Paper Citation Record · LEDGER

Monotonicity of the rank functions for concave compositions

As of 12 August 2026, this Paper Citation Record lists 10 of 10 outbound references and 1 inbound Pith citation observation for arXiv:2606.13274.

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

pith.paper-citation-record.v1
2606.13274 v1

Coverage vector

measured 10 of 10 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-27T06:31:51.240370Z

measured 11 of 11 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T07:58:47.855374Z

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 exact0
verified fuzzy0
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 51803995-8a1f-4e8a-b3a4-bcba8f25a087 · outbound

This paper cites an unresolved cited work.

Monotonicity of the rank functions for concave compositions Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-27T06:31:51.240370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation aef38737-5e78-4a79-ba13-9ebafe211b1b · outbound

This paper cites Andrews and F.

Monotonicity of the rank functions for concave compositions Andrews and F

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-27T06:31:51.240370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7d3e130c-a4df-452f-8cb5-b43baaafea92 · outbound

This paper cites Andrews, Robert C.

Monotonicity of the rank functions for concave compositions Andrews, Robert C

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-27T06:31:51.240370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5e9bc80f-f9ed-4179-bcbc-c788d586f8e9 · outbound

This paper cites an unresolved cited work.

Monotonicity of the rank functions for concave compositions Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-27T06:31:51.240370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c8c0610-f5f7-4eed-9cc1-63cba6f52c86 · outbound

This paper cites an unresolved cited work.

Monotonicity of the rank functions for concave compositions Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-27T06:31:51.240370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3e8ccc62-c371-4e9a-a3bf-d3bb42121bfb · outbound

This paper cites Ji and Wenston J.

Monotonicity of the rank functions for concave compositions Ji and Wenston J

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-27T06:31:51.240370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 56f1f720-0e1c-4835-90c3-0a8f1436eea0 · outbound

This paper cites Ramanujan.

Monotonicity of the rank functions for concave compositions Ramanujan

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-27T06:31:51.240370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 277a4ef0-481a-429e-83fb-0f6e326fc09b · outbound

This paper cites On the distribution of the rank statistic for strongly concave compositions.Bull.

Monotonicity of the rank functions for concave compositions On the distribution of the rank statistic for strongly concave compositions.Bull

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-27T06:31:51.240370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c625f8e9-3166-4440-925f-8e7acd5bb7a7 · outbound

This paper cites Positivity and tails of pentagonal number series.J.

Monotonicity of the rank functions for concave compositions Positivity and tails of pentagonal number series.J

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-27T06:31:51.240370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9746b49-c880-4f0f-acbd-8d29eb4aa3ba · outbound

This paper cites Unimodality and certain bivariate formal Laurent series.European J.

Monotonicity of the rank functions for concave compositions Unimodality and certain bivariate formal Laurent series.European J

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-27T06:31:51.240370Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation bc1ff6d2-ec6b-4199-8cca-aa1a331ac7c7 · inbound

Positivity and tails of Jacobi theta series cites this paper.

Positivity and tails of Jacobi theta series Monotonicity of the rank functions for concave compositions

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-14T07:58:47.855374Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.