---
title: "algorithm-bitset-subset-sum — Mova code model"
description: "Mova code model of algorithms/src/bitset_subset_sum/mod.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/bitset_subset_sum/mod.rs.groupant/"
---
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# algorithm-bitset-subset-sum

The groupant beside algorithms/src/bitset_subset_sum/mod.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
- **status:** partial descriptive instance
- **source:** [`algorithms/src/bitset_subset_sum/mod.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/bitset_subset_sum/mod.rs)
- **source SHA-256:** `46fc828212ab7df1…`
- **repository folder:** [`algorithms/src/bitset_subset_sum/mod.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/bitset_subset_sum/mod.rs.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` |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [approximant](#approximant) |
| **tests** | existing checks referenced | [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 relational specification | [behavior_complement](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial relational specification | [reverse_reconstruction](#reverse-reconstruction) |
| `permutation` | permutation | partial relational specification | [permutation](#permutation) |
| `zero_extension` | zero_extension | partial relational specification | [zero_extension](#zero-extension) |
| `scale_equivariance` | scale_equivariance | partial relational specification | [scale_equivariance](#scale-equivariance) |
| `single_use` | single_use | partial relational specification | [single_use](#single-use) |

## Model text


### descriptant

#### bitset_subset_sum mod.rs

Original std-only implementation and independent fixtures. Bellman, Dynamic Programming (1957); word-parallel implementation is original.

Prospective model saved before changes in $MOVA_DATA/runs/octopus-wave20-dp-2026-10-30/prospective.md. Current epoch 2026-10-30: exact optimization with explicit bounded-resource outcomes. Finite oracle agreement does not establish the caller's monotonicity premises. No timing or whole-Mova speed claim.

### approximant

#### Forward model

B[0]=1; B_next=B OR (B<<value), clipped above target. Return bit target. Descending destination words preserve the previous item layer even for in-word shifts and zero values.

#### Cost

O(m*(target/64+1)) word operations; O(target/64+1) u64 words. max_words bounds storage, checked bytes before fallible reserve.

#### Invariants and limits

Owned input slices remain unchanged. Deterministic ties and traversal; callback panics propagate and purity/monotonicity remain caller obligations. No allocator-refusal injection, no semantic AST proof, no universal finite-test proof. Checked arithmetic reports errors rather than wrapping.

#### Executable approximant gap

No executable surrogate is attached: categorical reachability/argmin has no justified relaxed metric here. Objective-only surrogate speed/error has not been measured. Existing knapsack surrogate is not automatically transferable. No 1/2/5/10% profile or approximate substitution is claimed.

### models

### behavior_complement

For input ([2],1), true is excluded: the reachable set is {0,2}. More generally false excludes existence of any subset summing exactly to target; true excludes absence of all witnesses.

### reverse_reconstruction

true at target 3 has compatible antecedents [3] and [1,2]; false at 3 admits [2] and []. The output fiber is all arrays with/without a subset of target weight, not a uniquely recoverable array.

### permutation

Permuting values preserves the reachable-sum set, with unchanged target and sufficient budget.

### zero_extension

Appending zero preserves every reachable target, since B OR (B<<0)=B.

### scale_equivariance

Multiplying all values and target by positive k preserves reachability when usize products and resource dimensions fit.

### single_use

For [64], target 128 is false. Descending words prevent a newly written word from supplying a second use of the item.

### tests

#### Checks

cargo test -p mova-algorithms bitset_subset_sum::tests

Independent small oracle and resource boundary fixtures live in ../tests.rs. Repeated debug/release and compiled mutation receipts: $MOVA_DATA/runs/octopus-wave20-dp-2026-10-30.

### combiner

#### Composition

Raw mod.rs syntax and mathematical recurrence are separate evidence. The partial syntax projection binds the exact source bytes but does not certify the recurrence. Oracle tests compare observable outputs; typed relations constrain lawful transformations and compatible preimages. For bitset_subset_sum, resource caps and checked failures remain separate from mathematical objective equivalence. Prospective expectations remain unchanged; finite validation cannot turn monotonicity assumptions into runtime validation.

### validation

#### Validation — 2026-10-30

Ten new native tests cover five exact kernels. Full mova-algorithms library: 557 tests pass in two debug and two release executions; sorted native test outcomes agree byte-for-byte across all four. Strict all-target Clippy and focused rustfmt pass. External receipts: $MOVA_DATA/runs/octopus-wave20-dp-2026-10-30/{debug1,debug2,release1,release2,clippy}.log.

Compiled production controls: zero initial subset bit, forced zero MITM objective, right-tie SMAWK reduction, forced zero layered-DP objective and forced zero BST objective all fail named equality assertions. Byte restoration followed by full positive library rerun passes. A separate SMAWK interpolation tie mutation fails lawful_matrices after adding half-integer squared-distance centers; the restored focused test passes. Receipts: controls.log, mutant-*.log, restored.log, smawk-restored.log in the same external run directory. The original constant-matrix fixture alone did not distinguish interpolation ties; the stronger fixture closes that observed gap.

Every source/test file has two independently generated identical syntax projections and current source SHA. An isolated ten-leaf modelcheck groupants run reports valid=true, diagnostics=[], ten sidecars, zero missing source sidecars; the temporary collection parent has no sidecar and makes no composition claim. Root integration owns global registry and ancestor binding checks.

No timing speedup, machine-independent resource guarantee, allocation-failure injection, monotonicity validation, or end-to-end Mova improvement is inferred. Successful finite tests certify the listed observations only. No teacher, model, corpus or live database operations were used.