns including MAX and repeated zero.

##### Cost and resources

O(n), <=10 LEB bytes/u64,4n planes; allocation count arithmetic not checked.

### cost

#### Cost and resources

O(n), <=10 LEB bytes/u64,4n planes; allocation count arithmetic not checked.

### composition

#### Composition

Private LEB/delta/zigzag/byteplane transformations.

LEB emits 7-bit groups; delta wraps x-prev; inverse wraps prev+d. Zigzag encodes signed wrapping difference. Planes transpose four little-endian bytes across all values.

The parent invokes scoped transformations through the actual functions named in their source ranges. Children partition useful observations, not a complete semantic proof; boundaries can omit helpers, tests and effects.

### models

### behavior_complement

Truncated continuation/too-long LEB and wrong plane length error. Trailing LEB bytes and overlarge terminal payload are not fully rejected.

### reverse_reconstruction

Plane transpose at fixed n is bijective; decoded LEB vector has multiple byte preimages from trailing/noncanonical encodings.

### modulo

Wrapping arithmetic handles descending src too, despite usual sorted production use.

### signed_boundary

u64 endpoints reinterpret as i64 differences; zigzag and inverse preserve two's complement bitpattern.

### empty_count

n0 decodes no LEB values even with extra bytes; plane n0 requires empty bytes.

### error_cursor

unleb increments position after each consumed byte; no rollback on error.


### tests

#### Evidence

Parent source checks (a fragment inherits only the behavior they actually exercise):

- cols::tests::roundtrip_and_filter
- cols::wave29::codec_boundaries_and_errors

Selected kg tests: 15 named outcomes, twice debug/twice release, equal sorted outcomes. Standalone actual global/build.rs: 3 named outcomes per run, twice debug/twice optimized; build_child is normally no-op, parent fixture invokes it against isolated synthetic seeds. Eight compiled source mutations (one per source) each compiled successfully and exited101 on the focused assertion; exact source restoration followed by positive rerun.

This fragment's untested branches remain source-derived. No live graph, DB, corpus, teacher, GPU or held-out evaluation was used. Command specs and numeric exits are retained in the external wave29 graphlang receipt. Strict kg Clippy reports existing source lints; see receipt.