Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-05-22T13:37:03.019623Z
Paper Citation Record · LEDGER
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula
As of 7 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 0 inbound Pith citation observations for arXiv:2506.13473.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
16 of 16 outbound references displayed
- verified exact0
- verified fuzzy9
- unresolved7
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 39317399-586e-4881-a22e-b54ba5ef561a · outbound
This paper cites Allen and D.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Allen and D
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-22T13:54:53.804007Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 3607e7d1-01eb-4b3a-b02b-318c2bac63c2 · outbound
This paper cites Allen, D.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Allen, D
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-22T13:54:53.817184Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 4eedaf3a-0e50-4c54-8fe2-f542e9ec1b53 · outbound
This paper cites an unresolved cited work.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-05-22T13:54:53.835722Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation cfd52f7a-9ea1-40f3-8d8e-88fb7ea6a0a0 · outbound
This paper cites Baernstein II, D.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Baernstein II, D
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-22T13:54:53.826493Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation b4e56dc6-04c3-437b-94e0-581c07873cdb · outbound
This paper cites Beckner, C.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Beckner, C
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-22T13:54:53.801131Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 175a7434-0336-4cf7-9c22-c13536e8b81d · outbound
This paper cites Brascamp and E.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Brascamp and E
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-22T13:54:53.813930Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 405ceb64-4143-44f5-92eb-a6c3ddac2275 · outbound
This paper cites an unresolved cited work.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Unresolved cited work
Reference 7
- Resolution
- unresolved
- raw_fallback, observed 2026-05-22T13:54:53.823427Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 22fe6a0a-5092-40f9-b8c6-f074152ace05 · outbound
This paper cites an unresolved cited work.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Unresolved cited work
Reference 8
- Resolution
- unresolved
- raw_fallback, observed 2026-05-22T13:54:53.810380Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 80b11157-ac17-447b-8171-60c299649ca9 · outbound
This paper cites an unresolved cited work.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-05-22T13:54:53.791218Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 07337443-6ae5-4076-91fb-5a6945d7cb8a · outbound
This paper cites Elbert and M.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Elbert and M
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-22T13:54:53.820479Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 13934003-f24e-4d65-9c39-327244ea386a · outbound
This paper cites Ferrari and N.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Ferrari and N
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-22T13:54:53.806977Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 3870c653-9558-4a77-8cbb-82e790781c14 · outbound
This paper cites Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Eigenvalue inequalities for the Dirichlet problem on spheres and the growth of subharmonic functions
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-22T13:54:53.797717Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation e13c467a-6421-428c-94fd-288934327756 · outbound
This paper cites an unresolved cited work.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-05-22T13:54:53.840442Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 0823df3c-ecc4-4b49-9fc7-b0626426c4f9 · outbound
This paper cites an unresolved cited work.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-05-22T13:54:53.832406Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 5a71297d-556a-49c7-bf13-510a2b73dc33 · outbound
This paper cites an unresolved cited work.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-05-22T13:54:53.794368Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Observation 47b69367-b15f-4e72-9e84-4d4f21f310c1 · outbound
This paper cites G. Peano.
A self-contained proof of the Alt-Caffarelli-Friedman monotonicity formula G. Peano
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-05-22T13:54:53.829457Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.
Pith citing papers
No inbound Pith citation observations are available.