📐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

Components

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.

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.

This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/algorithms/src/bitset_subset_sum/mod.rs.groupant/