What happens when a shortest-path assumption fails?

What will you examine?

Positive graph: A→B:2, A→C:5, B→C:1, B→D:4, C→D:1; source A.

Negative-edge graph: A→B:1, A→C:2, C→B:-3; source A.

Negative-cycle graph: A→B:1, B→A:-2; source A.

What does the question assume?

Finite weights, an existing source and explicitly listed neighbor vertices; heap ties need comparable labels.

Dijkstra requires nonnegative weights. Finite Bellman–Ford distances require no reachable negative cycle.

What should you compare?

Hand-derived positive distances are A:0, B:2, C:3, D:4. Both methods should be compared with this map.

The negative-edge graph has distances A:0, B:-1, C:2. The proposed Dijkstra helper rejects that input; Bellman–Ford should return the finite distances.

The reachable cycle has weight -1 and should be rejected. Retain distinct expected rejection, unexpected non-rejection, crash, timeout and missing-output cases.

What could the evidence establish?

Three fixed graphs do not establish universal correctness, performance or support for arbitrary input data.

Unreachable infinite distances need an explicit strict-JSON representation in any extension.

No qualified current predicate verifies these algorithms. An author's matching distance map remains an author observation.

Prepare, then authorize the work.

1. Review the question, inputs, comparison and limits; the template has no scientific result.

2. Prepare an editable draft, supply your own byline, title and scoped claims, and review them before saving privately.

3. Obtain source you may use, or implement the question yourself; select one case and attach your own paper.md in the source ZIP. Do not run submitted code on your host.

4. Upload opaque source bytes through your project. Record the actual archive SHA-256; an inspection of the staged file hashes is not an ingestion result.

5. Review and accept the current bounded ingestion quote. Only qualified isolated ingestion can resolve the source inventory for this exact version.

6. Then review and accept a separate quote for the one author job. Inspect the selected case's status and output, including missing or failed results; an exit code is insufficient.

7. Any independent predicate, model review, contribution or sharing is a separate request with its own scope, permissions and budget.

Bring source you may use.

The inspected original source remains local staging material. Its MIT/CC BY/CC0 terms are proposed, not a released license grant. Obtain permitted source or supply your own implementation. The source-version digest is not an archive digest.

Archive download unavailable. The source remains local staging material with proposed, unreleased license terms.