Paper Citation Record · LEDGER

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform

As of 8 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 1 inbound Pith citation observation for arXiv:2507.22010.

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

pith.paper-citation-record.v1
2507.22010 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T12:13:41.890720Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-10T19:27:56.364253Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-10T22:55:51.204977Z

Reference resolution

19 of 19 outbound references displayed

verified exact0
verified fuzzy15
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f2b93bee-751d-4761-ab83-d425de858682 · outbound

This paper cites Local structures on stratified spaces.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Local structures on stratified spaces

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:46.260924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 9fe36ce8-1f06-43df-a04a-86f26c47b197 · outbound

This paper cites Integral geometry of tame sets.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Integral geometry of tame sets

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:46.091235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 202547f0-0124-486e-8002-925d3148a346 · outbound

This paper cites Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T12:13:40.486914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 225ae76d-d3fa-4a5d-8169-768b8cd18fad · outbound

This paper cites Singular intersection homology.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Singular intersection homology

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:45.888877Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 6d315d35-c350-449e-b257-9b9e3185e2e8 · outbound

This paper cites The volume of a small geodesic ball of a Riemannian manifold.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform The volume of a small geodesic ball of a Riemannian manifold

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:45.730753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e4ae3efc-b0d9-414d-a4a4-bd89254bb80d · outbound

This paper cites Differential topology.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Differential topology

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:45.552982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation cc51fd93-a0ac-4a00-9607-2a5b15414295 · outbound

This paper cites Local analytic dimensions of a subanalytic set.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Local analytic dimensions of a subanalytic set

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:45.373626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b3879455-2f16-4d3d-addb-b827a9eff610 · outbound

This paper cites Topology of Word Em- beddings: Singularities Reflect Polysemy.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Topology of Word Em- beddings: Singularities Reflect Polysemy

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:45.246489Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b8820c54-2ca6-41f6-ad1c-4c53a58e5a06 · outbound

This paper cites Higher Algebra.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Higher Algebra

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:44.973809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c6fe71ed-86db-4181-a5c3-a977dee36ed0 · outbound

This paper cites Whitney stratifications are conically smooth.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Whitney stratifications are conically smooth

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:44.694968Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b25c890f-2588-4339-8cb1-f829b09e51d5 · outbound

This paper cites GitHub Repository for Memory Gym: Towards Endless Tasks to Benchmark Memory Capabilities of Agents.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform GitHub Repository for Memory Gym: Towards Endless Tasks to Benchmark Memory Capabilities of Agents

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:44.340917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 52a22759-9f1c-4b30-8ad3-75455e078b0c · outbound

This paper cites Memory Gym: Towards Endless Tasks to Benchmark Memory Capabilities of Agents.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Memory Gym: Towards Endless Tasks to Benchmark Memory Capabilities of Agents

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:44.077164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 540b6c00-ee34-4ddf-9f2a-112792c8b6ae · outbound

This paper cites The Intrinsic Dimension of Images and Its Impact on Learning.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform The Intrinsic Dimension of Images and Its Impact on Learning

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:43.719555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation af5f05bc-7e52-4fe3-afc2-4e91cb6781a6 · outbound

This paper cites Token embeddings violate the manifold hypothesis.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Token embeddings violate the manifold hypothesis

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T12:13:41.474569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 47ddd1ed-996f-47e8-9fab-986965bfd254 · outbound

This paper cites The structure of the token space for large language models.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform The structure of the token space for large language models

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T12:13:41.552123Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4cb5006a-c7fd-48ba-baa0-b4cba8d7d9f6 · outbound

This paper cites Manifolds.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Manifolds

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:42.762369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b1b13a07-8c6c-4c66-a453-c1d6e2b67ce6 · outbound

This paper cites Topological singularity detection at multi- ple scales.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Topological singularity detection at multi- ple scales

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:42.384762Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5cabc36b-e0eb-44a7-8b12-38cb517afd8f · outbound

This paper cites On stratifications and poset-stratified spaces.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform On stratifications and poset-stratified spaces

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T12:13:41.800332Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5847f864-58f9-4ce5-8336-f1e157b78268 · outbound

This paper cites Elementary Structure of Real Algebraic Varieties.

Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform Elementary Structure of Real Algebraic Varieties

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T12:13:42.189969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

Observation 98c11c16-5d6f-409b-b84c-8626b3cddf5f · inbound

Stratifying Reinforcement Learning with Signal Temporal Logic cites this paper.

Stratifying Reinforcement Learning with Signal Temporal Logic Exploring the Stratified Space Structure of an RL Game with the Volume Growth Transform

Reference 17

Resolution: verified exact; arxiv_id, observed 2026-05-10T22:55:51.212371Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.