Pith. sign in

Paper Citation Record · LEDGER

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

As of 11 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 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:40.314441Z digest=sha256:52b3e346f4c17a7d9521ac50186777f73f7001d2a72f8f1d24dbd959805c9485

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:40.403854Z digest=sha256:fc0719b7d28aeded1fb91d99762d7df2ebff9c0be12e127f3581bd40995d93b0

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.

source=pdf_text observed=2026-08-06T12:13:40.486914Z digest=sha256:7a0e88e67f7011e0cf0e6678efb4595b7ca3b78aad753d8bb015111f631d4b98

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:40.544254Z digest=sha256:ed3345e2267d8ed047cab73b443be3a5ca907f7617abe761af1f9033c9a1b85a

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:40.686489Z digest=sha256:790614d477fea45a71117e98f77d66e924ff7580dcb6f68973d6f33f7344b3c4

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:40.754657Z digest=sha256:2780063bc1dbe2526e1d135c0bfbe1ef7c433897d827279aea3549e6da984f36

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:40.866232Z digest=sha256:a10d7cf15ca2f217a86df6dd7fb9fbfe9f96e77c4a54be343ee4cc470e4921c3

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:40.954132Z digest=sha256:11b77caff55802ac36428a6db262a2da5a562691b56ca26df94b446897068f65

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:41.005473Z digest=sha256:0d575bb35f3d66e9fd6f070d37ab081f79db65189513453ca206cf593f88af2b

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:41.098098Z digest=sha256:01a70b8a566f22a754e462ceed544eccdb5603afafd2f7eea3e1c9c298b46c45

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:41.203458Z digest=sha256:b56e8ec940f9cd8cd4fcf97237496d26b59ea125f08c1c0e42f5dfeab941ad5d

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:41.260262Z digest=sha256:06b7f068b625511fef601c16487d299d4ba44dcdd8ab990606e31c0700998dda

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:41.365606Z digest=sha256:34a826212add3f2e07a46f5801b3afe6138c43ea923404cafaa8c687716f618b

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.

source=pdf_text observed=2026-08-06T12:13:41.474569Z digest=sha256:c3696937904055873666208000ad704b1085ea5e07384d6bcce035d09a42c44d

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.

source=pdf_text observed=2026-08-06T12:13:41.552123Z digest=sha256:0206957b9f4ef88f19efc380e810206d645a1e2679fd58333523054d9ad2f79e

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:41.605459Z digest=sha256:b58969761359e2e2cd7a15325224299452a08aefabf7bef87668c9305f70757d

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:41.705154Z digest=sha256:e8dc3b9d225aa439bdca6a00282d8a52b2bde0e1188e6e65a91c1e06e88060b0

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.

source=pdf_text observed=2026-08-06T12:13:41.800332Z digest=sha256:15773fc9e7b55d11b2704fe35d7e2a8ddb25e1f980501d6f7f611c5060af0750

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-08-06T12:13:41.890720Z digest=sha256:f4a958f2f612b44c2b82b196d45f1c1ad430479a1c609aa5b8aae85439f84b66

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 2026-08-11T06:34:44.6726+00:00.

source=pdf_text observed=2026-05-10T19:27:56.364253Z digest=sha256:f6b13ced594ab5775be2344116b4174a7e8918f0f92eb42df7723c022ed9a639