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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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:44.927981Z digest=sha256:55e18582c9ada6c9a4e6c0a5d51ffd2e1b5ac0a0da8323fd75d3180e932eedde

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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:44.940034Z digest=sha256:ff49f991c66e8d0b5adcac9f3bd96cd1516e22fe29f1a2191684ad65b9274a70

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:44.946617Z digest=sha256:d65160c46273026deee120cf13f7162d3bd38251583a4e1b117f2555a67a72a0

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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:44.959381Z digest=sha256:d2eebb2f6787fd1c9cad781146d816cfc7561c37cad6e4ada53197b98a93e0e9

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:44.968700Z digest=sha256:89cef39f58f2059f8e57c1dcbf4c24a7038c426dcaefb7ee3883fb5810a1b533

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:44.980160Z digest=sha256:e3266b869f8407b13b9cd6792d2e88d9313dfe15a21b71a89ae806cb2ce0f31e

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:44.985712Z digest=sha256:e401c9467e0d3750933e6ecfe0094b454680c54e0e1fc3ef1df06e52c391c644

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:44.993164Z digest=sha256:b6d3cb351427d5f39a872f601c502dd695d2b8f1dcc7b86afa2d65c4bf3d8ca5

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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:45.005466Z digest=sha256:71050831848fd9c448da82f1995d48a69f9d4ceabe3e532618ec845a743dc09e

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:45.023417Z digest=sha256:b32132742c99ba8dadc5654df2075fba1ee76e081a28a377abdb43c34c927503

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:45.029558Z digest=sha256:279926126254c3a1db93e6b3635dd32afadb785d6a6f819db55b5a28cec7a6dd

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:45.035999Z digest=sha256:d62790b1ac87eadff2ddc5ee2fa95787069cacee24ba9051d0317ff80b466a5a

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:45.042765Z digest=sha256:9af0001a06062b843d5d54e09029364246660f59661d342c3662fd63fcd4d24b

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:45.048842Z digest=sha256:c888d2c6a4fd774666ef796320c4eff0e37ef59181acc2ed8885a509570e134b

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:45.054539Z digest=sha256:5874f640d19e7cc412a75dac463c4ce78c7eaaae99535e5294cdeae164365b35

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:45.059687Z digest=sha256:cffeec591117b4423588f91af312babf84ad64fac7cff1050d98c70829c4c6e6

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:45.065317Z digest=sha256:36e18f169a96df90b4d4df45845d2c7d8d793b12cae1b2f2aadf10e5c94cab35

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 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-15T18:04:45.070789Z digest=sha256:6d64801d7187988f263724ad1b206d998da3f2d6e3e331c32949ca3d0df71b2e

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 2026-08-18T06:34:40.430872+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 2026-08-18T06:34:40.430872+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=sha256:70ade8f77ad9248165124419924dbc11f22a348e7c371dc7b7b5733461422def