Paper Citation Record · LEDGER

Expansions of $\binom{pn}{p+r}$ in Shifted Binomial Bases and a Modular Symmetry Criterion

As of 11 August 2026, this Paper Citation Record lists 5 of 5 outbound references and 0 inbound Pith citation observations for arXiv:2607.12173.

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

pith.paper-citation-record.v1
2607.12173 v2

Coverage vector

measured 5 of 5 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-02T06:50:38.515206Z

measured 5 of 5 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

5 of 5 outbound references displayed

verified exact0
verified fuzzy0
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation eee93e11-a6bd-4ada-999a-f84633c63ecc · outbound

This paper cites an unresolved cited work.

Expansions of $\binom{pn}{p+r}$ in Shifted Binomial Bases and a Modular Symmetry Criterion Unresolved cited work

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-02T06:50:38.271431Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7cbad442-f395-4e39-a475-b06327fe920f · outbound

This paper cites Rota,Finite Operator Calculus, Academic Press, New York, 1975.

Expansions of $\binom{pn}{p+r}$ in Shifted Binomial Bases and a Modular Symmetry Criterion Rota,Finite Operator Calculus, Academic Press, New York, 1975

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T06:50:38.330102Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d38990ec-018a-47e7-8318-ec842c0af165 · outbound

This paper cites Sprugnoli, Riordan arrays and combinatorial sums,Discrete Math.132(1994), 267– 290.

Expansions of $\binom{pn}{p+r}$ in Shifted Binomial Bases and a Modular Symmetry Criterion Sprugnoli, Riordan arrays and combinatorial sums,Discrete Math.132(1994), 267– 290

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-02T06:50:38.381681Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca401f7f-354f-4e56-a837-08473133787e · outbound

This paper cites Roman,The Umbral Calculus, Academic Press, New York, 1984.

Expansions of $\binom{pn}{p+r}$ in Shifted Binomial Bases and a Modular Symmetry Criterion Roman,The Umbral Calculus, Academic Press, New York, 1984

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-02T06:50:38.459749Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 781cbf46-661e-40cb-a6ef-7b84efde8cd6 · outbound

This paper cites Merlini, D.

Expansions of $\binom{pn}{p+r}$ in Shifted Binomial Bases and a Modular Symmetry Criterion Merlini, D

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-02T06:50:38.515206Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.