---
title: "qagen-select-quotas — Mova code model"
description: "Mova code model of qagen/src/select.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/qagen/src/select.rs.groupant/quotas.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**

This page as HTML: <https://groupants.elamur.ai/free/en/mova/qagen/src/select.rs.groupant/quotas.groupant/>

# qagen-select-quotas

The groupant beside qagen/src/select.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:** [`qagen/src/select.rs`](https://github.com/ElamurAI/mova-free/blob/main/qagen/src/select.rs)
- **source SHA-256:** `0c35caf4eda91c0a…`
- **covers:** Initialize q=0 and L=min(n,sum caps). Each pass opens unsaturated size keys, sets W=sum weights, and if W>0 computes a_i=floor(L*w_i/W), r_i=L*w_i mod W. Award L-sum(a) extra seats in decreasing r then lexical key order, clip to room, subtract awards and repeat. (bytes 6669–8257)
- **part of:** [qagen-select](https://md.groupants.elamur.ai/free/en/mova/qagen/src/select.rs.groupant/)
- **repository folder:** [`qagen/src/select.rs.groupant/quotas.groupant`](https://github.com/ElamurAI/mova-free/tree/main/qagen/src/select.rs.groupant/quotas.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** | partial | `../syntax.json` |
| **cost** | partial source model | [cost](#cost) |
| **descriptant** | partial source model | [epoch-memory](#epoch-memory) |
| **invariant** | partial source model | [invariant](#invariant) |
| **tests** | partial source model | [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 |
|---|---|---|---|
| `qagen-select-quotas-complement` | behavior_complement | partial source model | [behavior-complement](#behavior-complement) |
| `qagen-select-quotas-reverse` | reverse_reconstruction | partial source model | [reverse-reconstruction](#reverse-reconstruction) |
| `qagen-select-quotas-specialization` | hamilton_remainder_order | partial source model | [specialization](#specialization) |

## Model text


### forward
Initialize q=0 and L=min(n,sum caps). Each pass opens unsaturated size keys, sets W=sum weights, and if W>0 computes a_i=floor(L*w_i/W), r_i=L*w_i mod W. Award L-sum(a) extra seats in decreasing r then lexical key order, clip to room, subtract awards and repeat.

### behavior-complement
Exclude cap excess, keys absent from size, negative assignments and nonlexical ties. Positive weights exhausted implies termination even if zero-weight capacity remains. Missing caps are zero; cap-only keys never receive assignments.

### reverse-reconstruction
Fiber of q consists of all (size,cap,n) whose successive Hamilton rounds yield q. Positive common scaling of all weights preserves q when inputs remain representable. Clipped capacities and unused extra keys destroy injectivity; no unique recovery is claimed.

### invariant
Source-bound operational relation over supplied finite inputs; deterministic observations under fixed order and seed. No corpus/distribution assumption. Integer quota arithmetic assumes 32/64-bit usize.

### cost
Let B=|size| and C=|cap|, including cap-only keys. Initialization builds B zero quotas (conservatively O(B log(B+1)) key comparisons), clones all size keys and scans C capacities, even when n=0 and R=0. Each of R passes adds O(B log(B+C+1)) comparison/map work, including cap lookups; thus O(B log(B+1)+C+R B log(B+C+1)) unit-comparison work. String comparison costs and key-clone bytes are additional, not constant-time assumptions about arbitrary keys. Storage is O(B) entries plus cloned key bytes. R<=B+1 because a continuing clipped pass saturates a key. u128 division cost is not benchmarked.

### specialization
Type hamilton_remainder_order: scoped observation above, exact intended relation, no approximation-error budget asserted.

### checks
quota_small_exhaustive_rational_oracle; quota_exact_above_f64_integer_precision; quota_capacity_and_weight_sums_exceed_usize; quota_missing_extra_zero_and_capped_domains. See ../evidence.md for actual profiles and negative controls.

### epoch-memory
2026-10-30: model written from the existing mechanism before numerical repair. Source hash "0c35caf4eda91c0a5d36bce728f3846b360b483a66fa4ca3c884964839cd2554". Finite witnesses constrain this relation, not a general proof. Independent review qualified the cost model: initialization survives zero rounds, cap-only keys contribute their own scan and lookup size, and strings are not unit-cost byte sequences. Source, native receipts and syntax hashes remain unchanged.