Elamur Groupantsalgorithm-functional-graph-decomposition
The groupant beside algorithms/src/functional_graph_decomposition/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
Migration: consolidated into model.md, 2026-11-04, operator decision; fresh hash-bound references to the former files were rebound to the sections below.
descriptant
algorithm-functional-graph-decomposition
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-functional-graph-decomposition
Domain
<=1000000 valid zero-based successors; cycles, per-vertex cycle ID, original entry coordinate, distance.
Forward
Peel indegree-zero tails; enumerate residual cycles from least unseen original coordinate in successor order; reverse peeling propagates entry, ID and distance.
Invariant
Every vertex belongs to exactly one eventual cycle; entry is first cycle vertex encountered and distance is the exact number of successor applications to entry.
Cost
O(V) time and memory.
nonbehavior
Type: behavior_complement.
Exclude wrong coordinate conventions, noncanonical cycle rotations/order, positive cycle distances, or entries not reached at the reported distance.
preimages
Type: reverse_reconstruction.
Cycles reconstruct successor edges on cycle vertices exactly. Tail v with distance d>0 may point to any vertex with same entry and distance d-1, so tail predecessors are generally ambiguous. These choices reconstruct exactly the decomposition under canonical IDs.
transition
Type: specialized_relation.
For noncycle v, distance[v]=distance[successor[v]]+1 and entry and ID are inherited.
order
Type: specialized_relation.
Cycle vertices have entry[v]=v and distance zero; listed cycle orientation follows successor.
coordinate
Type: specialized_relation.
Relabeling preserves distances and cycle membership but recanonicalizes cycle IDs/rotations.
fiber
Type: specialized_relation.
Deleting a leaf tail preserves remaining entry coordinates and distances while coordinate renumbering must be explicit.
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: All successor functions up to six vertices (50070 cases including empty); independent per-start walk until repetition validates entry, distance and cycle edges.
Two debug and two release runs, compiled mutation detected by coordinates_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/functional_graph_decomposition/mod.rs.groupant/