Paper Citation Record · LEDGER

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs

As of 10 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2501.18563.

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

pith.paper-citation-record.v1
2501.18563 v2

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-09T23:02:42.047935Z

measured 17 of 17 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 2026-08-06T18:51:28.867971Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T18:51:30.765452Z

Reference resolution

16 of 16 outbound references displayed

verified exact2
verified fuzzy8
unresolved6
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 823c3ecf-72ee-4a02-8149-c8221bc3f4f8 · outbound

This paper cites an unresolved cited work.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-09T23:02:47.008155Z

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 f103717b-774e-4309-9654-691abebfaa98 · outbound

This paper cites an unresolved cited work.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-09T23:02:46.969222Z

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 51ed545c-e369-4606-ad9c-cd36b7d2ae8f · outbound

This paper cites an unresolved cited work.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-09T23:02:46.936681Z

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 186e63f9-7f34-4c8b-9dbf-aa7a4d63ebf2 · outbound

This paper cites an unresolved cited work.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-09T23:02:46.905522Z

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 a45c071c-f336-4238-9131-5b9fc9b802fa · outbound

This paper cites an unresolved cited work.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-09T23:02:46.879297Z

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 d51a913a-af06-43ea-8c1d-3a50da30eeac · outbound

This paper cites an unresolved cited work.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-09T23:02:46.847086Z

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 376c2f00-582a-45ea-9662-0687217fc8ce · outbound

This paper cites ϕ on i has a motif s.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs ϕ on i has a motif s

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:02:46.815589Z

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 b72deaf4-5e8a-4207-a1fb-8d17d6429085 · outbound

This paper cites β0 = u0 (11) β3t3 1 + β2t2 1 + β1t1 + β0 = u1 (12) β1 = u′ 0 (13) As in Table 9, we denote u(t1)−u(t0) t1−t0 as κ.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs β0 = u0 (11) β3t3 1 + β2t2 1 + β1t1 + β0 = u1 (12) β1 = u′ 0 (13) As in Table 9, we denote u(t1)−u(t0) t1−t0 as κ

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:02:46.788270Z

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 ce8e788f-31a8-4774-83c6-5a17966ccbb4 · outbound

This paper cites asymptotic doubling time.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs asymptotic doubling time

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:02:46.756060Z

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 8cb718c5-5039-473a-ade0-f73e014cbd4b · outbound

This paper cites half-life.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs half-life

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:02:46.732617Z

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 e92ff81f-d605-4f28-ac28-9431eb7d1a87 · outbound

This paper cites In the WSINDy variant, we choose the maximum number of terms during hyperparameter tuning (between 1 and 20).

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs In the WSINDy variant, we choose the maximum number of terms during hyperparameter tuning (between 1 and 20)

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:02:46.656890Z

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 e37a6e66-f7b5-47fe-8027-b143d61390d5 · outbound

This paper cites Finally, we add a Gaussian noise with a standard deviation σ = 0.01 for the low noise setting and σ = 0.2 for the high noise setting.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs Finally, we add a Gaussian noise with a standard deviation σ = 0.01 for the low noise setting and σ = 0.2 for the high noise setting

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:02:46.707500Z

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 04ba7f6d-b4f7-4e48-b721-8c1027cb0020 · outbound

This paper cites We then solve the initial value problem to obtain a trajectory for each.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs We then solve the initial value problem to obtain a trajectory for each

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:02:46.686566Z

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 926430ad-93b4-4c89-833f-0ed5603d7ffc · outbound

This paper cites 11 Published as a conference paper at ICLR 2025 Ricky T.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs 11 Published as a conference paper at ICLR 2025 Ricky T

Reference 2016

Resolution: verified exact; arxiv_id_nonexistent, observed 2026-08-09T23:02:46.579419Z

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 47b78a4f-8cf3-43ab-b82f-402cd9b0c2d4 · outbound

This paper cites frequency.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs frequency

Reference 2017

Resolution: verified fuzzy; raw_fallback, observed 2026-08-09T23:02:46.613617Z

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 84ca7595-5396-457f-9ab3-cdd6c974b531 · outbound

This paper cites doi: 10.1103/PhysRevE.101.010203.

No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs doi: 10.1103/PhysRevE.101.010203

Reference 2020

Resolution: verified exact; arxiv_id_nonexistent, observed 2026-08-09T23:02:45.874917Z

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.

Pith citing papers

Observation 8c43ec56-8390-4906-88ad-c1a4204a26bf · inbound

Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Time cites this paper.

Beyond the ATE: Interpretable Modelling of Treatment Effects over Dose and Time No Equations Needed: Learning System Dynamics Without Relying on Closed-Form ODEs

Reference 9

Resolution: metadata mismatch; local_arxiv, observed 2026-08-06T18:51:30.848952Z

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.