Paper Citation Record · LEDGER

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes

As of 11 August 2026, this Paper Citation Record lists 14 of 14 outbound references and 1 inbound Pith citation observation for arXiv:2506.09499.

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

pith.paper-citation-record.v1
2506.09499 v1

Coverage vector

measured 14 of 14 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T04:57:54.961074Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T15:25:39.718607Z

measured 1 of 1 external citation measurements

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

Source: pith, observed 2026-08-10T05:30:23.456663Z

Reference resolution

14 of 14 outbound references displayed

verified exact0
verified fuzzy9
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

0
pith, observed 2026-08-10T05:30:23.456663Z

Outbound references

Observation c63d7a00-7d4c-4b7d-a718-e0d3b8f633f4 · outbound

This paper cites D.1 and sec.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes D.1 and sec

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:55.153230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 324360ea-932b-480a-897b-e3af515f6142 · outbound

This paper cites D.3): Define RVs that indicate if goal-events or constraint-violation events have occurred.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes D.3): Define RVs that indicate if goal-events or constraint-violation events have occurred

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:55.141127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 60481b83-4dd0-4e9f-93c5-c604dd871418 · outbound

This paper cites D.4): Define an RV that indicates whether a goal, constraint-violation, or region-violation event has occurred over a time-span.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes D.4): Define an RV that indicates whether a goal, constraint-violation, or region-violation event has occurred over a time-span

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:55.127760Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5d8c0880-628b-499d-94b9-c1714aa05022 · outbound

This paper cites D.5): Define an RV for the first time an event occurs at a given time-step.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes D.5): Define an RV for the first time an event occurs at a given time-step

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:55.113853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 3e09644d-48dd-4ea4-b7b9-e882c54deaa4 · outbound

This paper cites [29] We start by defining the block matrix for the policy dynamics as an absorbing Markov chain.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes [29] We start by defining the block matrix for the policy dynamics as an absorbing Markov chain

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:55.180024Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8c3910bc-bc4d-46b9-8522-f814d9708819 · outbound

This paper cites First we define the class of transition kernels for the proof.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes First we define the class of transition kernels for the proof

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:55.166528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ce6ded43-eb8a-431f-bf73-5beb122f825f · outbound

This paper cites an unresolved cited work.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:57:55.100078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d5cdb290-ff47-4330-be11-a08b749c38d7 · outbound

This paper cites an unresolved cited work.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:57:55.086012Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 88205a0e-bebd-47f1-8f82-eee5d92e61fa · outbound

This paper cites an unresolved cited work.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:57:55.071390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 14b5dd79-fd49-4f6b-bc3f-604041292f6d · outbound

This paper cites LetB be the Bellman Operator defined: B(κ)(x) = max a [ f1(x,a ) +f2(x,a ) ∑ x′ P (x′|x,a )κ(x′) ] , A.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes LetB be the Bellman Operator defined: B(κ)(x) = max a [ f1(x,a ) +f2(x,a ) ∑ x′ P (x′|x,a )κ(x′) ] , A

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:55.055700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 091805f3-8d34-42e9-a513-9fe7e77fc14b · outbound

This paper cites Assumeκ is initialized to~κd0 π (σ,z,x ) = 0 =~κd0 π,σ(σ) and the constraint function is separablefc(σ,z,x ) = fσ c (σ)fz c (z)fx c (x).

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes Assumeκ is initialized to~κd0 π (σ,z,x ) = 0 =~κd0 π,σ(σ) and the constraint function is separablefc(σ,z,x ) = fσ c (σ)fz c (z)fx c (x)

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:55.040832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation d370b7fc-9e9c-47de-801f-83e1d41bdc51 · outbound

This paper cites We list the relationships below.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes We list the relationships below

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T04:57:55.025672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation fed8b12a-c993-49b9-8a4c-cd0ec06e3a69 · outbound

This paper cites an unresolved cited work.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:57:55.011531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6a076c5f-4fbc-48b7-8c46-caf4faaf2a43 · outbound

This paper cites an unresolved cited work.

A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T04:57:54.996848Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation 8012d98d-84ba-44f8-956a-e2339a894fa3 · inbound

Is Inter-Seed Cross-Play Enough? Evaluating the Robustness of Zero-Shot Coordination Algorithms to Implementation Details cites this paper.

Is Inter-Seed Cross-Play Enough? Evaluating the Robustness of Zero-Shot Coordination Algorithms to Implementation Details A Unified Theory of Compositionality, Modularity, and Interpretability in Markov Decision Processes

Reference 92

Resolution: metadata mismatch; local_arxiv, observed 2026-08-05T15:28:39.947112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.