---
title: "streaming-statistics — Mova code model"
description: "Mova code model of models/streaming-statistics.groupant: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/models/streaming-statistics.groupant/"
---
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# streaming-statistics

The groupant beside models/streaming-statistics.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

- **kind:** groupant_group
- **status:** partial source bound group
- **bound sources:** 8
- **repository folder:** [`models/streaming-statistics.groupant`](https://github.com/ElamurAI/mova-free/tree/main/models/streaming-statistics.groupant)
- **repository commit:** `855da7bd4a7b`

> **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](#forward) |
| **ast** | not materialized |  |
| **composition** | partial source model | [composition](#composition) |
| **cost** | partial source model | [cost](#cost) |
| **descriptant** | partial source model | [epoch-memory](#epoch-memory) |
| **invariant** | partial source model | [invariant](#invariant) |
| **tests** | bounded executed | [checks](#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 |
|---|---|---|---|
| `streaming-statistics-behavior-complement` | behavior_complement | partial source model | [behavior-complement](#behavior-complement) |
| `streaming-statistics-reverse-reconstruction` | reverse_reconstruction | partial source model | [reverse-reconstruction](#reverse-reconstruction) |
| `streaming-statistics-shared-count` | accepted_prefix_transport | partial source model | [shared-count](#shared-count) |
| `streaming-statistics-conservation` | stream_conservation | partial source model | [conservation](#conservation) |
| `streaming-statistics-summary-loss` | information_loss_relation | partial source model | [summary-loss](#summary-loss) |

## Model text


### model

## streaming-statistics

### forward

Summarize one accepted stream using bounded heavy-hitter counters, histogram rank/value intervals and online or merged moments.

### invariant

Accepted prefix counts agree under shared legal updates; counter, bucket and moment statistics retain different conservation and error relations.

### cost

Misra-Gries and Space-Saving O(k) worst update and O(k) state with deterministic BTreeMap order; histogram O(1) update/O(b) query/state, b<=10^6; moments O(1) update/merge/state.

### composition

Only shared successfully accepted inputs yield common N. There is no transaction across separate components. Exact counts, sorted ranks and direct finite mean/variance serve as independent fixture observations. The harness tests MG=SS jointly on 800 updates; histogram and moments use separate fixtures. A shared accepted-prefix execution across all four is not exercised.

### 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

["merged_moments_join_compensated_centered_sums","frequency_summaries_join_literal_histogram_certificates","histogram_intervals_join_sorted_rank_and_exact_counts"]

### limitations

Frequency error/N, quantile value/rank intervals and floating variance are different metrics. Moment arithmetic has no universal relative-error certificate. Map allocation failure lies outside the Result contract; histogram allocation is fallible.

### catalog

## Typed family relations

Each relation keeps its own domain and assurance.

### behavior-complement

Type: behavior_complement.

Exclude frequency intervals omitting the exact accepted-stream count, rank/value rectangles omitting the sorted requested rank, mismatched accepted-prefix N and successful nonfinite moment output. A rejected individual update must not mutate that component; no cross-component rollback is promised.

### reverse-reconstruction

Type: reverse_reconstruction.

Compatible streams lie in the intersection of frequency intervals, histogram bucket occupancies and moment constraints with execution consistency. Permutations and unrecorded identities/within-bucket values remain ambiguous; rounded moments may distinguish some permutations.

### shared-count

Type: accepted_prefix_transport.

Under legal updates for every component, MG.len=SS.len=histogram.len=moments.count=N. Rejection in one component invalidates this common-prefix premise unless caller coordinates updates.

### conservation

Type: stream_conservation.

MG counter sum+(k+1)*cancellations=N; SS estimate sum=N; histogram bucket sum=N; moments count=N. These equalities concern accepted updates and do not convert all output errors into one percentage.

### summary-loss

Type: information_loss_relation.

Frequency summaries omit most identities; histogram retains only bucket order/value intervals; moments retain low-order statistics. Equal low-order moments do not establish equal distributions or equal quantiles.

### 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 ["merged_moments_join_compensated_centered_sums","frequency_summaries_join_literal_histogram_certificates","histogram_intervals_join_sorted_rank_and_exact_counts"] 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](https://md.groupants.elamur.ai/free/en/mova/models/algorithm-library.groupant/#wave19-evidence) records receipts; conditional laws outside these fixture scopes are not promoted to executed checks. No joint universal percentage bound follows from family membership.