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Paper Citation Record · LEDGER

Formalizing Scarf, Brouwer, and Nash in Lean

As of 14 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 0 inbound Pith citation observations for arXiv:2607.05987.

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

pith.paper-citation-record.v1
2607.05987 v1

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-08T19:09:18.303005Z

measured 10 of 10 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

10 of 10 outbound references displayed

  • verified exact1
  • verified fuzzy7
  • unresolved1
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c242298f-d116-4819-9310-e8f3474dd03c · outbound

This paper cites , journal=.

Formalizing Scarf, Brouwer, and Nash in Lean , journal=

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T21:25:38.934778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-07-08T19:09:18.303005Z digest=sha256:2b95a6e65e3fd4d8569e278e8b33d12609a391e189053ca78bd0c7de7ff01d61

Observation 31a3feca-3fd3-405a-a725-da40e486a6ef · outbound

This paper cites 2019 , publisher =.

Formalizing Scarf, Brouwer, and Nash in Lean 2019 , publisher =

Reference 2

Resolution
verified exact
doi, observed 2026-07-08T19:15:30.176162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-07-08T19:09:18.303005Z digest=sha256:75ff3e733c17c4a291294e97a187db0b3a25de70213d3d3c3905f3baf45b877c

Observation 9160d5e6-6156-4053-8c5b-1f8f1455fa7d · outbound

This paper cites Beweis der.

Formalizing Scarf, Brouwer, and Nash in Lean Beweis der

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T21:25:38.933010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-07-08T19:09:18.303005Z digest=sha256:3158b75ced6504bec20b58c96f83d2dec657a8844ec422546fd084b998ce574a

Observation e76f32e1-e338-45b7-a4ab-2c0a3944079b · outbound

This paper cites Handbook of Mathematical Economics , editor=.

Formalizing Scarf, Brouwer, and Nash in Lean Handbook of Mathematical Economics , editor=

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T21:25:38.925908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-07-08T19:09:18.303005Z digest=sha256:fc7f5855c4ddeb57510ea26e54096d8f0263b3d1364dd985658ffc23709aaa26

Observation 9fb71885-6340-4e38-b620-507c18f5029f · outbound

This paper cites , journal=.

Formalizing Scarf, Brouwer, and Nash in Lean , journal=

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T21:25:38.936843Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-07-08T19:09:18.303005Z digest=sha256:75f5ee9b0c01f0a8476549d5b0cbe2eef57dde9bb735f7ebd4098f0d3bce31ad

Observation 2853ebc4-8c91-4bef-b4f7-45a0a85a4f11 · outbound

This paper cites an unresolved cited work.

Formalizing Scarf, Brouwer, and Nash in Lean Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-07-08T21:25:38.929535Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-07-08T19:09:18.303005Z digest=sha256:cf40076781365b5df82b0e6b16de16485a08ddc6cc0eb5a310f03e7d1a703fa2

Observation 8878f261-a5b9-4ffb-82b7-22ad72864d38 · outbound

This paper cites Proceedings of the 9th.

Formalizing Scarf, Brouwer, and Nash in Lean Proceedings of the 9th

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T21:25:38.924132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-07-08T19:09:18.303005Z digest=sha256:889928db70b1b369d51183c9bb83c2a94deb4e41f289a3ea1b7c85de8a16dbb7

Observation 3e282ad1-c2ba-4670-8735-550f01caca09 · outbound

This paper cites 2022 , url=.

Formalizing Scarf, Brouwer, and Nash in Lean 2022 , url=

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T21:25:38.927656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-07-08T19:09:18.303005Z digest=sha256:049173cfd066d7c6d32ba3d3b83cb30223171f0084bc62146521569ff4b8eff6

Observation c01671dd-52cf-489d-836f-c891a1136ac6 · outbound

This paper cites Generative Language Modeling for Automated Theorem Proving.

Formalizing Scarf, Brouwer, and Nash in Lean Generative Language Modeling for Automated Theorem Proving

Reference 9

Resolution
metadata mismatch
local_arxiv, observed 2026-07-08T19:15:30.419368Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-07-08T19:09:18.303005Z digest=sha256:fa5a90184d3807f794e254eada3b2a598b41e857b726d10d1f0ef012590642e3

Observation 987f07a6-e94f-4559-a566-8464ae7dad97 · outbound

This paper cites 1985 , publisher=.

Formalizing Scarf, Brouwer, and Nash in Lean 1985 , publisher=

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-07-08T21:25:38.931268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=arxiv_source observed=2026-07-08T19:09:18.303005Z digest=sha256:fd0fa8f8e415d9a33d658b01663c75eaf991d1e1181fe3caf2046aaac8a27cff

Pith citing papers

No inbound Pith citation observations are available.