| Sufficient criterion for time negligibility | statement | proposition 3.13 | arxiv |
| Approximation and representation | statement | theorem 3.11 | arxiv |
| Sparsity of nonapproximable points | statement | proposition 2.9 | arxiv |
| Causal speed on $\Prob(\X)$ | definition | definition 4.3 | arxiv |
| Reciprocal $p$-subslope | definition | definition 3.8 | arxiv |
| Inclusion in maximal achronal sets | statement | lemma 2.6 | arxiv |
| Characterization of causality | statement | theorem 2.26 | arxiv |
| Monotonicity | statement | proposition 2.29 | arxiv |
| Maximal weak subslope vs. maximal relaxed subslope | statement | proposition 4.12 | arxiv |
| Causal speed on $\X$ | definition | definition 4.2 | arxiv |
| Chronological continuity points | definition | definition 2.13 | arxiv |
| Sobolev class | definition | definition 3.2 | arxiv |
| Time negligibility of infinities | statement | corollary 3.31 | arxiv |
| Action estimate | statement | lemma 4.29 | arxiv |
| Invariance of Sobolev class under modifications | statement | corollary 3.29 | arxiv |
| Forward and backward slopes and local steepness | definition | definition 2.18 | arxiv |
| Integration by parts | statement | proposition 4.23 | arxiv |
| Existence, uniqueness and properties of gradient flows | statement | theorem 4.16 | arxiv |
| Weak subslope | definition | definition 4.8 | arxiv |
| Properties and a priori estimates | statement | theorem 4.19 | arxiv |
| Lattice and concavity} properties | statement | lemma 2.20 | arxiv |
| Lipschitz continuity and semiconvexity | statement | proposition 2.32 | arxiv |
| Coarea-type locality | statement | lemma 3.32 | arxiv |
| Monotonicity of subdifferentials | statement | lemma 4.24 | arxiv |
| Pathwise characterization of maximal weak subslope | statement | lemma 4.10 | arxiv |
| Chain rule for maximal weak subslope | statement | theorem 4.14 | arxiv |
| Convexity and continuity properties of reciprocal $p$-subslopes | statement | proposition 3.9 | arxiv |
| Steep functions | definition | definition 2.11 | arxiv |
| Minima of reciprocal $p$-subslopes are reciprocal $p$-subslopes of sums | statement | lemma 3.19 | arxiv |
| Recovery sequences for sums | statement | lemma 3.4 | arxiv |
| Identification of maximal weak and relaxed subslopes | statement | theorem 4.33 | arxiv |
| $p$-D'Alembertian | definition | definition 4.20 | arxiv |
| Competitors for Kantorovich duality | definition | definition 2.24 | arxiv |
| Energies and subslopes of torn functions | statement | lemma 3.23 | arxiv |
| Maximal weak subslope | statement | theorem 4.9 | arxiv |
| E77ZY8NQCH | statement | proposition 4.18 | arxiv |
| Modifications on time negligible sets | statement | corollary 3.20 | arxiv |
| Maximal relaxed subslope | definition | definition 3.10 | arxiv |
| Reciprocal subslopes of maxima and minima | statement | lemma 3.21 | arxiv |
| Sobolev class induced by maximal weak subslope | definition | definition 4.11 | arxiv |
| Locality of maximal weak subslope | statement | proposition 4.13 | arxiv |
| Gradient flow trajectory | definition | definition 4.15 | arxiv |
| Closedness | statement | corollary 2.17 | arxiv |
| Properties of representatives *{Lem. 3.2 | statement | proposition 2.12 | arxiv |
| Time semicontinuity | statement | lemma 2.31 | arxiv |
| Basic properties | statement | proposition 2.27 | arxiv |
| Superadditivity | statement | proposition 3.27 | arxiv |
| Measurable, everywhere defined, and causal representatives | statement | proposition 2.16 | arxiv |
| Time separation function | definition | definition 2.1 | arxiv |
| Lorentz--Wasserstein distance | definition | definition 2.22 | arxiv |
| Hamilton--Jacobi inequality with maximal relaxed subslope | statement | lemma 4.28 | arxiv |
| ``Almost-always'' regularity | statement | corollary 3.18 | arxiv |
| Pointwise maximality of maximal relaxed subslope | statement | proposition 3.25 | arxiv |
| $p$-Cheeger energy | definition | definition 3.1 | arxiv |
| Existence of a bounded 1-steep function | statement | lemma 2.21 | arxiv |
| Universal measurability of infima | statement | lemma 2.15 | arxiv |
| Metric measure spacetime | definition | definition 2.3 | arxiv |
| Test plan | definition | definition 4.6 | arxiv |
| Lower semicontinuity and convexity | statement | corollary 3.7 | arxiv |
| Convergence of perturbations | statement | corollary 3.28 | arxiv |
| Causal functions | definition | definition 2.10 | arxiv |
| Approximable points | definition | definition 2.7 | arxiv |
| Bound on local steepness constant | statement | proposition 2.33 | arxiv |
| Gradient flow | definition | definition 4.17 | arxiv |
| Locality | statement | proposition 3.30 | arxiv |
| Reverse triangle inequality | statement | proposition 2.23 | arxiv |
| Spatial upper semicontinuity | statement | lemma 2.30 | arxiv |
| Kuwada {type informational bound for aging along a gradient flow | statement | lemma 4.27 | arxiv |
| Mass allocation | statement | proposition 4.25 | arxiv |
| Time negligibility of achronal sets | statement | proposition 3.16 | arxiv |
| Kantorovich duality with steep functions | statement | theorem 2.25 | arxiv |
| Chain rule | statement | theorem 3.33 | arxiv |
| Compatibility of maximal weak subslopes | statement | lemma 4.31 | arxiv |
| Metric spacetimes | definition | definition 2.2 | arxiv |
| Lifting theorem | statement | theorem 4.4 | arxiv |
| Time negligible set | definition | definition 3.12 | arxiv |
| Supersolution to Hamilton--Jacobi equation | statement | theorem 2.34 | arxiv |
| Infinity sets | statement | proposition 3.15 | arxiv |
| Semicontinuity of the relaxed subslope | statement | corollary 3.26 | arxiv |
| Differentiation of reverse triangle inequality | statement | theorem 4.1 | arxiv |
| Achronal set | definition | definition 2.5 | arxiv |
| Energy dissipation | statement | proposition 4.26 | arxiv |
| Lattice and convexity} properties | statement | lemma 3.5 | arxiv |
| Heredity of bounds for a short time | statement | lemma 4.30 | arxiv |
| Compatibility of maximal relaxed subslopes | statement | lemma 4.32 | arxiv |
| Characterizing $\L^0$ convergence | statement | lemma 2.14 | arxiv |
