Elamur Groupantsalgorithm-minimum-arborescence-tests
The groupant beside algorithms/src/minimum_arborescence/tests.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 |
oracle | oracle_relation | partial source derived | oracle |
mutant | counterfactual_relation | partial source derived | mutant |
coverage | coverage_relation | partial source derived | coverage |
Model text
descriptant
algorithm-minimum-arborescence-tests
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.
Independent cost review falsified the original scan bound. The revised scan stops at every prior traversal; prospective repair and parent source retained in $MOVA_DATA/runs/octopus-wave26-combinatorial-2026-10-30/arbo-repair-prospective.md and arbo-parent.rs.
model
algorithm-minimum-arborescence-tests
Domain
Finite fixture/assertion observations; trusted compiler and test runner; passing is not unrestricted equivalence.
Forward
4096 directed graph subsets on four vertices, four roots each, mixed signed costs; independent edge-subset reachability/indegree oracle.
Invariant
Oracle is independently formulated; compare objective/feasibility plus witness invariants, not exact tie witness except named fixtures.
Cost
O(VE+V^2) time, O(V+E) memory.
nonbehavior
Type: behavior_complement.
Accepted fixture/output pairs exclude mismatched oracle objectives, invalid witnesses and wrong tested errors. Outside-fixture behavior remains unconstrained.
preimages
Type: reverse_reconstruction.
A pass reconstructs all implementations agreeing on the finite observations, including faulty unseen extensions. A failed assertion reconstructs unequal compared values at that fixture; it does not uniquely identify a source bug.
oracle
Type: oracle_relation.
4096 directed graph subsets on four vertices, four roots each, mixed signed costs; independent edge-subset reachability/indegree oracle.
mutant
Type: counterfactual_relation.
Compiled production mutant must fail the named contractions_extremes_errors assertion; exact restoration followed by positive rerun.
coverage
Type: coverage_relation.
Adding fixtures intersects the passing implementation set; profile repeats constrain profile-dependent bugs without proving universal correctness.
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.
Cost repair epoch 2026-10-30
Added completed_traversals_are_not_rewalked: root-reaching chains through 512 vertices assert exactly n-1 primary parent advances. Exhaustive 701 root-fixed parent functions through n=5 compare cycle sets and noncycle labels with independent repeated-vertex walks. Nested contraction family k=2,3,4,8,16,32,64,128 has a necessary root-to-star edge of cost k and a matching zero-edge completion witness; tiny instances also use independent edge-subset oracle. Reverting the visited predicate must fail the named visit-count assertion after compilation.
The initial implementation revisited completed root-reaching chains per start. Independent review exhibited 1065024 primary steps for n257/e383 in the nested family, contradicting the originally declared asymptotic bound. Retain that falsified epoch; the revised source enforces a single stamp per round. Counts are operation observations, not runtime benchmarks.
evidence
Evidence
2026-10-30: 4096 directed graph subsets on four vertices, four roots each, mixed signed costs; independent edge-subset reachability/indegree oracle.
Two debug and two release runs, compiled mutation detected by contractions_extremes_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.
Repair epoch: five focused tests twice debug/release, identical normalized outcomes; compiled completed-traversal stop-condition mutant failed the visit-count assertion and exact restoration passed. Nested-contraction counted probe compares parent and repaired sources without timing. Refreshed paired syntax and source bindings; strict algorithm all-target Clippy. Repair logs use arbo-* in the same receipt directory.
Counted nested family (k=8,16,32,64,128): parent primary advances 324, 2312, 17424, 135200, 1065024; repaired 100, 392, 1552, 6176, 24640. Both return objective k in every case. These are operation counts, not elapsed time or throughput. The retained parent source and instrumented sources are external receipts.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/algorithms/src/minimum_arborescence/tests.rs.groupant/