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Paper Citation Record · LEDGER

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects

As of 7 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2505.02781.

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

pith.paper-citation-record.v1
2505.02781 v4

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-22T16:04:15.040529Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

13 of 13 outbound references displayed

  • verified exact2
  • verified fuzzy7
  • unresolved4
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 57e4fdae-7ba8-4736-b427-5b6113739fa2 · outbound

This paper cites Judea Pearl.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects Judea Pearl

Reference 1

Resolution
verified exact
arxiv_id, observed 2026-05-22T16:04:58.368986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:e0a00dc1798921e656427f4f019741b6e973430544436893d4d4ede278539a82

Observation f2b6773d-548a-42fd-bfb5-db1c760a1a9b · outbound

This paper cites Thomas Verma and Judea Pearl.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects Thomas Verma and Judea Pearl

Reference 2

Resolution
verified exact
doi, observed 2026-05-22T16:04:58.377706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:17f94c8213bed24bc4a22155fbe80cf2a40b379dda21d38ab6f33510a49bbacf

Observation c816babb-50f4-40cc-9020-45f147092d22 · outbound

This paper cites SinceDPNepA,G iq, there exists noZĂVsuch that pA | ùD|Zq Gi.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects SinceDPNepA,G iq, there exists noZĂVsuch that pA | ùD|Zq Gi

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T16:04:58.713755Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:11e2d86a380a048b963bd73146201365d01986be1eb1f93cb17a5b01352a3673

Observation b1416648-8767-4e40-8178-0876e41d4685 · outbound

This paper cites Then, sample a random permutationσoft1,¨ ¨ ¨,|V|uto define a topological (causal) order.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects Then, sample a random permutationσoft1,¨ ¨ ¨,|V|uto define a topological (causal) order

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T16:04:58.721964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:8ed36d39c896284719d7d76a35e3b9bc69ffb9899521468d10f3817b89971c9b

Observation ddaf37aa-699e-415f-8b9c-c66b9d0d034f · outbound

This paper cites Search for a pair of variablespX,Yqsuch that (i) XÑYis in the DAG (to ensure the existence of a direct effect) and (ii) all adjacents ofYare oriented in the essential graph.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects Search for a pair of variablespX,Yqsuch that (i) XÑYis in the DAG (to ensure the existence of a direct effect) and (ii) all adjacents ofYare oriented in the essential graph

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T16:04:58.730082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:e451ecb5f684a2419aac345ea67016ebab702d51ca7009800547311f5024e7ce

Observation f4392ecd-89eb-4dc8-9844-7db02f65740a · outbound

This paper cites The final graph thus guarantees that the direct effect fromXtoYis identifiable.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects The final graph thus guarantees that the direct effect fromXtoYis identifiable

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T16:04:58.705194Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:6d770f2ccfdc3fdfce5c54f895794f359ebacd6e61563d5a2fd3ec2913592311

Observation 1d993ed9-cd0f-437d-b1fb-9ac6d834b749 · outbound

This paper cites an unresolved cited work.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-05-22T16:04:58.693012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:81da1b1d5dcc980df4b01f5497df0ec56f41ac46c7439e9ef84961ee13aefe2b

Observation 2067a68e-0a78-4ae3-9f04-220599c1c56e · outbound

This paper cites This guarantees thatCDEpx,x 1,yqisnotidentifiable, according to Theorem 5.4 of [Flanagan, 2020].

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects This guarantees thatCDEpx,x 1,yqisnotidentifiable, according to Theorem 5.4 of [Flanagan, 2020]

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T16:04:58.697455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:7edab05476d18da40d11755c1ddf6e4b0b7c059460beb03a2cb4f4721e65ec28

Observation ef34e59f-2b69-48ab-b1c8-28add015ec67 · outbound

This paper cites The data is then simulated using the linear/non-linear SCM procedure described below.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects The data is then simulated using the linear/non-linear SCM procedure described below

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T16:04:58.717844Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:0323c04fd54a72bf2ffa3e6a03c7b7f1ceb63ef38bbcd7a9b4f2fe803e51d387

Observation efbdfc25-e01b-42d9-8300-bf6046c32782 · outbound

This paper cites an unresolved cited work.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-05-22T16:04:58.725567Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:75ec4e65c06e7cf73ccc8d5992247cd0aa2537d945233f4ae7fda8d793d93c19

Observation 5f3eb191-56e9-44ef-80c7-4b85773d22ef · outbound

This paper cites an unresolved cited work.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-05-22T16:04:58.701167Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:d1d298fd804278ce71854a60df473f3e92f9cfc10a65eaca7ebe5cb7d27b27c9

Observation e74debfa-a55f-4041-a02c-6fc2f44b693a · outbound

This paper cites For thenonlinearcase, we simulate binary variables to model categorical data commonly encountered in practice.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects For thenonlinearcase, we simulate binary variables to model categorical data commonly encountered in practice

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-05-22T16:04:58.689179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:be021cc504c934d9860bc9dd84852d001470b576d3e7816e1761c164cd5b496a

Observation c4acd470-dd18-4d15-bf4e-7409ca25b740 · outbound

This paper cites an unresolved cited work.

Local Markov Equivalence for PC-style Local Causal Discovery and Identification of Controlled Direct Effects Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-05-22T16:04:58.709408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

source=pdf_text observed=2026-05-22T16:04:15.040529Z digest=sha256:81f2dc6fcdcd8256a75c8c1a15d2fb0fbc3e1bf6e302d7433b2db1976bc82015

Pith citing papers

No inbound Pith citation observations are available.