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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 14 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 2026-08-14T06:32:32.682623+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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.296821Z digest=sha256:0855ceac524f3f6bae342cc845d59653a4d9381e38b6be803fc1c7a3a89e3178

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.306005Z digest=sha256:36cc521a5f78bfc7ca078367e9c8738f2c94b2abd30834f6130c19c1193a6698

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.314779Z digest=sha256:eb16ea0e050a7585fc07e9a20a4ab6c55f72f5893c79950f20d14cc7ffc7226a

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.321547Z digest=sha256:13e95012ea968c5c4315f450aed9e5cf83a5330e08208eca987ff7c0f5818e6f

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.328323Z digest=sha256:a91256ccbad890fa3a655e49e897da15b8086a87254a93440638832a9f79fecb

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.333567Z digest=sha256:c2eaa8ea04358ac13b7e01e63dd78dbb8b0d99456d12b4a6f41181d34269d456

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.341366Z digest=sha256:baff5be981d47acbf844e9481228bbb93d031605a8ba129d14d138e117c36f3a

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.375178Z digest=sha256:aabc0dec55eeb253a7e1088ad0e7c7532503043ed7e65cfe2e8915c9fae66d81

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.389386Z digest=sha256:0ebafb386c53e7bf04331ba994ccaa09b8fd6a1b1e547c642dfb892fb3713369

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.416997Z digest=sha256:7ce2c0cf49a473defddf165913519a983cca806d77d88be12e806c92f41c524c

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:b3a28d7a4992c4c978e6882540658b7369adc2600466a677496a9f4e167c3b73

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.437912Z digest=sha256:6127e24e335be88ac7403f111fc1af4a027f1f521ec564ba02c345d668f80146

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.443907Z digest=sha256:e7413a00ef39a550204f8e6b3e7453e734321ff9543940ab14e6739e0079a84b

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.456309Z digest=sha256:53f2f675a005dd3042cda91ed4e7c6a04cd332c52d5be01bbac852de02119112

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.480116Z digest=sha256:d1f0ef28dd0f73719419b74382f4df3a78e2ebf0e56d70ab2d1d5c9d82cde669

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.484566Z digest=sha256:2d00668980c2dcd537569dceddf7f15560a55ed73b9700817af5eb4b4a6ae907

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.494256Z digest=sha256:689d6558b2eb1ebbbe081e91f36a6afef6febece41e2c2559df47ed54d59e403

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.508835Z digest=sha256:4c9f850dd392c6b0b2408965e3836550eac67bd9d160bbc0d47ae36e1c451d54

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.681734Z digest=sha256:4a6c31d91037e4b35ec48e8d3a93bd481c931fe4377fcbdf12bb527e75c82c5b

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.697407Z digest=sha256:4b5ddda469d072e6abc049a5b6c844b2ede6a244482e85b6ab8e2e44e63d6262

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 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-11T13:00:54.719634Z digest=sha256:46ebdbd9c92720af94d918739dc865f8730c968c83a39d17499d35cd0d1d4b7f

Pith citing papers

No inbound Pith citation observations are available.