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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 2026-08-12T06:34:41.77262+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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.296821Z digest=sha256:7927e3bac92bdbe7ceee51692eaab725ff4984c5d8e98cc8c18c07a7c867eda6

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.306005Z digest=sha256:d5c6d3c8005457916c6932c3c458e457453ba8ff9a98ce485a96302a45cf280c

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.314779Z digest=sha256:22d3f6b81752330921c98a48c37efb2d2796765b44a08588b0f5337d5ab6e737

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.321547Z digest=sha256:1c555af3585a155ca0992fd53121cf5f1e54a22e1a66d7849b0df4c205e22526

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.328323Z digest=sha256:0c5114740ab0ed13a3d0446ab2da3be5cb578c18e63b0a23abfd529201aeb030

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.333567Z digest=sha256:5c62445f923b76f5145b81c563dea8d294c9e1fee7e0fe446efbb3d32c19d620

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.341366Z digest=sha256:8fcbb723e8254923274b40c9e647f66ea516f2fbaafd0d605ede9b47227d8e97

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.375178Z digest=sha256:b905d5902e526666098db317138f026f5d8d86bdc2966eac9170ba838f42d43b

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.389386Z digest=sha256:6da482b053b2d0f5d77661106d6b6c9bca8bc14e47ee18022b755d757a4647ab

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.416997Z digest=sha256:254cb138e633473f3ae269fb6804ecd7862bf2415f0b7ae02cf71c08bf3411d6

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.437912Z digest=sha256:0cb087abee71f0464e8c5152fd96140c5878bdf0a4b5c26b8c6cc54d6a7945bc

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.443907Z digest=sha256:41f6425a7d7596dad450c14cee280a54c5fe766a8349c85400d2ee3221c5a5b1

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.456309Z digest=sha256:687d4ca22eff3d8f9092f87b0be714de7c363df7e71edca3934455ab15253e91

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.480116Z digest=sha256:f3efce6579667062932312dc22b557e11f8566d8490feb2136b26736cdd57bbe

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.484566Z digest=sha256:2eaca75e05344d7de617a35c31bdb78f43df898316ca48749b94aa23cfd5a217

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.494256Z digest=sha256:445d170086455b339edebafc10dc9bf3abeb8b849251671ece36ee8d1df366ef

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.508835Z digest=sha256:6a8594c6664c9f57773d240ede8c1e80c125c5cc0cb438cc4961704b5a59f412

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.681734Z digest=sha256:ce5a97cc789db71f31276743461a04268113bf7dc06c1f435d49285911db7893

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.697407Z digest=sha256:4e62725d7bd581812e2e593e357264bc6e34d88782b0f648db5be4a55a3e55b4

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 2026-08-12T06:34:41.77262+00:00.

source=pdf_text observed=2026-08-11T13:00:54.719634Z digest=sha256:ceccbf50a67473e8794160652d68d1750871e710de5b152a414a55dad0c11ed7

Pith citing papers

No inbound Pith citation observations are available.