Paper Citation Record · LEDGER

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications

As of 22 August 2026, this Paper Citation Record lists 25 of 25 outbound references and 0 inbound Pith citation observations for arXiv:2505.17964.

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

pith.paper-citation-record.v1
2505.17964 v2

Coverage vector

measured 25 of 25 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:45:06.440571Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

25 of 25 outbound references displayed

verified exact0
verified fuzzy23
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5af69c07-fdee-4103-9a2c-eabe4d7c2677 · outbound

This paper cites Global lyapunov func- tions: A long-standing open problem in mathematics with symbolic transformers.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Global lyapunov func- tions: A long-standing open problem in mathematics with symbolic transformers

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:12.316684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation bb862214-d33c-4a56-9916-2de96807d769 · outbound

This paper cites Bondy and U.S.R.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Bondy and U.S.R

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:12.147862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7754683c-b535-4fff-a45d-2b03f5124c13 · outbound

This paper cites Language models are few-shot learners.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Language models are few-shot learners

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:11.933996Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 741e4cdd-b2c7-493b-87ba-1376f1895a30 · outbound

This paper cites Chang and H.L.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Chang and H.L

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:11.750524Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 77bcf2f1-0572-4733-a47d-e82a2ad16893 · outbound

This paper cites Advancing mathematics by guiding human intuition with AI.Nature, 600(7887):70–74, 2021.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Advancing mathematics by guiding human intuition with AI.Nature, 600(7887):70–74, 2021

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:11.414644Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9ac9ea3b-3dff-4bb6-8dbe-7cd5b62bef81 · outbound

This paper cites Patti, Jayson Lynch, Avi Shporer, Nakul Verma, Eugene Wu, and Gilbert Strang.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Patti, Jayson Lynch, Avi Shporer, Nakul Verma, Eugene Wu, and Gilbert Strang

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:11.332285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 89e4b70c-76da-4aa2-8100-0d482c5b3b03 · outbound

This paper cites Token-hungry, yet precise: Deepseek r1 highlights the need for multi-step reasoning over speed in math.ArXiv, 2024.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Token-hungry, yet precise: Deepseek r1 highlights the need for multi-step reasoning over speed in math.ArXiv, 2024

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:11.138648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 56d129ae-a7db-4c7b-8453-5b371e3004b7 · outbound

This paper cites Testing for Global Network Structure Using Small Subgraph Statistics.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Testing for Global Network Structure Using Small Subgraph Statistics

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T14:45:03.759449Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 42261b2a-deb4-4789-8e14-deeab6bba75e · outbound

This paper cites DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T14:45:03.860896Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation abbe76c0-0399-4816-a98b-82a728ac5124 · outbound

This paper cites Harary.Graph Theory.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Harary.Graph Theory

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:10.954994Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f24f65ec-b367-4fbf-885e-0956a1d1b438 · outbound

This paper cites On the number of cycles in a graph.Matem- aticky casopis, 21(1):55–63, 1971.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications On the number of cycles in a graph.Matem- aticky casopis, 21(1):55–63, 1971

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:10.767174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ff1880b4-bee1-43ec-bb78-50c590adc44b · outbound

This paper cites Measuring mathematical problem solving with the MATH dataset.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Measuring mathematical problem solving with the MATH dataset

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:10.562463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation f0c71eea-4022-4cec-b278-0698fca3cce6 · outbound

This paper cites Optimal adaptivity of signed- polygon statistics for network testing.The Annals of Statistics, 49(6):3408–3433, 2021.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Optimal adaptivity of signed- polygon statistics for network testing.The Annals of Statistics, 49(6):3408–3433, 2021

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:10.296409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation df5835af-39a5-4ce3-a195-144f5140569a · outbound

This paper cites Optimal estimation of the number of network communities.Journal of the American Statistical Association, 118(543):2101–2116, 2023.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Optimal estimation of the number of network communities.Journal of the American Statistical Association, 118(543):2101–2116, 2023

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:10.072903Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3c358178-70b8-4aa6-8f10-c0dd075fca53 · outbound

This paper cites Network goodness-of-fit for the block-model family.Journal of the American Statistical Association, pages 1–27, 2025.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Network goodness-of-fit for the block-model family.Journal of the American Statistical Association, pages 1–27, 2025

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:09.851331Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2254b7bd-7aed-4341-adbe-e84be5ad59c2 · outbound

This paper cites Spectrum estimation from samples.The Annals of Statistics, 45(6):2218–2247, 2017.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Spectrum estimation from samples.The Annals of Statistics, 45(6):2218–2247, 2017

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:09.588854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5a4ca4a2-2970-41c1-aefa-d46c7829fa5b · outbound

This paper cites Hypertree proof search for neural theorem proving.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Hypertree proof search for neural theorem proving

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:09.275679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 005f97dc-a65f-4a8b-a1a1-c5634e5ec676 · outbound

This paper cites Two sample tests for high-dimensional covariance matrices.The Annals of Statistics, 40(2):908–940, 2012.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Two sample tests for high-dimensional covariance matrices.The Annals of Statistics, 40(2):908–940, 2012

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:08.980219Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8fc51f7d-2a58-43e9-ba9f-2ae920350778 · outbound

This paper cites On the number of cycles in a graph.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications On the number of cycles in a graph

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:08.735736Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 6d736cf8-5850-459c-89d3-586dbb331fb3 · outbound

This paper cites The number of fixed length cycles in an undirected graph.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications The number of fixed length cycles in an undirected graph

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:08.487085Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b2eefb41-9823-4e02-8694-e842feed3bdd · outbound

This paper cites Pawan Kumar, Emilien Dupont, Francisco J.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Pawan Kumar, Emilien Dupont, Francisco J

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:08.221886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4d1974db-4275-44cc-a068-4e719f893505 · outbound

This paper cites Stanley.Enumerative Combinatorics.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Stanley.Enumerative Combinatorics

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:07.917976Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0eeab453-e831-4282-a8d2-c6619370a5bc · outbound

This paper cites Trinh andet al.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Trinh andet al

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:07.568035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation cc8c55c7-1408-4d20-81b4-81ceb4a196e3 · outbound

This paper cites Chain-of-thought prompting elicits reasoning in large language models.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications Chain-of-thought prompting elicits reasoning in large language models

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:07.213164Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation b3f68aa6-b596-46dc-afe4-28dedd409256 · outbound

This paper cites miniF2F: A cross-system benchmark for formal olympiad-level mathematics.

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications miniF2F: A cross-system benchmark for formal olympiad-level mathematics

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:45:06.849790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

No inbound Pith citation observations are available.