Elamur Groupantsalgorithm-maximum-weight-closure
The groupant beside algorithms/src/maximum_weight_closure/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
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 | source derived | Forward |
| ast | partial | syntax.json |
| cost | symbolic unmeasured | Cost |
| descriptant | present | descriptant |
| invariant | source derived | Invariant |
| tests | bounded executed | 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 |
|---|---|---|---|
nonbehavior | behavior_complement | partial source derived | nonbehavior |
preimages | reverse_reconstruction | partial source derived | preimages |
transition | specialized_relation | partial source derived | transition |
order | specialized_relation | partial source derived | order |
coordinate | specialized_relation | partial source derived | coordinate |
fiber | specialized_relation | partial source derived | fiber |
errors | error_partition | partial source derived | errors |
Model text
descriptant
algorithm-maximum-weight-closure
Original std-only implementation or original independent fixtures. See source citations. Prospective model was saved before implementation in $MOVA_DATA/runs/octopus-wave26-combinatorial-2026-10-30/prospective.md.
Preserve original coordinates, deterministic ties and distinct validation/resource/infeasibility outcomes. Repeated observations constrain this epoch only.
model
algorithm-maximum-weight-closure
Domain
<=512 i64 weights, <=131072 zero-based implications; positive sum plus one fits u64; sorted selected coordinates and i128 weight.
Forward
Build source-positive, negative-sink, implication arcs with capacity P+1; reuse Dinic; residual source side maximizes closed weight P-flow.
Invariant
A finite minimum cut cannot sever implication capacity P+1 since empty closure has cut P; selected weight equals P-cut.
Cost
Dinic O(V^2 E) time, O(V+E) memory.
nonbehavior
Type: behavior_complement.
Exclude nonclosed selected sets, unsorted coordinates, wrong weight or suboptimal closure and wrapping capacity totals.
preimages
Type: reverse_reconstruction.
Compatible instances make the selected set closed and globally optimal with the reported sum; exact preimages also require residual tie choice. Many weight distributions share a sum and zero-weight disconnected vertices may be absent.
transition
Type: specialized_relation.
Cut capacity equals P minus selected weight for every implication-respecting source side.
order
Type: specialized_relation.
Implication cycles require all-or-none selection within each strongly connected component.
coordinate
Type: specialized_relation.
Increasing one vertex weight cannot lower optimum, though selected witness can change.
fiber
Type: specialized_relation.
Duplicate implications and self implications preserve objective; no universal witness uniqueness is claimed.
errors
Type: error_partition.
Public size caps precede input-order validation, then arithmetic/search. Exact cover budget exhaustion is not infeasibility; closure capacity overflow is not infeasibility. Bounded index arithmetic cannot overflow. Checked i128 arborescence arithmetic remains defensive. Allocation failure is process-level, not returned; no callbacks or external writes. Empty cases and deterministic ties follow API docs.
Limits
Partial syntax, no macro expansion/type resolution or full formal proof. No justified generic numerical surrogate for categorical witnesses/errors; supported 1/2/5/10% profiles remain absent, not fabricated. No timing claims. Allocation failure untested.
evidence
Evidence
2026-10-30: 4096 implication graphs on four vertices under three weight vectors (12288 cases); independent 16-subset closure oracle and witness checks.
Two debug and two release runs, compiled mutation detected by extremes_and_errors, restored positive rerun, strict all-target Clippy and twice-identical partial syntax. Logs: $MOVA_DATA/runs/octopus-wave26-combinatorial-2026-10-30. No timing measurement. Allocation failures and defensive i128 overflow unexercised.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/algorithms/src/maximum_weight_closure/mod.rs.groupant/