The problem
Systems may be called decentralized because data or computation is distributed even when coordination or authority remains centralized. The paper calls the missing transferable definition the Decentralization Problem.
General purpose
Turn an ambiguous system-level claim into subject-specific, graph-grounded statements.
The formal response
The ontology separates realization multiplicity δ, vertex support λ, and the anchor-relative count µ of center regions reached by a subject.
The analytical response
Each declared subject–anchor pair receives Void Tolerance and Imperviousness values after it crosses the logical boundary µ > 1.
The tool
Provide a graph, an evaluation profile, vertex realizations, and center regions; the workbench returns classifications, vectors, aggregates, visualizations, comparisons, and proposition traces.
Paper basis: Abstract; §§II, VII–XI, XII, and XIV.
Model
Draw or upload a topology and place subject realizations on its vertices.
Evaluate
Inspect pair vectors, their profile aggregate, and the ontology classification.
Explore
Generate batches, explain repeated values, and compare selected systems.
From a topology to a qualified decentralization claim
Start with the visual workflow. Open the method view when you need the proposition trace and implementation scope.
Topology
Specify vertices and connections on a square plane.
Profile
Declare each subject–anchor pair and set δ and λ through vertex assignments.
Centers
Define Ca; singleton completion supplies uncovered vertices.
Vectors
Infer µ, classify the pair, then evaluate both analytical coordinates.
Begin with a paper example or a generated batch
The canvas includes the worked federated-learning and permissioned-blockchain models. Patterned simulation presets are experimental generator heuristics.
Modeling layer
Specify one system model
Define Gt, the evaluation profile Es, subject projections, and anchor center regions.
Topology realization Gt
0 vertices · 0 edges
Drag vertices to arrange · Wheel to zoom · Drag empty space to pan
Current canvas only
Canvas result
One evaluated canvas snapshot.
Canvas not evaluated
Complete the pre-evaluation checks on the canvas, then evaluate the model.
Model batches
Simulate system models
Generate and evaluate reproducible models.
Browser limits250,000 vertices/model · 100,000 models/batchWorkload checks protect memory.
Randomize a preset
Choose free or patterned generation.
Presets are generator heuristics, not ontology classes.
Topology generator
Choose one family or a weighted mix.
Weighted mixed-family catalogue
Enable any families and assign relative weights. A weight of 4 is selected four times as often as a weight of 1.
Topology parameters
Anchor and center synthesis
Generate one Ca per anchor and simulated system.
These actor/domain models are transparent generator heuristics. The paper fixes the center-family semantics, not empirical probabilities for owners, authorities, trust roots, or governing bodies.
Subject synthesis
Generate support, multiplicity, placement, and ε; then select an anchor strategy.
Placement changes support; entries using the same anchor share one generated center family Ca.
Distribution preview
Deterministic and seed-based.
Generate and evaluate batch
Estimate pending.
Simulation batch only
Batch results
Generated systems only.
No simulation batch
Generate a batch to populate this workspace. Canvas evaluations remain in Canvas result.
Arbitrary model set
Compare systems
Compare canvas, uploaded, and simulated models. Aggregate claims require compatible subject–anchor profiles and center interpretations.
No systems selected
Evaluate the current canvas and add it, upload one or more complete JSON snapshots, or add systems from a simulation batch.
Paper-aligned implementation
Ontological, logical, modeling, and analytical layers
The evaluator preserves the paper's separation of δ, λ, anchor-relative µ, logical classification, and analytical degree.
Running worked-example checks…
Multiplicity, support, and centers
For subject u, δ(pu) counts realization particulars, λ(pu) counts supporting vertices, and µ(pu,a) counts the completed anchor-center regions intersecting that support.
- Centralized pair
- µ(pu,a) = 1
- Decentralized pair
- µ(pu,a) > 1
- Distributed subject
- λ(pu) > 1
- Dimensionality
- |{(u,a)∈Es : µ>1}|
Proposition 1 — Void Tolerance
TL(u,a) = 0if µ(pu,a) = 1TL(u,a) = 1if |Gs| = 0, |Gt| > 1, λ > 1TL(u,a) = exp(−rv² · |Gs|ε / |Gt|)otherwise
rv counts subject-supporting articulation vertices. |Gs| is the largest combined order outside the subject-prioritized reference component after removal.
Proposition 2 — Imperviousness
IL(u,a) = 0if |E(Gt)| = 0 or µ(pu,a) = 1IL(u,a) = 1if re = |Gt| − 1 and λ > 1IL(u,a) = exp(1 − (λ/|Gt|)−ε²/re)otherwise
re is the minimum number of edge deletions required to compromise a subject-supporting vertex.
Decentralization vectors and aggregate
Each declared pair yields d⃗u,a = [TL(u,a), IL(u,a)]T. The profile aggregate is the equal element-wise arithmetic mean.
A(Es) = (1/|Es|) Σ(u,a)∈Es d⃗u,a
Like-for-like comparison requires compatible evaluation profiles, center interpretations, parameter assignments, and aggregation assumptions.
Implementation scope
- Undirected, simple graphs; self-loops and duplicate edges are rejected.
- Every evaluation is a fixed-time snapshot.
- Each declared anchor owns one system-level center family; regions may overlap and uncovered vertices receive singleton completion.
- Ownership, authority, trust, and governance are editable naming templates, not fixed ontology subclasses.
- Disconnected graphs are accepted with an explicit component-forest warning.
- ε > 0 changes pair sensitivity, not aggregate vector weighting.
- Ontology classes depend on µ, never on arbitrary metric thresholds.
- Coverage λ/|G| and λ/δ are descriptive visual aids; distribution remains λ > 1.
- Simulation laws, actor/domain models, jitter, and edge noise are experimental generators—not additions to the ontology.
Source
“Defining Decentralization: An Ontological Perspective,” §§VIII–XI, Definition 5, Propositions 1–2, and Figures 4–6.