Paper Citation Record · LEDGER

The Geometry of Nonlinear Reinforcement Learning

As of 9 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2509.01432.

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

pith.paper-citation-record.v1
2509.01432 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T12:37:43.138992Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-30T09:24:21.047027Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

31 of 31 outbound references displayed

verified exact4
verified fuzzy11
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 7017f336-dd9e-45ff-8230-88b646aeb530 · outbound

This paper cites Maximum a Posteriori Policy Optimisation.

The Geometry of Nonlinear Reinforcement Learning Maximum a Posteriori Policy Optimisation

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-05T12:37:41.058718Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a833dc7-94fc-4146-b840-4d5c48f00440 · outbound

This paper cites an unresolved cited work.

The Geometry of Nonlinear Reinforcement Learning Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-05T12:37:45.041818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 00258e82-80e4-45ea-8e95-57830cc71bbb · outbound

This paper cites Embedding Safety into RL: A New Take on Trust Region Methods.

The Geometry of Nonlinear Reinforcement Learning Embedding Safety into RL: A New Take on Trust Region Methods

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:37:43.877379Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 7a1ef6a6-4859-4cd6-84de-2a19d6439ba4 · outbound

This paper cites Central Path Proximal Policy Optimization.

The Geometry of Nonlinear Reinforcement Learning Central Path Proximal Policy Optimization

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-05T12:37:41.630698Z

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Unavailable: canonical work link unavailable.

Observation da82822d-3ba2-44a5-917e-2123bfae2ef0 · outbound

This paper cites Challenging Common Assumptions in Convex Reinforcement Learning.

The Geometry of Nonlinear Reinforcement Learning Challenging Common Assumptions in Convex Reinforcement Learning

Reference 12

Resolution: metadata mismatch; local_arxiv, observed 2026-08-05T12:37:43.566193Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 9b485471-8f66-456a-bb8a-ff4990223dc6 · outbound

This paper cites Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning.

The Geometry of Nonlinear Reinforcement Learning Advantage-Weighted Regression: Simple and Scalable Off-Policy Reinforcement Learning

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-05T12:37:41.925676Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cd88364a-c138-46fb-9d54-6033d95ee3aa · outbound

This paper cites ∇θ log π(a′|s′) X s,a Mπ(s, a|s′, a′)rπ(s, a) # (30) = (1 − γ)Es′,a′∼ω.

The Geometry of Nonlinear Reinforcement Learning ∇θ log π(a′|s′) X s,a Mπ(s, a|s′, a′)rπ(s, a) # (30) = (1 − γ)Es′,a′∼ω

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:37:45.051249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation aeb9da49-ed6c-420a-af72-5dde93a64e1d · outbound

This paper cites Mirror descent policy optimization.

The Geometry of Nonlinear Reinforcement Learning Mirror descent policy optimization

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:37:45.091767Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0b3b05ba-0956-46ea-af58-317195781842 · outbound

This paper cites Policy Mirror Descent for Regularized Reinforcement Learning: A Generalized Framework with Linear Convergence.

The Geometry of Nonlinear Reinforcement Learning Policy Mirror Descent for Regularized Reinforcement Learning: A Generalized Framework with Linear Convergence

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-05T12:37:42.367138Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a9aeef1b-a7fe-40fa-8600-2d5e8c36dc54 · outbound

This paper cites Interestingly, it also appears in the differential of the map between policy and state-action spaces.

The Geometry of Nonlinear Reinforcement Learning Interestingly, it also appears in the differential of the map between policy and state-action spaces

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:37:45.061885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c10c0bf0-b641-4ffe-83d7-6b67e25d83fe · outbound

This paper cites The reward isrπ(s, a) = P i zi[log pπ(i|s) − log zi].

The Geometry of Nonlinear Reinforcement Learning The reward isrπ(s, a) = P i zi[log pπ(i|s) − log zi]

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:37:45.031379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bf70a841-3077-48e5-9eeb-61078b2c0de7 · outbound

This paper cites an unresolved cited work.

The Geometry of Nonlinear Reinforcement Learning Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-05T12:37:45.020228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e2bf02d1-78b0-4fe9-b301-dc9c0ef871f9 · outbound

This paper cites an unresolved cited work.

The Geometry of Nonlinear Reinforcement Learning Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-05T12:37:45.010369Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e82d5808-1bfc-4614-9f81-0debb65398b8 · outbound

This paper cites This results in anintractable policy divergence with Hessian 16 GTML 2025 HC(θ) = Es∼ωπ F (θ) + X i βiϕ′′(bi − Vci (θ))∇2 θVci (θ) θ=θk.

The Geometry of Nonlinear Reinforcement Learning This results in anintractable policy divergence with Hessian 16 GTML 2025 HC(θ) = Es∼ωπ F (θ) + X i βiϕ′′(bi − Vci (θ))∇2 θVci (θ) θ=θk

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:37:44.999360Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation c0433396-15d7-4f67-b278-5d0b262b1b41 · outbound

This paper cites 17 GTML 2025 When this standard geometry is restricted to the manifoldΩ, i.e.

The Geometry of Nonlinear Reinforcement Learning 17 GTML 2025 When this standard geometry is restricted to the manifoldΩ, i.e

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:37:44.988359Z

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No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 69823b71-98d0-4259-bac2-dcf6352681f2 · outbound

This paper cites Definition C.1(Successor Representation).

The Geometry of Nonlinear Reinforcement Learning Definition C.1(Successor Representation)

Reference 1993

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:37:45.071461Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d3426bb7-af16-429d-8bb2-cc5bfcfd3252 · outbound

This paper cites Dual-Force: Enhanced Offline Diversity Maximization under Imitation Constraints.

The Geometry of Nonlinear Reinforcement Learning Dual-Force: Enhanced Offline Diversity Maximization under Imitation Constraints

Reference 1994

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:37:44.142127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b1fc9aea-a97a-4876-811b-c0960063ca8f · outbound

This paper cites Diversity is All You Need: Learning Skills without a Reward Function.

The Geometry of Nonlinear Reinforcement Learning Diversity is All You Need: Learning Skills without a Reward Function

Reference 1999

Resolution: unresolved; no resolver link, observed 2026-08-05T12:37:41.228201Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 14ad5aa8-9218-485c-9508-bfe56b4e9f54 · outbound

This paper cites Motivation for a General Hessian FrameworkThe existence of at least two distinct, natural geometries on the same occupancy manifold is a key insight.

The Geometry of Nonlinear Reinforcement Learning Motivation for a General Hessian FrameworkThe existence of at least two distinct, natural geometries on the same occupancy manifold is a key insight

Reference 2001

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:37:44.977412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 785880e8-847f-4a4d-b36e-ed8247e1eb0f · outbound

This paper cites Discovering Diverse Nearly Optimal Policies with Successor Features.

The Geometry of Nonlinear Reinforcement Learning Discovering Diverse Nearly Optimal Policies with Successor Features

Reference 2006

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:37:43.327076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 577f2040-8e0c-4fc8-84f9-032c966a58e6 · outbound

This paper cites Prompt, plan, perform: Llm-based humanoid control via quantized imitation learning.

The Geometry of Nonlinear Reinforcement Learning Prompt, plan, perform: Llm-based humanoid control via quantized imitation learning

Reference 2007

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:37:45.100499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e2546c89-beba-4e33-9484-133f4faf63b9 · outbound

This paper cites ∞X t=0 γtf (st, at) # = Es,a∼dµ π [f (s, a)] (5) 8 GTML 2025 Proof. (1 − γ)Eτ ∼π,µ.

The Geometry of Nonlinear Reinforcement Learning ∞X t=0 γtf (st, at) # = Es,a∼dµ π [f (s, a)] (5) 8 GTML 2025 Proof. (1 − γ)Eτ ∼π,µ

Reference 2008

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:37:45.081576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation e23415ff-ead5-4ac1-be5c-778fe12aa0a4 · outbound

This paper cites an unresolved cited work.

The Geometry of Nonlinear Reinforcement Learning Unresolved cited work

Reference 2015

Resolution: unresolved; no resolver link, observed 2026-08-05T12:37:42.043518Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 40b258de-e9bb-4761-8430-f7f02e90b5ad · outbound

This paper cites Quality-Diversity Actor-Critic: Learning High-Performing and Diverse Behaviors via Value and Successor Features Critics.

The Geometry of Nonlinear Reinforcement Learning Quality-Diversity Actor-Critic: Learning High-Performing and Diverse Behaviors via Value and Successor Features Critics

Reference 2016

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:37:44.503773Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation b5e69283-05ea-44f4-a252-07ef7c669a48 · outbound

This paper cites Variational Intrinsic Control.

The Geometry of Nonlinear Reinforcement Learning Variational Intrinsic Control

Reference 2018

Resolution: unresolved; no resolver link, observed 2026-08-05T12:37:41.314647Z

Source-reported events for the cited work

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Observation 6b51656a-4d66-476c-bf2c-b372f13c1876 · outbound

This paper cites cc/paper_files/paper/2019/file/873be0705c80679f2c71fbf4d872df59-Paper.pdf.

The Geometry of Nonlinear Reinforcement Learning cc/paper_files/paper/2019/file/873be0705c80679f2c71fbf4d872df59-Paper.pdf

Reference 2019

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:37:45.109888Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation fe7a6825-0ebf-4860-99c5-caa4cffe3680 · outbound

This paper cites A unified view of entropy-regularized Markov decision processes.

The Geometry of Nonlinear Reinforcement Learning A unified view of entropy-regularized Markov decision processes

Reference 2020

Resolution: unresolved; no resolver link, observed 2026-08-05T12:37:41.845185Z

Source-reported events for the cited work

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Observation 8ba514d3-52d7-4f4c-b52e-f0152f3eb758 · outbound

This paper cites Concave Utility Reinforcement Learning: the Mean-Field Game Viewpoint.

The Geometry of Nonlinear Reinforcement Learning Concave Utility Reinforcement Learning: the Mean-Field Game Viewpoint

Reference 2022

Resolution: metadata mismatch; local_arxiv, observed 2026-08-05T12:37:44.810808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 0003b65f-ac2a-4d90-bd5a-7a38a7dc51b4 · outbound

This paper cites Safe RLHF: Safe Reinforcement Learning from Human Feedback.

The Geometry of Nonlinear Reinforcement Learning Safe RLHF: Safe Reinforcement Learning from Human Feedback

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-05T12:37:41.141219Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cbecf1e9-e25b-42d0-a701-e49ea4ca7953 · outbound

This paper cites Fast Task Inference with Variational Intrinsic Successor Features.

The Geometry of Nonlinear Reinforcement Learning Fast Task Inference with Variational Intrinsic Successor Features

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-05T12:37:41.422027Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b588e5e9-9603-43e3-81cf-0272262e8a24 · outbound

This paper cites Proximal Policy Optimization Algorithms.

The Geometry of Nonlinear Reinforcement Learning Proximal Policy Optimization Algorithms

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-05T12:37:42.090426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation ca580af9-5ac7-4c3c-93c9-5f55179017f4 · inbound

Priced Motion Through Optimal Faces: A Normal-Fan Geometry for Non-Stationary Adversarial MDPs cites this paper.

Priced Motion Through Optimal Faces: A Normal-Fan Geometry for Non-Stationary Adversarial MDPs The Geometry of Nonlinear Reinforcement Learning

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-06-30T09:24:31.577549Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.