Paper Citation Record · LEDGER

Alien operators for PDF evolution

As of 7 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2509.01994.

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

pith.paper-citation-record.v1
2509.01994 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T12:05:09.915732Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+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

28 of 28 outbound references displayed

verified exact5
verified fuzzy13
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5f5e6173-8a99-4cee-ae44-f37969f7ac50 · outbound

This paper cites Gribov and L.N.

Alien operators for PDF evolution Gribov and L.N

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.233552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation fb9e8869-3216-4e4d-b0d5-972b71a1fc4e · outbound

This paper cites Altarelli and G.

Alien operators for PDF evolution Altarelli and G

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.224030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 4ac9c229-2b07-4940-bd25-4873ea41a8cb · outbound

This paper cites Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e+e− Annihilation by Perturbation Theory in Quantum Chromodynamics.

Alien operators for PDF evolution Dokshitzer, Calculation of the Structure Functions for Deep Inelastic Scattering and e+e− Annihilation by Perturbation Theory in Quantum Chromodynamics

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.214914Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation c1c2e5c6-af94-4fbd-95b1-fcdd7eed05c2 · outbound

This paper cites Dixon and J.C.

Alien operators for PDF evolution Dixon and J.C

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.204861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 8052e04d-6592-4368-8dac-910e67732ff9 · outbound

This paper cites Kluberg-Stern and J.B.

Alien operators for PDF evolution Kluberg-Stern and J.B

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.195277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation d5f63f5a-62c0-499c-b16e-14e986bd1d6f · outbound

This paper cites Kluberg-Stern and J.B.

Alien operators for PDF evolution Kluberg-Stern and J.B

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.184940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation f3d95e8c-3db7-4c66-a143-cfd012ea14c5 · outbound

This paper cites Joglekar and B.W.

Alien operators for PDF evolution Joglekar and B.W

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.175323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 45141f44-5bb1-4af2-8d25-f8daed717831 · outbound

This paper cites Joglekar, Local Operator Products in Gauge Theories.

Alien operators for PDF evolution Joglekar, Local Operator Products in Gauge Theories

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.163910Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 8e9b50cd-f525-4ed3-9995-9ea444583b3e · outbound

This paper cites Joglekar, Local Operator Products in Gauge Theories.

Alien operators for PDF evolution Joglekar, Local Operator Products in Gauge Theories

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.152741Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 421dd95e-045f-4d90-b219-99d3ba404cc8 · outbound

This paper cites Renormalization of gluonic leading-twist Operators in covariant Gauges.

Alien operators for PDF evolution Renormalization of gluonic leading-twist Operators in covariant Gauges

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-05T12:05:08.955237Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd73d507-8209-4b90-a3c3-165e94392c6c · outbound

This paper cites Four-loop splitting functions in QCD -- The quark-to-gluon case.

Alien operators for PDF evolution Four-loop splitting functions in QCD -- The quark-to-gluon case

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-05T12:05:08.981969Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f99e65f5-957a-4745-bba9-8fa258e37fe7 · outbound

This paper cites Four-loop splitting functions in QCD -- The quark-quark case.

Alien operators for PDF evolution Four-loop splitting functions in QCD -- The quark-quark case

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-05T12:05:09.056694Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3619fb56-34e5-474a-90f2-691728160dd9 · outbound

This paper cites Four-loop splitting functions in QCD -- The gluon-to-quark case.

Alien operators for PDF evolution Four-loop splitting functions in QCD -- The gluon-to-quark case

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-05T12:05:09.100654Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5f6fe88-d949-4dd9-be67-13a64ad1ce0c · outbound

This paper cites The double fermionic contribution to the four-loop quark-to-gluon splitting function.

Alien operators for PDF evolution The double fermionic contribution to the four-loop quark-to-gluon splitting function

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-05T12:05:09.172717Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 61e232b3-6666-47c0-b946-c0de98b2104d · outbound

This paper cites Four-loop splitting functions in QCD -- The gluon-gluon case --.

Alien operators for PDF evolution Four-loop splitting functions in QCD -- The gluon-gluon case --

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-05T12:05:09.230827Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72262713-d652-4d67-ae85-b30e683932d0 · outbound

This paper cites Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions.

Alien operators for PDF evolution Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-05T12:05:09.316496Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 91d2ed2d-7aa0-4fef-9793-589ce764a3d5 · outbound

This paper cites Renormalization of twist-two operators in covariant gauge to three loops in QCD.

Alien operators for PDF evolution Renormalization of twist-two operators in covariant gauge to three loops in QCD

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-05T12:05:09.390301Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83de7c12-2739-4442-97d6-aa4dcc30a9bd · outbound

This paper cites Constraints for twist-two alien operators in QCD.

Alien operators for PDF evolution Constraints for twist-two alien operators in QCD

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-05T12:05:09.510782Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 17656d03-f41b-4582-bb17-8a56f263c530 · outbound

This paper cites Hamberg and W.L.

Alien operators for PDF evolution Hamberg and W.L

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.143253Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 6142ea1e-38c4-4bd3-a9de-bab1bf0caa2e · outbound

This paper cites Renormalization of non-singlet quark operator matrix elements for off-forward hard scattering.

Alien operators for PDF evolution Renormalization of non-singlet quark operator matrix elements for off-forward hard scattering

Reference 20

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:05:10.017716Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation c880fea8-2a32-424d-a4e1-c4b314028411 · outbound

This paper cites Basis transformation properties of anomalous dimensions for hard exclusive processes.

Alien operators for PDF evolution Basis transformation properties of anomalous dimensions for hard exclusive processes

Reference 21

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:05:10.002641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 86063678-8e47-44cc-8819-212cb2e37286 · outbound

This paper cites Schneider, The summation package sigma: Underlying principles and a rhombus tiling application , Discrete Math.

Alien operators for PDF evolution Schneider, The summation package sigma: Underlying principles and a rhombus tiling application , Discrete Math

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.132686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 4b94326a-6d42-4d7a-82fb-75ba761444a0 · outbound

This paper cites Schneider, Symbolic summation assists combinatorics , Seminaire Lotharingien de Combinatoire 56 (01, 2007) 1.

Alien operators for PDF evolution Schneider, Symbolic summation assists combinatorics , Seminaire Lotharingien de Combinatoire 56 (01, 2007) 1

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.123031Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation de19c167-9d06-4244-9a65-16ebb7b68670 · outbound

This paper cites Schneider, Simplifying Multiple Sums in Difference Fields , in LHCPhenoNet School: Integration, Summation and Special Functions in Quantum Field Theory , p.

Alien operators for PDF evolution Schneider, Simplifying Multiple Sums in Difference Fields , in LHCPhenoNet School: Integration, Summation and Special Functions in Quantum Field Theory , p

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T12:05:10.113106Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation a6e4f92c-6fea-48d9-979a-2d6702f9cf53 · outbound

This paper cites Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction.

Alien operators for PDF evolution Modern Summation Methods for Loop Integrals in Quantum Field Theory: The Packages Sigma, EvaluateMultiSums and SumProduction

Reference 25

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:05:09.988039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation b6bd4f12-f236-4732-b202-188cdee02cc1 · outbound

This paper cites Two-loop operator matrix elements calculated up to finite terms.

Alien operators for PDF evolution Two-loop operator matrix elements calculated up to finite terms

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:05:09.974149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 07a4e1ca-7504-4294-8341-52567704e7a9 · outbound

This paper cites The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms.

Alien operators for PDF evolution The Two-Loop Massless Off-Shell QCD Operator Matrix Elements to Finite Terms

Reference 27

Resolution: verified exact; local_arxiv, observed 2026-08-05T12:05:09.959425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation ab82b161-56aa-452b-bef4-3bfdfec75e7b · outbound

This paper cites Leading Twist-Two Gauge-Variant Counterterms.

Alien operators for PDF evolution Leading Twist-Two Gauge-Variant Counterterms

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-05T12:05:09.915732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.