Paper Citation Record · LEDGER

Equivalence of sub-Laplacian on Polarized groups

As of 18 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2501.00576.

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

pith.paper-citation-record.v1
2501.00576 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T23:01:08.272339Z

measured 18 of 18 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

18 of 18 outbound references displayed

verified exact0
verified fuzzy15
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4c58eacb-4cc5-4e15-9d4b-0361758e13a7 · outbound

This paper cites Bonﬁglioli, E.

Equivalence of sub-Laplacian on Polarized groups Bonﬁglioli, E

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.508509Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ae350c7a-d902-4dba-a997-8d5846b4b513 · outbound

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

Equivalence of sub-Laplacian on Polarized groups Metric Lie Groups. Carnot-Carath\'eodory spaces from the homogeneous viewpoint

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-10T23:01:08.209388Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d99d8462-fece-405a-9d0e-d66c6705746d · outbound

This paper cites an unresolved cited work.

Equivalence of sub-Laplacian on Polarized groups Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:01:08.498305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation dcd4fcd5-c817-4e8d-897e-1831b259730b · outbound

This paper cites Harmonic morphisms between Riemannian man ifolds.

Equivalence of sub-Laplacian on Polarized groups Harmonic morphisms between Riemannian man ifolds

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.487957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation be94db96-6157-4b1e-a60d-6ede994b68d2 · outbound

This paper cites Riemannian submersions commuting with the Laplacian.

Equivalence of sub-Laplacian on Polarized groups Riemannian submersions commuting with the Laplacian

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.478060Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 690c3d5e-69e2-4667-8872-a58a7a1827da · outbound

This paper cites On the geometry of harmonic morphisms.

Equivalence of sub-Laplacian on Polarized groups On the geometry of harmonic morphisms

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.467989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation df9c805d-8db2-4339-883c-6cc4dd251754 · outbound

This paper cites Quasiregular maps on Car not groups.

Equivalence of sub-Laplacian on Polarized groups Quasiregular maps on Car not groups

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.456676Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a0b070e5-61bc-40f4-b573-4c8bdf46ad9e · outbound

This paper cites Helgason.

Equivalence of sub-Laplacian on Polarized groups Helgason

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.444237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 338d41a1-b4ac-45f3-b54e-8ebab89690d5 · outbound

This paper cites A mapping of Riemannian manifolds which pr eserves harmonic functions.

Equivalence of sub-Laplacian on Polarized groups A mapping of Riemannian manifolds which pr eserves harmonic functions

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.432852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8b0c3a33-84d5-4d45-9304-80f937c3cd4b · outbound

This paper cites Isometries of nilpotent met ric groups.

Equivalence of sub-Laplacian on Polarized groups Isometries of nilpotent met ric groups

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.420578Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b720f3c1-8f8e-4da0-8396-11e0431fd51a · outbound

This paper cites A primer on Carnot groups: homogenous grou ps, Carnot- Carathéodory spaces, and regularity of their isometries.

Equivalence of sub-Laplacian on Polarized groups A primer on Carnot groups: homogenous grou ps, Carnot- Carathéodory spaces, and regularity of their isometries

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.409448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fcfd12be-1a1e-4a51-9a5d-092035891a7d · outbound

This paper cites Isometries of Carnot groups and sub-Finsler homogeneous manifolds.

Equivalence of sub-Laplacian on Polarized groups Isometries of Carnot groups and sub-Finsler homogeneous manifolds

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.397948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a958ffc5-ee95-4af3-bdcf-0afe8a951e7b · outbound

This paper cites an unresolved cited work.

Equivalence of sub-Laplacian on Polarized groups Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-10T23:01:08.383353Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ee2c0e85-3a78-4b68-a2cb-bc79ca6a1015 · outbound

This paper cites McDuﬀ and D.

Equivalence of sub-Laplacian on Polarized groups McDuﬀ and D

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.369980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f9331b23-785d-4676-8735-847bf8c7fa26 · outbound

This paper cites Horizontally conformal submersions of CR-s ubmanifolds.

Equivalence of sub-Laplacian on Polarized groups Horizontally conformal submersions of CR-s ubmanifolds

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.355299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 378b0fa6-41db-41ca-b764-a524def252db · outbound

This paper cites The morphism property of subelliptic e quations on the roto-translation group.

Equivalence of sub-Laplacian on Polarized groups The morphism property of subelliptic e quations on the roto-translation group

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.342833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a9d68216-b821-48a9-a9ef-a3f33bb47777 · outbound

This paper cites Contact and Pansu diﬀerentiable maps on C arnot groups.

Equivalence of sub-Laplacian on Polarized groups Contact and Pansu diﬀerentiable maps on C arnot groups

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.330568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f1f0da16-8018-46e7-be36-7b5ce920337c · outbound

This paper cites Manifold maps commuting with the Laplacian.

Equivalence of sub-Laplacian on Polarized groups Manifold maps commuting with the Laplacian

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-10T23:01:08.318333Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

No inbound Pith citation observations are available.