Paper Citation Record · LEDGER

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure

As of 11 August 2026, this Paper Citation Record lists 18 of 18 outbound references and 0 inbound Pith citation observations for arXiv:2509.09726.

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

pith.paper-citation-record.v1
2509.09726 v1

Coverage vector

measured 18 of 18 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T20:45:22.608447Z

measured 18 of 18 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 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

18 of 18 outbound references displayed

verified exact2
verified fuzzy4
unresolved12
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6de14d8f-51b0-4903-963e-a24e77ae46d6 · outbound

This paper cites online" 'onlinestring :=.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure online" 'onlinestring :=

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T20:45:22.539831Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 39267814-420a-4f19-8192-aa04b4e4deb7 · outbound

This paper cites write newline.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure write newline

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T20:45:22.544654Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0d0a4914-6da0-4d90-aed8-1f920ea481f2 · outbound

This paper cites an unresolved cited work.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T20:45:22.549125Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6ff5345c-aeba-49a2-9f2c-d6efa9eb292a · outbound

This paper cites an unresolved cited work.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Unresolved cited work

Reference 4

Resolution: verified exact; doi, observed 2026-08-04T20:45:22.642107Z

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.

Observation 5fb17305-e538-474c-82b6-6e70098ffdd1 · outbound

This paper cites an unresolved cited work.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-04T20:45:22.869628Z

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.

Observation 79936039-83d0-4070-a037-19c57bf7b266 · outbound

This paper cites an unresolved cited work.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-08-04T20:45:22.856762Z

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.

Observation df4d26e8-9663-4d33-86aa-bcf093cc0966 · outbound

This paper cites Holland - Minkley, Regina Barzilay, and Robert L.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Holland - Minkley, Regina Barzilay, and Robert L

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:45:22.843594Z

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.

Observation accfed93-a838-4be0-8da9-b85ce3c67705 · outbound

This paper cites Jiang, Wenda Li, and Mateja Jamnik.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Jiang, Wenda Li, and Mateja Jamnik

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:45:22.829991Z

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.

Observation 71c35d3f-8388-4799-be39-af556091aab1 · outbound

This paper cites an unresolved cited work.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-04T20:45:22.816358Z

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.

Observation a99bde0e-1868-4eb7-bf3c-3d8782325c1b · outbound

This paper cites an unresolved cited work.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-04T20:45:22.802725Z

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.

Observation 378f3af4-9aff-4c9c-becc-95e063559b4a · outbound

This paper cites an unresolved cited work.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-04T20:45:22.783803Z

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.

Observation 49078bd9-5e85-4b93-a54c-1d94a9ee4c12 · outbound

This paper cites an unresolved cited work.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-04T20:45:22.761780Z

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.

Observation 764a9e2a-41b6-456f-9f62-c0872c837e86 · outbound

This paper cites Jiang, Daniel Raggi, Wenda Li, and Mateja Jamnik.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Jiang, Daniel Raggi, Wenda Li, and Mateja Jamnik

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:45:22.746882Z

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.

Observation 5ce21e24-1a8b-4952-b01c-6c2094b1994d · outbound

This paper cites Ren, Junxiao Song, Zhihong Shao, Wanjia Zhao, Haocheng Wang, Bo Liu, Liyue Zhang, Xuan Lu, Qiushi Du, Wenjun Gao, Haowei Zhang, Qihao Zhu, Dejian Yang, Zhibin Gou, Z.F.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Ren, Junxiao Song, Zhihong Shao, Wanjia Zhao, Haocheng Wang, Bo Liu, Liyue Zhang, Xuan Lu, Qiushi Du, Wenjun Gao, Haowei Zhang, Qihao Zhu, Dejian Yang, Zhibin Gou, Z.F

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-04T20:45:22.731844Z

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.

Observation 96c2826e-a2d1-4e65-8614-78621848b77a · outbound

This paper cites an unresolved cited work.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-04T20:45:22.717171Z

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.

Observation f35be57e-474c-4c43-9431-dccb5102090e · outbound

This paper cites Leanabell-Prover: Posttraining Scaling in Formal Reasoning.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Leanabell-Prover: Posttraining Scaling in Formal Reasoning

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T20:45:22.600541Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0d717b1-6b40-4538-a86c-2403d50de8c3 · outbound

This paper cites Autoformalization in the Wild: Assessing LLMs on Real-World Mathematical Definitions.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Autoformalization in the Wild: Assessing LLMs on Real-World Mathematical Definitions

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-04T20:45:22.673692Z

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.

Observation 68a3b8ce-0882-4f7f-9b36-f235a05f6a15 · outbound

This paper cites an unresolved cited work.

Natural Language Translation of Formal Proofs through Informalization of Proof Steps and Recursive Summarization along Proof Structure Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-04T20:45:22.703017Z

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.

Pith citing papers

No inbound Pith citation observations are available.