Limitations & scope

Honest accounting is part of the contract. This page summarises the bounds; the full, continuously-maintained list lives in the canonical LIMITATIONS.md at the repository root.

The regime that bounds every accuracy number. All empirical results come from a deliberately constrained matched-capacity protocol: 1 layer, hidden_dim = 32, 10–20 epochs, Adam(lr = 1e-2), no batch normalisation, no learning-rate schedule, ~1.4–2.3k parameters per arm. On NCI1 the best arm reaches ~0.61–0.63 and the MLP baseline ~0.52, versus the ~0.80+ that properly-trained GNNs reach in the literature; the standard GNN baselines (GIN, GAT) collapse to the class prior (0.500) under this protocol. Every “outperforms X” statement is therefore at equal, deliberately-constrained capacity — it isolates architectural mechanism and is not a benchmark-performance or expressiveness claim.

Empirical scope

• Datasets: MUTAG (188), PROTEINS (1113), NCI1 (4110), COLLAB (5000, pending). One domain family (chemistry / proteins / social).
• Architecture: one architectural class (one-layer Hodge MP / message passing). Deeper architectures, attention, polynomial filters, and full simplicial networks are untested.

• Statistical power: minimum detectable effect

  r

  = 0.289 at n = 30. Null results are failures to reject at the tested power, not positive equality claims.

• Multiple testing: the NCI1 Hodge-vs-MLP result survives investigation-wide Benjamini–Hochberg but not Bonferroni.

Toolkit scope (selected)

• Only Vietoris–Rips and cubical persistent homology ship; no alpha/witness complexes, no diagram distances (bottleneck/wasserstein) in the core.
• The Hodge message-passing layer is a minimal building block (σ(L̃ₖ x W + b)), not a competitive simplicial neural network.
• The embedding audit is a prototype with a heuristic significance threshold.
• No GPU-batched persistence; large point clouds and dense clique complexes are compute-heavy.

What is explicitly not claimed

• “Topology helps graph classification” — not supported across datasets.
• “Hodge is better than GNNs” — refuted (H008c; and the GNN baselines here are capacity-starved, not competitive).
• “L₁ captures unique structural signal” — not yet tested at rigor (triangle-rich COLLAB run is pending).
• Any result beyond the tested configuration.

For the complete, authoritative list of failure modes and deferred features, see LIMITATIONS.md.