Paper Citation Record · LEDGER

Aligning Graphical and Functional Causal Abstractions

As of 16 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 3 inbound Pith citation observations for arXiv:2412.17080.

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

pith.paper-citation-record.v1
2412.17080 v4

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T05:55:10.636221Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T21:22:10.212333Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: pith, observed 2026-08-05T10:19:46.547765Z

Reference resolution

12 of 12 outbound references displayed

verified exact0
verified fuzzy7
unresolved4
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 147c5bc0-cb84-42bb-9173-6c937a29ce37 · outbound

This paper cites an unresolved cited work.

Aligning Graphical and Functional Causal Abstractions Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-11T05:55:10.978742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 81e6e947-9d49-4926-9697-216845436562 · outbound

This paper cites an unresolved cited work.

Aligning Graphical and Functional Causal Abstractions Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-11T05:55:10.963748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation a8790d94-0dd2-42e4-9326-909bfe45d9e4 · outbound

This paper cites The Finite Graphical Model is the basis for the deﬁnition of t heα -abstraction.

Aligning Graphical and Functional Causal Abstractions The Finite Graphical Model is the basis for the deﬁnition of t heα -abstraction

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:55:10.948546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 2acc59e5-cf05-47b4-a103-0ec07f7b0824 · outbound

This paper cites an unresolved cited work.

Aligning Graphical and Functional Causal Abstractions Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-11T05:55:10.932837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation d652d82f-beb3-420a-9f3e-8a76de53dd81 · outbound

This paper cites Mapping all relevant variables to the variables of the abstraction.

Aligning Graphical and Functional Causal Abstractions Mapping all relevant variables to the variables of the abstraction

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:55:10.918184Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation ccd6c9bf-2988-4b3a-8bf2-27f8d47ce5e2 · outbound

This paper cites Mapping the range of the pre-imageϕ −1(V ) inM to the range of V inM′.

Aligning Graphical and Functional Causal Abstractions Mapping the range of the pre-imageϕ −1(V ) inM to the range of V inM′

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:55:10.902183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 390aea8a-399a-4533-a04b-ac702bde5064 · outbound

This paper cites an unresolved cited work.

Aligning Graphical and Functional Causal Abstractions Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-11T05:55:10.885410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c7963158-0f41-46f5-810b-7d34b071609d · outbound

This paper cites Acyclicity requires there exist no edge Ci→ Ci, therefore such reliance must also be removed.

Aligning Graphical and Functional Causal Abstractions Acyclicity requires there exist no edge Ci→ Ci, therefore such reliance must also be removed

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:55:10.870193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation dca20e20-befa-4954-877d-9085023e735b · outbound

This paper cites It follows immediately that ϕ induces a partition P over R.

Aligning Graphical and Functional Causal Abstractions It follows immediately that ϕ induces a partition P over R

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:55:10.855281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 172c7893-e41f-41ba-9b3b-301f31c6d250 · outbound

This paper cites This is immediately equivalent to the subjectivity requirement imposed on range mappings in the c onstructiveτ-abstraction.

Aligning Graphical and Functional Causal Abstractions This is immediately equivalent to the subjectivity requirement imposed on range mappings in the c onstructiveτ-abstraction

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:55:10.838555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 17ea5adc-9edf-45d0-9f8d-9220f61a86ce · outbound

This paper cites In other words, there must exist a surjective map from the set of low level interventions to th e set of high level interven- tions.

Aligning Graphical and Functional Causal Abstractions In other words, there must exist a surjective map from the set of low level interventions to th e set of high level interven- tions

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T05:55:10.823224Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation c872ec6d-4f06-4df0-bb68-edfaa540adce · outbound

This paper cites doi: https://doi.org/10.1016/j.ij ar.2017.05.006.

Aligning Graphical and Functional Causal Abstractions doi: https://doi.org/10.1016/j.ij ar.2017.05.006

Reference 2017

Resolution: malformed identifier; no resolver link, observed 2026-08-11T05:55:10.583804Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 052b0a2f-1366-41e2-bad1-fdfb74cc9be6 · inbound

Causal Abstraction Learning based on the Semantic Embedding Principle cites this paper.

Causal Abstraction Learning based on the Semantic Embedding Principle Aligning Graphical and Functional Causal Abstractions

Reference 43

Resolution: unresolved; no resolver link, observed 2026-08-09T19:12:34.266961Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06c5e801-52a2-4d5b-bf1a-26ab7404d33a · inbound

Causal discovery on vector-valued variables and consistency-guided aggregation cites this paper.

Causal discovery on vector-valued variables and consistency-guided aggregation Aligning Graphical and Functional Causal Abstractions

Reference 54

Resolution: unresolved; no resolver link, observed 2026-08-15T21:22:10.212333Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 969a82a6-2f64-49d7-893c-286297fdb9b5 · inbound

Using causal abstractions to accelerate decision-making in complex bandit problems cites this paper.

Using causal abstractions to accelerate decision-making in complex bandit problems Aligning Graphical and Functional Causal Abstractions

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-05T10:19:46.552516Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.