Proof lineage
These graphs include only citations needed for a marked mathematical statement—not background, illustration, or general literature context. Each deeper layer follows only dependencies that can affect the target paper.
Available maps
arXiv:2607.17021v1
A statement-restricted graph for the proof-critical sources behind the homogeneous-dynamics thickness theorem, its weighted Diophantine application, and the paper's separately marked ancillary claims. Contextual citations and results reproved in full are excluded.
48 nodes · 53 proof-critical links
Open dependence graph →Uniform Distribution Theory 17(1), 89–104 (2022) · arXiv:2107.08084v1
A statement-restricted graph for the winning, hyperplane-absolute-winning, exponent-bound, and best-approximation claims in the published paper. Historical and metric-context citations that do not enter those proofs are excluded.
11 nodes · 13 proof-critical links
Open dependence graph →arXiv:2503.21180v3
A statement-restricted graph for the transference, second-moment, lacunary escaping-set, and product-dimension inputs used in the paper. Historical attributions, contextual literature, and arguments reproduced in the focal paper or an included source are excluded; published books are terminal.
7 nodes · 6 proof-critical links
Open dependence graph →arXiv:2504.02258v1
Statement-restricted proof-dependence graph for the submanifold genericity theorems, the multiplicative Dani correspondence, the full-measure half of the Khintchine-type theorem, and Proposition 1.7. It includes the uncited cusp-volume input required on p. 28, its independent Schmidt 1957 proof repair, and two source-use failures: BEG20 is applied after dropping its strong-spectral-gap hypothesis, and BG23 is cited with the wrong theorem number.
33 nodes · 38 proof-critical links
Open dependence graph →arXiv:2506.00941v2
Statement-restricted proof-dependence graph for the projection formula, the braid, graphical and natural-unit-interval interpretations, and the type-B signed-source-component extension. It traces the two independent projection sources and the signed-graph arrangement inputs to exact published claims, while stopping at published books and monographs. Context, comparison, historical citations and results reproved internally are excluded. The type-A and natural-unit-interval results check, but an exact rank-two counterexample disproves the type-B projection and coefficient branch.
14 nodes · 16 proof-critical links
Open dependence graph →arXiv:2603.24885v1
Statement-restricted proof-dependence graph for the contribution-one theorem and its tree-contribution consequences. The graph follows the exact face-bijection input through Bernardi's region bijection and its counting step. It excludes background, historical citations, independently sufficient alternative sources, and results reproved inside the focal paper.
5 nodes · 5 proof-critical links
Open dependence graph →arXiv:2603.24886v1
A statement-restricted dependence graph for the right-inverse construction, the bijectivity criterion for (m, epsilon)-arrangements, and the necessity theorem inside the transitive class. Only external results that can affect those marked claims are included. Historical comparisons, alternative proofs, and citations used only for context are excluded; expansion stops at published books and monographs.
4 nodes · 3 proof-critical links
Open dependence graph →Results in Mathematics 80(8), 236 (2025) · arXiv:2401.00614v3
A statement-restricted graph for arXiv:2401.00614v3. It traces the uniform-distribution, Schmidt-game, Hausdorff-dimension, and Borel-determinacy results actually imported by the v3 proofs. Theorem 2.6 is marked self-contained. Contextual citations, an earlier bound that is not used, and the different determinacy citation added only in the later journal version are excluded.
6 nodes · 6 proof-critical links
Open dependence graph →arXiv:2603.25988v1
A statement-restricted graph for the total-density criteria, their uniform-approximation consequences, the convex-hull criterion, and the separately marked optimality branch. Context, historical attributions, alternative proof sources, and arguments reproduced inside the focal paper are excluded.
4 nodes · 3 proof-critical links
Open dependence graph →Mathematika 72(2), e70089 (2026) · arXiv:2508.01912v1
A statement-restricted graph for the zero–full measure theorem, its weighted transference inputs, and the separately marked second-moment and geometry-of-numbers branches. Contextual citations, analogies, alternative routes, and sources whose needed result is reproved in the focal paper are excluded.
18 nodes · 19 proof-critical links
Open dependence graph →