Elamur Groupantsalgorithm-k-core
The groupant beside algorithms/src/k_core/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 | bounded checked | 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 |
compatible_inputs | reverse_reconstruction | partial source derived | compatible_inputs |
subset_certificate | maximality_certificate | partial source derived | subset_certificate |
nested_cores | parameter_monotonicity | partial source derived | nested_cores |
idempotence | fixed_point | partial source derived | idempotence |
edge_extension | monotone_extension | partial source derived | edge_extension |
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
k_core mod
Original std-only Rust. Prospective model is retained beside implementation. Source citations identify algorithm provenance; no copied implementation. Exact bounded graph semantics are useful independently of any unmeasured optimization. Finite oracle checks and mutant discrimination improve confidence; groupant count alone proves no improvement.
model
k_core mod model
Forward
Simple undirected graph n<=256,m<=65536. Repeatedly delete vertices with live degree below k; return ascending survivors, unique maximal induced minimum-degree-k subgraph. FIFO deletion, each edge visited O(1) after O(V^2+E) validation. O(V^2+E) time/storage. k=0 retains all. Seidman (1983).
Invariant
Deleted vertices cannot belong to any minimum-degree-k induced subgraph. For live vertices degree equals count of live neighbors; survivor set is maximal.
Cost
Simple undirected graph n<=256,m<=65536. Repeatedly delete vertices with live degree below k; return ascending survivors, unique maximal induced minimum-degree-k subgraph. FIFO deletion, each edge visited O(1) after O(V^2+E) validation. O(V^2+E) time/storage. k=0 retains all. Seidman (1983).
nonbehavior
Type: behavior_complement. Let R be the deterministic relation specified by Forward including validation precedence and tie rules, X the declared input type and Y its Result type. Behavior complement is (X times Y) minus R. Specifically outputs violating Deleted vertices cannot belong to any minimum-degree-k induced subgraph. For live vertices degree equals count of live neighbors; survivor set is maximal. are excluded; a valid-input Err or a wrong successful witness is excluded. Resource, cycle and structural rejections are determined before algorithmic output.
compatible_inputs
Type: reverse_reconstruction. Given survivor set S, compatible graphs make G[S] minimum degree at least k and every vertex outside S eventually peelable. For k=1, a three-vertex path and a triangle differ but both can yield all vertices when no isolated vertices. Errors identify violated validation predicates.
subset_certificate
Type: maximality_certificate. Output equals union of all vertex subsets whose induced minimum degree is at least k. Union preserves the minimum-degree predicate and gives unique maximality.
nested_cores
Type: parameter_monotonicity. For k<=l, core_l(G) is a subset of core_k(G). core_0(G) is every vertex; k>=n gives empty on simple n-vertex graphs.
idempotence
Type: fixed_point. Restrict G to returned vertices, retaining their labels. Applying k-peeling again deletes none.
edge_extension
Type: monotone_extension. Adding an absent undirected edge cannot remove vertices from a k-core; the prior induced feasible set still witnesses membership.
Limits
Partial syntax omits macro expansion and type resolution. No executable approximate profile: categorical graph semantics and feasibility have no justified percentage relaxation here. Integer operations are bounded by caps; flow uses checked i128/u64 arithmetic, with Overflow defensive under current caps. No callbacks. Allocator failure is outside typed status.
evidence
Evidence — 2026-10-30
Eleven tests across five algorithms, including independent exhaustive small-domain characterization. This file belongs to k_core. Two debug and two optimized runs matched normalized statuses. Strict clippy-driver --test -D warnings passed. A compiled production mutant failed a named assertion; exact bytes restored and positive rerun passed. Raw receipts: $MOVA_DATA/runs/octopus-wave25-graphs-2026-10-30/k_core-*.txt. No timing or whole-system improvement claim. Source SHA-256: 37a416e1386fa1f72fcf9fa8771e88af0a2a98d0bf51b94df3605c8462065707.
prospective
Prospective model — 2026-10-30
Simple undirected graph n<=256,m<=65536. Repeatedly delete vertices with live degree below k; return ascending survivors, unique maximal induced minimum-degree-k subgraph. FIFO deletion, each edge visited O(1) after O(V^2+E) validation. O(V^2+E) time/storage. k=0 retains all. Seidman (1983). Allocation failure is outside typed errors. Resource caps precede vertex/edge validation. No callbacks. Exact categorical output has no justified percentage surrogate; executable approximation profiles unsupported.
This page in Markdown → https://md.groupants.elamur.ai/free/en/mova/algorithms/src/k_core/mod.rs.groupant/