| Stable and unstable manifolds | definition | definition 1 | arxiv |
| Stability of the empirical modal projection | statement | lemma E.1 | arxiv |
| Gromov-Hausdorff convergence of the GGDPC dendrogram | statement | theorem 5.3 | arxiv |
| GGDPC dendrogram via single linkage clustering | statement | proposition 5.2 | arxiv |
| Local geometry near the local mode; see also Lemma 5 | statement | lemma F.2 | arxiv |
| Population bound for the 1NN uphill shift in the tube | statement | lemma F.9 | arxiv |
| Convergence of the GGDPC graph distance | statement | theorem 7.1 | arxiv |
| Regularity of the gradient-flow length | statement | lemma F.3 | arxiv |
| 8SKVH1XGAJ | definition | definition 4 | arxiv |
| Essential uniform finiteness of the population GGDPC graph distance | statement | proposition H.1 | arxiv |
| Sufficient conditions for local sample uphill availability | statement | proposition G.1 | arxiv |
| $C^N$-conjugation | definition | definition 2 | arxiv |
| Sample GGDPC path through a boundary saddle | statement | lemma G.2 | arxiv |
| Stability of the oracle GGDPC path | statement | theorem 6.2 | arxiv |
| Wasserstein-1 convergence of the density waterfall | statement | theorem 7.2 | arxiv |
| Length stability in a separatrix tube | statement | lemma F.7 | arxiv |
| Stability of the critical points of $\hat p$ | statement | lemma G.3 | arxiv |
| Population bound for the 1NN uphill shift outside the modal core | statement | lemma F.4 | arxiv |
| Completion of the sample path in the modal region | statement | lemma G.6 | arxiv |
| Hierarchy of the GGDPC dendrogram | statement | proposition 5.1 | arxiv |
| Consistency of GGDPC modes | statement | theorem 4.1 | arxiv |
| Stability of the sample GGDPC path | statement | theorem 6.3 | arxiv |
| Oracle GGDPC path through a boundary saddle point | statement | lemma F.8 | arxiv |
| K4AM9TSA4W | statement | proposition B.1 | arxiv |
| Uniform local sample count | statement | lemma F.1 | arxiv |
| Basin invariance of the oracle GGDPC path | statement | lemma F.10 | arxiv |
| Basin invariance of the sample GGDPC path | statement | lemma G.5 | arxiv |
| Convergence of GGDPC under the ARI | statement | theorem 4.2 | arxiv |
| $C^N$-linearization | definition | definition 3 | arxiv |
| Gradient flow separation from the separatrix | statement | lemma 6.1 | arxiv |
| Integrated graph distance control near the full separatrix | statement | lemma I.1 | arxiv |
| Sample update before the terminal modal neighborhood | statement | lemma G.4 | arxiv |
| Stability of the fixed-$\epsilon$ oracle GGDPC path length | statement | lemma F.6 | arxiv |
| Uniform sample coverage | statement | lemma C.1 | arxiv |
| Local repulsion from the separatrix without linearization | statement | lemma D.1 | arxiv |
| Oracle modal-core length | statement | lemma F.5 | arxiv |
