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

The groupant beside world/src/induce.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:** [`world/src/induce.rs`](https://github.com/ElamurAI/mova-free/blob/main/world/src/induce.rs)
- **source SHA-256:** `0297cbe15b922cb5…`
- **covers:** K(a,b,c)=a|(b<<21)|(c<<42), zero slots omitted. skeys emits C(A,1)+C(A,2)+C(A,3). add_fixes iff head=gold.head AND rel!=gold.rel; breaks iff both equal. Filter fix>=min, sort net desc, cardinality asc, Rule asc. (bytes 10798–19325)
- **part of:** [world-induce](https://md.groupants.elamur.ai/free/en/mova/world/src/induce.rs.groupant/)
- **repository folder:** [`world/src/induce.rs.groupant/subset-counts.groupant`](https://github.com/ElamurAI/mova-free/tree/main/world/src/induce.rs.groupant/subset-counts.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 | [approximant](#approximant) |
| **ast** | partial | `../syntax.json` |
| **composition** | partial | [composition](#composition) |
| **cost** | partial | [cost](#cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | partial bounded parent tests | [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) |
| `world_induce_subset_counts_invariants` | world_induce_subset_counts_invariants | partial source derived model | [world_induce_subset_counts_invariants](#world-induce-subset-counts-invariants) |
| `world_induce_subset_counts_resource_cost` | world_induce_subset_counts_resource_cost | partial source derived model | [world_induce_subset_counts_resource_cost](#world-induce-subset-counts-resource-cost) |
| `world_induce_subset_counts_representation_join` | world_induce_subset_counts_representation_join | partial source derived model | [world_induce_subset_counts_representation_join](#world-induce-subset-counts-representation-join) |
| `world_induce_subset_counts_domain_partition` | world_induce_subset_counts_domain_partition | partial source derived model | [world_induce_subset_counts_domain_partition](#world-induce-subset-counts-domain-partition) |

## Model text


### descriptant

#### world-induce-subset-counts

K(a,b,c)=a|(b<<21)|(c<<42), zero slots omitted. skeys emits C(A,1)+C(A,2)+C(A,3). add_fixes iff head=gold.head AND rel!=gold.rel; breaks iff both equal. Filter fix>=min, sort net desc, cardinality asc, Rule asc.

##### Modeling epoch 2026-10-31

Prospective source/branch/cost hypotheses were saved externally before source edits. This partial source-derived model retains observed boundaries rather than claiming complete verification. Pure codes/counting/parsing/changes/threshold tests; feature extraction, persistent effects and live learning remain partial, no surrogate.

### approximant

#### Forward relation

K(a,b,c)=a|(b<<21)|(c<<42), zero slots omitted. skeys emits C(A,1)+C(A,2)+C(A,3). add_fixes iff head=gold.head AND rel!=gold.rel; breaks iff both equal. Filter fix>=min, sort net desc, cardinality asc, Rule asc.

Domain: Aligned shapes; valid internal feature f<32,v<65535; count/index width bounds.

No executable percent surrogate: these categorical/effect observations lack a useful approximation metric. Future supported caps1/2/5/10% need a defined domain/metric and real reference evidence; no error or speed bound is claimed.

### invariant

Collision-free keys require nonzero21bit codes and<=3slots; input codes sorted unique. u32 decrement assumes balanced prior insertion; source does not check underflow balance.

Cost component: [cost.md](https://md.groupants.elamur.ai/free/en/mova/world/src/induce.rs.groupant/subset-counts.groupant/#cost).

### cost

Cubic subset work, G candidate sort and up to16 worker local maps/count vectors.

### composition

CPU native test supplies features directly; GPU route re-encodes enum labels and offsets tou32, separate unexecuted claim.

### models

### behavior_complement

Four distinct atoms yield14 keys, excluding4-way subset. Wrong heads never counted. Same from/subset shares break count among all to targets; empty candidates return empty.

### reverse_reconstruction

Decode valid packed key injectively recovers included codes, not full word feature vector. Count fiber includes arbitrary sentence order and incorrect-head words; cannot recover individual repair examples.

### world_induce_subset_counts_invariants

Collision-free keys require nonzero21bit codes and<=3slots; input codes sorted unique. u32 decrement assumes balanced prior insertion; source does not check underflow balance.

### world_induce_subset_counts_resource_cost

Cubic subset work, G candidate sort and up to16 worker local maps/count vectors.

### world_induce_subset_counts_representation_join

CPU native test supplies features directly; GPU route re-encodes enum labels and offsets tou32, separate unexecuted claim.

### world_induce_subset_counts_domain_partition

Aligned shapes; valid internal feature f<32,v<65535; count/index width bounds.

### tests

#### Scoped evidence

Parent selected test names: ["induce::wave29_worldlearn::counting_requires_correct_heads_and_orders_candidates", "induce::wave29_worldlearn::packed_subsets_and_empty_bootstrap", "induce::wave29_worldlearn::permissive_parse_and_set_valued_changes"]. These finite tests touch only the named behaviors, not every statement in this fragment. See [parent evidence](https://md.groupants.elamur.ai/free/en/mova/world/src/induce.rs.groupant/#tests). control-induce: compiled source mutation failed with exit101; source restored byte-for-byte and15positive tests passed.

Scope bytes [10798,19325) are bound to the shared parent syntax projection and full source hash. Pure codes/counting/parsing/changes/threshold tests; feature extraction, persistent effects and live learning remain partial, no surrogate.