Paper Citation Record · LEDGER

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group

As of 17 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2509.06563.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2509.06563 v1

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:31:35.875763Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T19:57:58.374690Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

12 of 12 outbound references displayed

verified exact3
verified fuzzy0
unresolved9
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d6541aac-285c-4671-9bc4-ef837c0b3fe3 · outbound

This paper cites Failure of the measure contraction property via quotients in higher-step sub-Riemannian structures.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group Failure of the measure contraction property via quotients in higher-step sub-Riemannian structures

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T16:31:35.781723Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5233dd7a-e6f1-4819-9677-3ab472215cd2 · outbound

This paper cites Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group Optimal transport in Lorentzian synthetic spaces, synthetic timelike Ricci curvature lower bounds and applications

Reference 7

Resolution: verified exact; raw_fallback, observed 2026-08-15T16:31:36.310972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 3aa5b38d-9121-4c46-b2bf-fccd9ed631a2 · outbound

This paper cites On the geometry of synthetic null hypersurfaces.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group On the geometry of synthetic null hypersurfaces

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T16:31:35.822498Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 55384c59-4c3c-49e6-a5ed-9f4446c0f1f7 · outbound

This paper cites Metric Lie Groups. Carnot-Carath\'eodory spaces from the homogeneous viewpoint.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group Metric Lie Groups. Carnot-Carath\'eodory spaces from the homogeneous viewpoint

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-15T16:31:35.834164Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d394bb0c-0dda-4b65-8d67-0afb91d224e0 · outbound

This paper cites Universal non-CD of sub-Riemannian manifolds.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group Universal non-CD of sub-Riemannian manifolds

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T16:31:35.875763Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0262ba7-3b94-4cdf-9843-35608efc4d71 · outbound

This paper cites Sub-Riemannian structures do not satisfy Riemannian Brunn-Minkowski inequal- ities.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group Sub-Riemannian structures do not satisfy Riemannian Brunn-Minkowski inequal- ities

Reference 57

Resolution: verified exact; raw_fallback, observed 2026-08-15T16:31:36.163520Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation c54478dd-6f79-44bb-ad6c-31b0fcc18aff · outbound

This paper cites Reachable sets for the Heisenberg sub-Lorentzian structure onR3. An estimate for the distance function.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group Reachable sets for the Heisenberg sub-Lorentzian structure onR3. An estimate for the distance function

Reference 65

Resolution: unresolved; no resolver link, observed 2026-08-15T16:31:35.845468Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 683e1c8c-c6eb-4ece-a498-1c3b74d81348 · outbound

This paper cites Birkhäuser Verlag, 1996, pp.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group Birkhäuser Verlag, 1996, pp

Reference 144

Resolution: verified exact; doi, observed 2026-08-15T16:31:36.000173Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 40375c91-d4ea-4e72-b643-8b5b94acdffd · outbound

This paper cites Cambridge University Press, 2020, pp.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group Cambridge University Press, 2020, pp

Reference 181

Resolution: unresolved; no resolver link, observed 2026-08-15T16:31:35.734307Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca4ebe6d-e253-4317-98e8-37899efa87c1 · outbound

This paper cites Existence and uniqueness of optimal transport maps.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group Existence and uniqueness of optimal transport maps

Reference 259

Resolution: unresolved; no resolver link, observed 2026-08-15T16:31:35.790118Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 114c6c59-f44b-4bf7-893e-3a9c4e0ae08d · outbound

This paper cites A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group A nonlinear d'Alembert comparison theorem and causal differential calculus on metric measure spacetimes

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-15T16:31:35.768777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 22c5817f-ae03-46a0-a528-af3384279ef7 · outbound

This paper cites Optimal transport on the sub-Lorentzian Heisenberg group.

Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group Optimal transport on the sub-Lorentzian Heisenberg group

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-15T16:31:35.774616Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation f25c3aac-552a-4aaa-acad-2fa42d3cc624 · inbound

Sub-Finslerian Interpolation Inequalities cites this paper.

Sub-Finslerian Interpolation Inequalities Hausdorff dimension and failure of synthetic curvature bounds in the sub-Lorentzian Heisenberg group

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T19:57:58.374690Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.