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Paper Citation Record · LEDGER

On Minkowski's monotonicity problem

As of 19 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 1 inbound Pith citation observation for arXiv:2507.20082.

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

pith.paper-citation-record.v1
2507.20082 v1

Coverage vector

measured 26 of 26 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:04:45.081784Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T10:13:20.682567Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

26 of 26 outbound references displayed

  • verified exact0
  • verified fuzzy14
  • unresolved12
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 66f01ded-bedd-4cd7-8f67-7ccbd612fcd0 · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:04:45.682980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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Observation 6a2e9588-a784-44f5-a227-fcff05c6a9ef · outbound

This paper cites Bonnesen and W.

On Minkowski's monotonicity problem Bonnesen and W

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.660105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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Observation 80ee7417-acca-41d5-9e80-1a9dbad3b497 · outbound

This paper cites Colesanti and D.

On Minkowski's monotonicity problem Colesanti and D

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.639939Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:44.940034Z digest=sha256:f40fd594a701fb9d1cbfe4b09a1686e723981a22f593d626a31225fdc0dc1783

Observation d8686c87-dbd3-4a85-8858-8b3b49b5655e · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:04:45.617397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:44.946617Z digest=sha256:c0615b26cd42a23a27223aaeffedc2f482630b2b70a3408f9d23ff4fcb07298e

Observation 21bc83e6-bbe1-4146-be5d-a53b841e69ce · outbound

This paper cites The Monge-Ampère equation, volume89of Progress in Nonlinear Differential Equations and their Applications.

On Minkowski's monotonicity problem The Monge-Ampère equation, volume89of Progress in Nonlinear Differential Equations and their Applications

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.598423Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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Observation b230fc18-1c67-404e-9887-27631b22b0e0 · outbound

This paper cites Hartman and L.

On Minkowski's monotonicity problem Hartman and L

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.578620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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Observation cb73e8b6-41ac-481d-a94c-480648d21899 · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:04:45.552102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:44.968700Z digest=sha256:7fd561a3fc5bf5c1379c12c10d38754e3a08bf935d591e5ac14cc8b3bd7a0b12

Observation 457489fb-da86-46fc-9081-d17d2b0f4ada · outbound

This paper cites Hug and P.

On Minkowski's monotonicity problem Hug and P

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.527216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:44.980160Z digest=sha256:622ae5a1861b5d6d3e89499b785098904b05cb8356b5151da24133e7bef46b7a

Observation 3d12d415-b92d-4ad6-9d80-382c17b4a6c5 · outbound

This paper cites Kline.Mathematical thought from ancient to modern times.

On Minkowski's monotonicity problem Kline.Mathematical thought from ancient to modern times

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.505921Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:44.985712Z digest=sha256:3eee5018adf80e33085cc5177f5295a1a11ae69f27646886643405d7fa3d7257

Observation 6ed347a5-1500-4e2b-b27a-1170d71db9ca · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:04:45.485131Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:44.993164Z digest=sha256:dd1beb2ea0dcba5bc17124fd635fb050c52548b3c0a24d7e3d807c1658c9d781

Observation 93703b88-e92b-4fab-b69f-7aa706b4d3e6 · outbound

This paper cites Minkowski.

On Minkowski's monotonicity problem Minkowski

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.466933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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Observation 3cfc692d-2522-482a-a72c-40c4b846196d · outbound

This paper cites Minkowski.

On Minkowski's monotonicity problem Minkowski

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.446594Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:45.005466Z digest=sha256:0fa487e0fa74a02658510f3334e923e368672848e397662ad3a903ac26b51c9c

Observation 10fe6506-44b6-4900-b7ee-584207ce11bc · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 13

Resolution
unresolved
no resolver link, observed 2026-08-15T18:04:45.011975Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T18:04:45.011975Z digest=sha256:f227d7404aee0cefb0b8c61573337e87442566d52e3dd02c9a3be70dabda9b65

Observation 35c08899-a5e3-44e5-b057-cdcc80614f7f · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-15T18:04:45.018147Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T18:04:45.018147Z digest=sha256:c99f1421754370b16a6c7577bad8ca5b337b392d3d9164db351d818506f3a1af

Observation 9f180d66-e02c-44df-a180-e06fdd288c98 · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:04:45.392358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:45.023417Z digest=sha256:8edef8140656d72b36c0d68c7364329a97b17ff7d7716d2e247f4831e5a67955

Observation 46fe1916-a58f-4b36-9459-423d1b69eb87 · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:04:45.373665Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:45.029558Z digest=sha256:2e1f429bf130c4928b71e8483a1fb25e81deb87195efbf7cd9e4b667a4dfb58a

Observation eaa8a0b3-b6c2-4214-b565-958bd86679df · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:04:45.353450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:45.035999Z digest=sha256:ecb1ed7a25a59aae9eda3f977135d5cbd91a86af47fd00fc9b8bb609a6d22309

Observation 4c6b7a0f-3836-4d07-af3c-ecac773f87dc · outbound

This paper cites Schneider.

On Minkowski's monotonicity problem Schneider

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.336214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:45.042765Z digest=sha256:b3b93f562f245e24f0a366368dfe5399a068f02d835e5af5aa5d7dc65d92e2eb

Observation 818d5bdc-6567-4bbd-a95b-cc361f6ba902 · outbound

This paper cites Schneider.

On Minkowski's monotonicity problem Schneider

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.318671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:45.048842Z digest=sha256:b8fd3a4e4b8e0f6b1decae9ec6dc47d3890e472505b21dda302e0ca30f13e455

Observation 383842d0-3239-4916-bac6-e3e2b047217d · outbound

This paper cites Schneider.

On Minkowski's monotonicity problem Schneider

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.298106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:45.054539Z digest=sha256:b61cb9be33508ad96cca6ce9b0c8f2b567025dd67b5b0c3f9406042b7f4358a1

Observation 41d9e760-9053-40ca-b84e-b82b6ebd9d07 · outbound

This paper cites Schneider.

On Minkowski's monotonicity problem Schneider

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.278230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:45.059687Z digest=sha256:5d443df1e3be912724f72785d33c6b81b3b6998aee2173a6b292c2cdd75f055a

Observation 49d805ca-f770-4b49-8b02-3b939c42c849 · outbound

This paper cites Shenfeld and R.

On Minkowski's monotonicity problem Shenfeld and R

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.259929Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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Observation 4ce24a6f-01c5-48a9-8f58-e0f9144bfb58 · outbound

This paper cites Shenfeld and R.

On Minkowski's monotonicity problem Shenfeld and R

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T18:04:45.242225Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

source=pdf_text observed=2026-08-15T18:04:45.070789Z digest=sha256:ae7678f03a5db16c4412bd04f12cedb8ea97f056c55177bac4256f107c9d43de

Observation 54b80f99-db57-4e15-b63f-307a081d720b · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:04:45.221895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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Observation 64129cc0-49e7-43ce-aa55-1e3ac53eafd2 · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-15T18:04:45.203246Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

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Observation 6b57a7a2-3f0e-474a-b741-eaee858afc66 · outbound

This paper cites an unresolved cited work.

On Minkowski's monotonicity problem Unresolved cited work

Reference 2024

Resolution
unresolved
no resolver link, observed 2026-08-15T18:04:44.974160Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T18:04:44.974160Z digest=sha256:110ae48b6ed1ea9a6dab35fb718e632c3a096759f989b9fb058ba5e6f25845f7

Pith citing papers

Observation c7451bbc-5986-46c6-93e8-7cb72eebf14d · inbound

Godbersen's conjecture and the $L_p$-Rogers-Shephard inequality cites this paper.

Godbersen's conjecture and the $L_p$-Rogers-Shephard inequality On Minkowski's monotonicity problem

Reference 45

Resolution
unresolved
no resolver link, observed 2026-08-01T10:13:20.682567Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-01T10:13:20.682567Z digest=sha256:e22e87ac4771de518c085434062780971b3ae0239bcee4507065b57e79fb0a58