Limitations & scope

This page is the concise website summary. The canonical engineering and scientific limitations document is LIMITATIONS.md at the repository root.

Every graph-classification result is configuration-bound. The main experiments are short-budget matched-capacity mechanism studies, primarily one layer, hidden_dim = 32, 10 to 20 epochs, Adam at 1e-2, and no batch normalisation. They are not competitive benchmark submissions and do not establish state-of-the-art model quality.

Empirical scope

• The H003 NCI1 Hodge-residual versus MLP comparison has a positive difference of +8.6 pp at the tested configuration. The former investigation-wide 59-comparison sensitivity table that once contextualized it (BH-surviving, Bonferroni-failing) is withdrawn and retained only in git history.
• Later H008c and H010 controls do not support a unique L_0 Hodge advantage. The matched normalized-adjacency arm is higher on MUTAG and NCI1 under the declared H010 family threshold, while PROTEINS detects no significant operator difference.
• H008c shows that the tested external-residual adjacency formulation recovers NCI1 performance after the normalized internal-self formulation does not. Because those formulations place and parameterize the self path differently, the result should not be generalized into a universal claim that residual connections alone are the sole mechanism.
• The historical H009 run is invalidated and carries no inferential status. Its corrective replication H009-R, run with the repaired invariant-tested operator, does not show a learned scalar sheaf improvement over fixed Hodge (p_BH = 0.428), and H41 remains inconclusive because the sheaf-versus-gin-residual deficit (p_BH = 0.0342) does not cross the preregistered 0.01 falsification threshold. Neither result is an equivalence claim.
• H011 on NCI1 does not show a positive L_1 advantage over the node-level controls. NCI1 is also structurally unsuitable for the intended triangle-rich mechanism because 96% of its graphs contain no triangles.
• H011b on COLLAB remains unresolved. The one-seed smoke result is directional only; the preregistered 30-seed confirmatory run has not completed.

Statistical scope

• A non-significant comparison is not an equivalence result. The project uses “no significant difference detected” unless an explicit equivalence procedure is performed.
• The hypothesis sequence is adaptive: later hypotheses were generated from earlier results, although each new experiment was preregistered before its own result was observed.
• The investigation-wide 59-comparison BH calculation was reported as a retrospective multiplicity sensitivity analysis over the realized comparison set, not as a prospectively guaranteed 5% program-level FDR procedure. It is currently withdrawn pending regeneration from the validated comparison set.
• Exact Wilcoxon power or minimum-detectable-effect guarantees are not stated without an explicit generative model or simulation. Future confirmatory studies should preregister a power or sensitivity analysis tied to the planned endpoint and threshold.

Toolkit scope

• RipsFiltration exposes Vietoris-Rips persistence. Alpha, Cech, witness, and general lower-star filtrations are not part of that public API.
• Differentiable cubical persistence and CubicalTopologyLoss are implemented and gradient-tested, but no powered end-to-end segmentation study currently demonstrates downstream benefit.
• The public feature pipeline provides persistence images and Betti curves. It is not a broad catalog of every persistence representation or diagram metric.
• HodgeMessagePassing is a minimal fixed-complex building block, not a variable-topology batched simplicial neural-network framework.
• The embedding audit is a prototype diagnostic with a heuristic persistence threshold, not an exact topological certification system.
• Persistence and clique-complex construction can become expensive on large or dense inputs. The current package does not claim a general high-throughput GPU persistence backend.

What is not claimed

• Topology improves graph classification or machine learning in general.
• Hodge propagation is generally better than a well-tuned GNN.
• H008c proves a universal residual-only causal mechanism.
• A non-significant result establishes equality.
• The current L_1 architecture provides unique higher-order signal on triangle-rich data.
• CubicalTopologyLoss improves every segmentation task.
• Results generalize beyond their stated datasets, architectures, training budgets, and statistical designs.

For detailed numerical, API, numerical-stability, and platform limitations, use the canonical LIMITATIONS.md.