Paper Citation Record · LEDGER

The spectral Einstein functional for the Dirac operator with torsion

As of 22 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 3 inbound Pith citation observations for arXiv:2412.08028.

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

pith.paper-citation-record.v1
2412.08028 v4

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T18:36:41.142894Z

measured 26 of 26 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-11T00:19:52.627443Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T13:00:57.953861Z

Reference resolution

23 of 23 outbound references displayed

verified exact0
verified fuzzy21
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation bfa60adf-10d2-4a8a-bf5e-46d99945c9e7 · outbound

This paper cites Dabrowski., A.

The spectral Einstein functional for the Dirac operator with torsion Dabrowski., A

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.674686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 09ab3e4e-332e-4412-8568-ab8601d85b9e · outbound

This paper cites Connes.: Quantized calculus and applications.

The spectral Einstein functional for the Dirac operator with torsion Connes.: Quantized calculus and applications

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.655650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0d04e14b-63f7-49a1-be0f-0cf2be4c4d43 · outbound

This paper cites Connes.: The action functinal in Noncommutative geom etry.

The spectral Einstein functional for the Dirac operator with torsion Connes.: The action functinal in Noncommutative geom etry

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.637459Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d7dbc89d-ea4d-4348-b375-c842ca1892cb · outbound

This paper cites Connes, J.

The spectral Einstein functional for the Dirac operator with torsion Connes, J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.621820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 71411f6c-bc08-4a24-8ba1-f31a8870d88a · outbound

This paper cites Connes., A H.

The spectral Einstein functional for the Dirac operator with torsion Connes., A H

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.605271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 904308b5-b1d1-41f3-b942-3c8fa59aa690 · outbound

This paper cites Kastler.: The Dirac Operator and Gravitation.

The spectral Einstein functional for the Dirac operator with torsion Kastler.: The Dirac Operator and Gravitation

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.586846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 1a177fd0-0d81-4029-9a18-d3b836a80bdd · outbound

This paper cites Kalau and M.

The spectral Einstein functional for the Dirac operator with torsion Kalau and M

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.568766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c4c194d7-c61f-4cc1-87fa-87684c16480f · outbound

This paper cites an unresolved cited work.

The spectral Einstein functional for the Dirac operator with torsion Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-11T18:36:41.550810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0e5c3421-a7c9-4a0a-8598-f85de8d28256 · outbound

This paper cites W ang.: Diﬀential forms and the W odzicki residue for Ma nifolds with Boundary.

The spectral Einstein functional for the Dirac operator with torsion W ang.: Diﬀential forms and the W odzicki residue for Ma nifolds with Boundary

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.529262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5373ea35-daa3-4ed4-b59c-c89c2bf94fa5 · outbound

This paper cites W ang.: Gravity and the Noncommutative Residue for Ma nifolds with Boundary.

The spectral Einstein functional for the Dirac operator with torsion W ang.: Gravity and the Noncommutative Residue for Ma nifolds with Boundary

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.503895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 51aa33f7-4f20-4c36-98b3-443ef9b5d382 · outbound

This paper cites W ang.: Lower-Dimensional Volumes and Kastler-kala u-W alze Type Theorem for Manifolds with Boundary.

The spectral Einstein functional for the Dirac operator with torsion W ang.: Lower-Dimensional Volumes and Kastler-kala u-W alze Type Theorem for Manifolds with Boundary

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.482767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5aa1306c-59ea-4b21-ba31-b65f49fe9871 · outbound

This paper cites W ang., Y.

The spectral Einstein functional for the Dirac operator with torsion W ang., Y

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.464753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation aa1e2b07-f3f0-4e12-9c3a-7320f17d9aef · outbound

This paper cites W ang, Y.

The spectral Einstein functional for the Dirac operator with torsion W ang, Y

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.440347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation f9a5f7cd-4a60-4b58-b440-8f0f3aa6631c · outbound

This paper cites Connes.: Noncommutative Geometry.

The spectral Einstein functional for the Dirac operator with torsion Connes.: Noncommutative Geometry

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.423406Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e8d91897-6400-41b3-9e50-f1fec9f3a7ad · outbound

This paper cites Figueroa., J.

The spectral Einstein functional for the Dirac operator with torsion Figueroa., J

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.408047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b14fe3c1-cfe3-45b2-a32d-0d514728a1be · outbound

This paper cites W odzicki.

The spectral Einstein functional for the Dirac operator with torsion W odzicki

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.387969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4945ca59-cc63-4d6d-b0ab-ef20c4def411 · outbound

This paper cites Ackermann., J.

The spectral Einstein functional for the Dirac operator with torsion Ackermann., J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.364725Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c4c07b32-dce9-4f09-9c1c-a14afd9a2e13 · outbound

This paper cites Pf¨ aﬄe., C.

The spectral Einstein functional for the Dirac operator with torsion Pf¨ aﬄe., C

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.342507Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 87071161-5b28-4fa5-97c1-b291b9f35698 · outbound

This paper cites Pf¨ aﬄe., C.

The spectral Einstein functional for the Dirac operator with torsion Pf¨ aﬄe., C

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.321715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b4c47d16-d8da-42af-b22c-3078a707a90d · outbound

This paper cites Iochum., C.

The spectral Einstein functional for the Dirac operator with torsion Iochum., C

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.294861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4f4307c4-9f35-42b4-a3e8-0c0ffd56401b · outbound

This paper cites Pf¨ aﬄe., C.

The spectral Einstein functional for the Dirac operator with torsion Pf¨ aﬄe., C

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.257522Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e5cb3391-5ab6-4b3b-8788-2e7e052d88e5 · outbound

This paper cites Hanisch., F.

The spectral Einstein functional for the Dirac operator with torsion Hanisch., F

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T18:36:41.228878Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 43ae8bb5-92d9-4165-8782-0b7b80645602 · outbound

This paper cites Dabrowski., P.

The spectral Einstein functional for the Dirac operator with torsion Dabrowski., P

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T18:36:41.142894Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 3aef7c74-11bf-46ca-b99f-909cc25ad1e5 · inbound

An impediment to torsion from spectral geometry cites this paper.

An impediment to torsion from spectral geometry The spectral Einstein functional for the Dirac operator with torsion

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T00:19:52.627443Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 54f115b3-e67a-4add-9c6c-65c1d69f36eb · inbound

The spectral Einstein functional for the nonminimal de Rham-Hodge operator cites this paper.

The spectral Einstein functional for the nonminimal de Rham-Hodge operator The spectral Einstein functional for the Dirac operator with torsion

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-08T16:34:28.645565Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab586717-e8fb-4283-ab5c-d6bd78b78a1b · inbound

The spectral torsion for the one form rescaled Dirac operator cites this paper.

The spectral torsion for the one form rescaled Dirac operator The spectral Einstein functional for the Dirac operator with torsion

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:00:58.045473Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.