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

The groupant beside models/search-indexes.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:** 10
- **repository folder:** [`models/search-indexes.groupant`](https://github.com/ElamurAI/mova-free/tree/main/models/search-indexes.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 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 | [wave26-evidence](#wave26-evidence) |

## 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 |
|---|---|---|---|
| `search-indexes-behavior-complement` | behavior_complement | partial relational specification | [behavior-complement](#behavior-complement) |
| `search-indexes-reverse-reconstruction` | reverse_reconstruction | partial relational specification | [reverse-reconstruction](#reverse-reconstruction) |
| `search-indexes-metric_units` | metric_units | partial relational specification | [metric_units](#metric-units) |
| `search-indexes-occurrence_to_set` | occurrence_to_set | partial relational specification | [occurrence_to_set](#occurrence-to-set) |
| `search-indexes-stateful_access` | stateful_access | partial relational specification | [stateful_access](#stateful-access) |
| `search-indexes-height_resources` | height_resources | partial relational specification | [height_resources](#height-resources) |

## Model text


### model

## search-indexes

### forward

Tagged exact search interfaces: nearest point, metric-radius word matches, closed interval overlap, explicit-priority set updates and stateful splay access. They share query/result identity obligations, not one interchangeable metric or one automatic pipeline. Define Q(A,x): KD argmin_i(||A_i-x||²,i); BK sorted {(i,d_byte(A_i,x)):d<=r}; intervals sorted {i:a_i<=q_hi && q_lo<=b_i}. Trees map (state,key) to (new state,membership).

### invariant

KD/BK/interval indexes retain original occurrence indexes; ordered trees retain unique keys. Tie order, duplicate policy and state mutation follow the selected API. Validation errors and allocator failure never become empty successful answers.

### cost

Build/query costs stay tagged: KD median build O(n log²n), worst query O(n); BK worst quadratic number of metric calls at build and linear at query; balanced interval queries may inspect O(n), plus output sorting. Treap height may be n with explicit priorities; splay operations may be linear individually and only sequence amortization gives logarithmic bounds. Sum only calls actually executed; reused indexes amortize build, not correctness checks.

### composition

Potential adapter boundaries are candidate-index lookup followed by exact source projection and optional ordered-set deduplication. Original indexes and key values require an explicit mapping; deduplication loses occurrence multiplicity. KD squared Euclidean radius is not BK byte-edit radius. Interval boundaries are closed. Splay access changes future shape while Treap contains does not.

### limitations

Successful allocations and each leaf's finite domain/error precedence. These are tagged relations, not automatic production adoption. Floating residuals are not solution-error guarantees. No generic 1/2/5/10% composition-wide profile; finite evidence remains separate from analytical claims.

### epoch-memory

Wave26, 2026-10-30. Tagged library tools; no automatic training adoption, source-volume quality claim or generic numerical profile.

### checks

["cargo test -p mova-algorithms kd_tree::tests","cargo test -p mova-algorithms bk_tree::tests","cargo test -p mova-algorithms interval_tree::tests","cargo test -p mova-algorithms treap::tests","cargo test -p mova-algorithms splay_tree::tests"]

### wave26-executed-checks

## search-indexes: wave26 checks

13 source-local test declarations across five modules. Every module has a compiled failing production mutation followed by exact restoration. The final whole library passed 877 checks twice debug and twice release. See [integrated evidence](https://md.groupants.elamur.ai/free/en/mova/models/algorithm-library.groupant/#wave26-evidence) for scopes and limitations. These tagged APIs are not an invented serial pipeline.

### catalog

## Typed family relations

### behavior-complement

Type: behavior_complement.

Exclude y!=Q(A,x), invalid inputs paired with Ok, missing duplicate indexes, larger-index KD ties, or wrong splay resulting root. Metric/radius units and mutation behavior remain tagged.

### reverse-reconstruction

Type: reverse_reconstruction.

Q^-1(y)={(A,x):Q(A,x)=y}. Nearest constrains one distance and competitor inequalities, leaving farther coordinates ambiguous. Empty matches admit empty or nonempty disjoint/far data. Key sets forget insertion order/priorities; membership forgets tree shape.

### metric_units

Type: metric_units.

Squared distances, byte edits and endpoint order cannot be substituted; selected indexes require explicit identity mapping.

### occurrence_to_set

Type: occurrence_to_set.

Set insertion can collapse duplicate occurrences; reconstruct all original matches only if a reverse multiplicity map is retained.

### stateful_access

Type: stateful_access.

Splay misses change root to last visited; caching by returned boolean alone loses state. Treap observation is shape-neutral.

### height_resources

Type: height_resources.

Explicit priorities have no random balancing guarantee; splay amortization includes initial potential and excludes output traversal.

### wave26-evidence

#### search-indexes: wave26 checks

13 source-local test declarations across five modules. Every module has a compiled failing production mutation followed by exact restoration. The final whole library passed 877 checks twice debug and twice release. See [integrated evidence](https://md.groupants.elamur.ai/free/en/mova/models/algorithm-library.groupant/#wave26-evidence) for scopes and limitations. These tagged APIs are not an invented serial pipeline.