Paper Citation Record · LEDGER

A Short Proof of Knuth's Old Sum

As of 13 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2412.00040.

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

pith.paper-citation-record.v1
2412.00040 v2

Coverage vector

measured 12 of 12 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-12T14:56:41.901219Z

measured 12 of 12 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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

12 of 12 outbound references displayed

verified exact0
verified fuzzy8
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f4d109cb-669f-46bf-9572-3ef2958ba54f · outbound

This paper cites an unresolved cited work.

A Short Proof of Knuth's Old Sum Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-12T14:56:42.129195Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2571e156-3ef4-406d-b73c-2fdf8cafc23a · outbound

This paper cites an unresolved cited work.

A Short Proof of Knuth's Old Sum Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-12T14:56:42.116020Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2e0b1784-293e-4adb-8a39-d7d5fb030d81 · outbound

This paper cites Alzer, Combinatorial identities and hypergeometric functions, II, Discrete Mathematics Letters 13 (2024), 1--5.

A Short Proof of Knuth's Old Sum Alzer, Combinatorial identities and hypergeometric functions, II, Discrete Mathematics Letters 13 (2024), 1--5

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:56:42.102894Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation d303b091-1b9b-42dc-9249-97d450486469 · outbound

This paper cites an unresolved cited work.

A Short Proof of Knuth's Old Sum Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-12T14:56:42.089465Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9676260b-c347-4020-a4ea-5a080b28c935 · outbound

This paper cites Gradshteyn and I.

A Short Proof of Knuth's Old Sum Gradshteyn and I

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:56:42.075904Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 17dc8f8b-35fe-486d-8b8e-2adebc1e2e57 · outbound

This paper cites Lim, A note on a generalization of Riordan combinatorial identity via a hypergeometric series approach, Notes on Number Theory and Discrete Mathematics 29 :3 (2023), 421--425.

A Short Proof of Knuth's Old Sum Lim, A note on a generalization of Riordan combinatorial identity via a hypergeometric series approach, Notes on Number Theory and Discrete Mathematics 29 :3 (2023), 421--425

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:56:42.060256Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation dcf670cf-34dc-43e7-a161-46cd22bd5e0a · outbound

This paper cites Miki\'c, A proof of a famous identity concerning the convolution of the central binomial coefficients, Journal of Integer Sequences 19 (2016), 1--10, Article 16.6.6.

A Short Proof of Knuth's Old Sum Miki\'c, A proof of a famous identity concerning the convolution of the central binomial coefficients, Journal of Integer Sequences 19 (2016), 1--10, Article 16.6.6

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:56:42.041735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 70ad4ca3-d75c-432a-b101-d49c76c67fc7 · outbound

This paper cites Prodinger, Knuth old sum - a survey, EACTS Bulletin 52 (1994), 232--245.

A Short Proof of Knuth's Old Sum Prodinger, Knuth old sum - a survey, EACTS Bulletin 52 (1994), 232--245

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:56:42.012113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7c11184f-424a-4938-8f45-e55cc3912ec2 · outbound

This paper cites an unresolved cited work.

A Short Proof of Knuth's Old Sum Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-12T14:56:41.995950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 802690c8-2567-4e19-acc8-1604ffaa892d · outbound

This paper cites Riordan, Combinatorial Identities, John Wiley & Sons, Inc., New York, (1971).

A Short Proof of Knuth's Old Sum Riordan, Combinatorial Identities, John Wiley & Sons, Inc., New York, (1971)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:56:41.978800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f7a8b401-0d27-423c-9036-652857e54a79 · outbound

This paper cites Simons, A curious identity, The Mathematical Gazette 85 (2001), 296--298.

A Short Proof of Knuth's Old Sum Simons, A curious identity, The Mathematical Gazette 85 (2001), 296--298

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:56:41.962573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b423bd63-5a27-4f57-bfa9-970caccf9291 · outbound

This paper cites Tefera and A.

A Short Proof of Knuth's Old Sum Tefera and A

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-12T14:56:41.944917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Pith citing papers

No inbound Pith citation observations are available.