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Paper Citation Record · LEDGER

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces

As of 13 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2412.13700.

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

pith.paper-citation-record.v1
2412.13700 v2

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T13:00:54.719634Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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

31 of 31 outbound references displayed

  • verified exact1
  • verified fuzzy12
  • unresolved18
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9b627047-9f61-42ef-ae86-53511be6b22f · outbound

This paper cites an unresolved cited work.

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces Unresolved cited work

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-11T13:00:54.286576Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:00:54.286576Z digest=sha256:ca5c04289b9dd3b8f03862b18a3b7a3ea668564df1d6458d7cbc3e23446ab9d1

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-11T13:00:54.292525Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:00:54.292525Z digest=sha256:d73f1d7376eb3c503b8a1159cace6db23ecd2db017a2a34d22047e7272adb94b

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:55.288352Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.296821Z digest=sha256:5868f4930b5dd120cb13d2f169c2cd5a0c2691bc5aa39ded0b20eb679a33a8c3

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:55.273018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.306005Z digest=sha256:6072d17c7ff1c353527eae4679d33595f88639835f69687c907254e2fb01c59b

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:55.249447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.314779Z digest=sha256:ac894834bfb003ccf5f35a14e63f78c227bec30b156ce5ffc930d2b8447bbb17

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:55.224147Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.321547Z digest=sha256:9d1d8b6cafb4ea9ea793016d3ca31c90ce8091b5a91bc3f07254f32bd4812280

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:55.205430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.328323Z digest=sha256:6ea70fbcb9e02052f123b90c86925a1b42ef94f956d2bcee805a686c7462d98c

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:55.190440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.333567Z digest=sha256:4feaa3a2294f838c6d68b4647f58f66862be667fb22819bfeeaeacddac0ffd27

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:55.175184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.341366Z digest=sha256:4520617d8b6ada8fd1361b08a2453db31f116b9912a44cf233a22195270afe25

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-11T13:00:54.346805Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:00:54.346805Z digest=sha256:a5b3df0c401f5e191fe8fb00b3af7c28c48e3dd0bf8ef38b93c326de0944e47a

Reference 11

Resolution
unresolved
no resolver link, observed 2026-08-11T13:00:54.352836Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:00:54.352836Z digest=sha256:567fa3b59c31ca610c3feafed5d89b63b909cc8c471f19680bb591e67beacf3f

Observation c61e3202-85d2-4c4f-9045-406a9eb55340 · outbound

This paper cites an unresolved cited work.

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-11T13:00:55.132351Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.375178Z digest=sha256:7b9f5bce5f713722e551d86ce3e0d464edc9735f6a053706d9e0669e5a22db9f

Observation 391806a1-448f-4cdb-8e23-7e7781d1cc1e · outbound

This paper cites an unresolved cited work.

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-11T13:00:55.113534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.389386Z digest=sha256:6d8686df181345823f26f3ba6a184e5cf0d5bc17654dc677ec0674e7d104d75a

Reference 14

Resolution
unresolved
no resolver link, observed 2026-08-11T13:00:54.401737Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:00:54.401737Z digest=sha256:4763a14020f46760e895f83d34cf1ffd8ed9e11f6f76d60c99faa4d7407cccab

Reference 15

Resolution
unresolved
no resolver link, observed 2026-08-11T13:00:54.408378Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:00:54.408378Z digest=sha256:a26077fc6123161116d188a846346216634889796d1a10808dc13c6db66c45e0

Reference 16

Resolution
verified exact
local_arxiv, observed 2026-08-11T13:00:54.811462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.416997Z digest=sha256:239f56725389603ba02eece655c59280c9673b27a9be6e7eb45c3526a3b0f1d0

Reference 17

Resolution
unresolved
no resolver link, observed 2026-08-11T13:00:54.424824Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:00:54.424824Z digest=sha256:b608dc8bbde803bf1fb22e81ee84a66ed55317f32e222f688f57f49405967bea

Reference 18

Resolution
unresolved
no resolver link, observed 2026-08-11T13:00:54.431788Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:00:54.431788Z digest=sha256:94274598be7aca624312f537691b059c9d60ae119d41730aac53876e9ffb51cd

Observation d7704ef0-0d58-4aab-b741-36c2cb3571bb · outbound

This paper cites Yu, Advances in strength theories for materials u nder complex stress state in the 20th century, Appl.

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces Yu, Advances in strength theories for materials u nder complex stress state in the 20th century, Appl

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:55.046486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.437912Z digest=sha256:00dbf16f8110086547120df529c1ca0bc74e8eca7eb15374355b2759d47d74d4

Observation 9da8f778-de1f-4e5f-8c82-b89d11c9e855 · outbound

This paper cites an unresolved cited work.

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-11T13:00:55.030653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.443907Z digest=sha256:93f5537fee4fd7c00bc0ed5b546b67ffbf4c6604248d8daafbf0802a95e38519

Observation ba5a0aaf-2de1-408f-9042-a799caccda5c · outbound

This paper cites an unresolved cited work.

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces Unresolved cited work

Reference 21

Resolution
unresolved
no resolver link, observed 2026-08-11T13:00:54.449210Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:00:54.449210Z digest=sha256:d06e8a4303408598231c7ceabdb68f23cb7521a2e59e825cd245509b6048f12f

Observation 9b411922-23bd-48d9-988c-5c96e2805138 · outbound

This paper cites an unresolved cited work.

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-11T13:00:54.988723Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.456309Z digest=sha256:ba873ebbd74392daad08bafa69a9c491a280f74d51ef6db5fa46024588b2f0a3

Reference 23

Resolution
unresolved
no resolver link, observed 2026-08-11T13:00:54.464362Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:00:54.464362Z digest=sha256:283d95c334b6863fb1a0b4106803d7780cb5c0117597af5763132fb8f85fe0c0

Observation 36a6a2c8-714c-4996-b68d-d0bec8b70c58 · outbound

This paper cites an unresolved cited work.

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces Unresolved cited work

Reference 24

Resolution
unresolved
no resolver link, observed 2026-08-11T13:00:54.474947Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T13:00:54.474947Z digest=sha256:a12f06722c818862862d06e214d5e5b5fbcb7029ea1f34483774c7d7a72032fb

Observation 41361ee9-6b5a-4b7c-a3da-a49463660d0c · outbound

This paper cites an unresolved cited work.

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-11T13:00:54.951340Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.480116Z digest=sha256:360a7006e35b45c9984e155ef55a0ba376127b926253e2fdb1fe8657b98644e1

Observation d35e816e-9dc3-4451-90f9-43737bafe532 · outbound

This paper cites an unresolved cited work.

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-11T13:00:54.934992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.484566Z digest=sha256:c7e693a981135fb4a107e4e1a9382d963fc0e50a0b4e060e1587566829c70a69

Observation a190572a-94f7-42ba-aa88-9e594cddd370 · outbound

This paper cites an unresolved cited work.

On the construction of explicit analytical driving forces for crack nucleation in the phase field approach to brittle fracture with application to Mohr-Coulomb and Drucker-Prager strength surfaces Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-11T13:00:54.915078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.494256Z digest=sha256:c43a2928e2cd271f8e1cf342154841c868a459f18753565aa9166033fe43ac9c

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:54.897192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.508835Z digest=sha256:35c48d9039944b3e977b08bab991a57ab8687debf95b780eb614b4d67dea8c31

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:54.879488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.681734Z digest=sha256:0bc5032f566d542c2d0aa48b2b0d37fded7623b39d2c1f386f1c4280704e1ada

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:54.855189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.697407Z digest=sha256:65d33f3dc9648a438c987f8fe8b55869543d9eec5831a007a0b8f52ffc7b8583

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T13:00:54.835625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

source=pdf_text observed=2026-08-11T13:00:54.719634Z digest=sha256:812eaaff6240574c3e6ea398e15c2b8c88642a2f584d9a75d70903db8188c0ce

Pith citing papers

No inbound Pith citation observations are available.