Paper Citation Record · LEDGER

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM

As of 19 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2608.01349.

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

pith.paper-citation-record.v1
2608.01349 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:19:42.055130Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

41 of 41 outbound references displayed

verified exact21
verified fuzzy8
unresolved9
parse uncertain0
malformed identifier3
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1342ee1d-ef8a-4c9d-a7ed-6f2bab5e9e3f · outbound

This paper cites Counting chiral primaries in N = 1, d=4 superconformal field theories.Nucl.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Counting chiral primaries in N = 1, d=4 superconformal field theories.Nucl

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T15:19:41.861754Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 208e1fad-6cbd-4a23-9510-b952ece6ac75 · outbound

This paper cites An Index for 4 dimensional super conformal theories.Commun.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM An Index for 4 dimensional super conformal theories.Commun

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T15:19:41.866966Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 086dc8fa-06b0-41fa-85e7-b50bf380e85d · outbound

This paper cites Invasion of the giant gravitons from anti-de Sitter space.JHEP, 06:008, 2000.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Invasion of the giant gravitons from anti-de Sitter space.JHEP, 06:008, 2000

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T15:19:41.871471Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c1b3dcb4-ff41-4408-9199-506fa13dcf67 · outbound

This paper cites Giant Gravitons from Holomorphic Surfaces.JHEP, 11:027, 2000.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Giant Gravitons from Holomorphic Surfaces.JHEP, 11:027, 2000

Reference 4

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.394647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4218e49e-f7ec-42ea-a769-da97a86bc9b4 · outbound

This paper cites Supersymmetric States ofN = 4Yang–Mills from Giant Gravitons.JHEP, 12:006, 2007.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Supersymmetric States ofN = 4Yang–Mills from Giant Gravitons.JHEP, 12:006, 2007

Reference 5

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T15:19:42.828713Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 047b3ab8-084a-450d-a3bb-5606386d68f2 · outbound

This paper cites Schur index of theN = 4 U(N)supersymmetric Yang-Mills theory via the AdS/CFT correspondence.Phys.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Schur index of theN = 4 U(N)supersymmetric Yang-Mills theory via the AdS/CFT correspondence.Phys

Reference 6

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.379105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 61a21863-b069-4ae6-92cb-f51d439c8ddf · outbound

This paper cites Finite-N superconformal index via the AdS/CFT correspondence.PTEP, 2021:123B05, 2021.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Finite-N superconformal index via the AdS/CFT correspondence.PTEP, 2021:123B05, 2021

Reference 7

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.363336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5f1ee1cb-2a4e-4709-a50f-ea51d1e9f8e4 · outbound

This paper cites The giant graviton expansion.JHEP, 08:025, 2024.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM The giant graviton expansion.JHEP, 08:025, 2024

Reference 8

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.346908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 54ef9f43-4a31-4a55-9572-ed8d4fa5b028 · outbound

This paper cites Unitary matrix models, free fermion ensembles, and the giant graviton expansion.Pure Appl.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Unitary matrix models, free fermion ensembles, and the giant graviton expansion.Pure Appl

Reference 9

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.331739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3546b058-c064-4b6b-bb8c-f636ebaf0dde · outbound

This paper cites Liu and Neville Joshua Rajappa.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Liu and Neville Joshua Rajappa

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T15:19:41.907392Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca23f26a-3e63-4bfd-9c6a-c12b40ea1aee · outbound

This paper cites Comments on the Giant-Graviton Expansion of the Superconformal Index.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Comments on the Giant-Graviton Expansion of the Superconformal Index

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:19:42.812274Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0948ce2a-ccc5-4443-b9c3-2b044ecdbabf · outbound

This paper cites Giant graviton expansion from eigenvalue instantons.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Giant graviton expansion from eigenvalue instantons

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:19:42.795307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a52f2802-1c0e-42dd-a4c2-64a324c74d90 · outbound

This paper cites Liu, and Neville Joshua Rajappa.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Liu, and Neville Joshua Rajappa

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:19:42.775971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3384d2de-8337-48f3-ae3a-b8457a8203a2 · outbound

This paper cites The giant graviton expansion in AdS5×S 5.SciPost Phys., 17:098, 2024.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM The giant graviton expansion in AdS5×S 5.SciPost Phys., 17:098, 2024

Reference 14

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.306822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4c99bd1d-9c6c-4e86-bb23-95a9f7c38d48 · outbound

This paper cites Large $N$ Schur index of $\mathcal N=4$ SYM from semiclassical D3 brane.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Large $N$ Schur index of $\mathcal N=4$ SYM from semiclassical D3 brane

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T15:19:41.932124Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 84185903-d890-4222-9442-0b3efec4013c · outbound

This paper cites On the brane expansion of the Schur index.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM On the brane expansion of the Schur index

Reference 16

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.291115Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c925ec53-ef45-4ecf-ad56-8f5e821e368a · outbound

This paper cites Giant graviton expansion of Schur index and quasimodular forms.JHEP, 05:282, 2024.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Giant graviton expansion of Schur index and quasimodular forms.JHEP, 05:282, 2024

Reference 17

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.276698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1ed49b5d-bcdd-437b-9752-1246b2d50223 · outbound

This paper cites Simple-Sum Giant Graviton Expansions for Orbifolds and Orientifolds.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Simple-Sum Giant Graviton Expansions for Orbifolds and Orientifolds

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T15:19:41.950649Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38f95d76-3da7-43c3-b6f7-c9a67b7432ae · outbound

This paper cites an unresolved cited work.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Unresolved cited work

Reference 19

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.262344Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0445a7b7-f117-43d5-9d49-ec4857d54f4c · outbound

This paper cites Alday, Mathew Bullimore, Martin Fluder, and Lotte Hollands.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Alday, Mathew Bullimore, Martin Fluder, and Lotte Hollands

Reference 20

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T15:19:42.758107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7958db53-f9d8-4b75-8206-42317ef4b719 · outbound

This paper cites The superconformal index and an elliptic algebra of surface defects.JHEP, 10:062, 2014.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM The superconformal index and an elliptic algebra of surface defects.JHEP, 10:062, 2014

Reference 21

Resolution: malformed identifier; raw_fallback, observed 2026-08-15T15:19:42.738661Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 04fc7c0e-d55f-4735-af1d-4edaecc0bdf4 · outbound

This paper cites 2d Index and Surface operators.JHEP, 03:080, 2014.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM 2d Index and Surface operators.JHEP, 03:080, 2014

Reference 22

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.247485Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5b42d922-21e4-4ba5-87b8-de872746abfd · outbound

This paper cites M2-brane surface operators and gauge theory dualities in Toda.JHEP, 04:183, 2016.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM M2-brane surface operators and gauge theory dualities in Toda.JHEP, 04:183, 2016

Reference 23

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.233058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 5f3786ef-4c63-4e16-b6e9-6a539f31e97c · outbound

This paper cites Constable, Johanna Erdmenger, Zachary Guralnik, and Ingo Kirsch.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Constable, Johanna Erdmenger, Zachary Guralnik, and Ingo Kirsch

Reference 24

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.218889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f75e7417-0daa-42d1-b5a2-088b154c2ac0 · outbound

This paper cites The Field Theory of Intersecting D3-branes.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM The Field Theory of Intersecting D3-branes

Reference 25

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.203325Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7fa1a3b5-6856-4661-84c9-86794575b0f4 · outbound

This paper cites 4D and 2D superconformal index with surface operator.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM 4D and 2D superconformal index with surface operator

Reference 26

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:19:42.613831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cad6fb1e-43b7-4adf-8e29-d40bbef25583 · outbound

This paper cites Holographic Tests for Giant Graviton Expansion.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Holographic Tests for Giant Graviton Expansion

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:19:42.722059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3db8d67d-76bf-4133-95b4-ef30e45fd1b4 · outbound

This paper cites Schur line defect correlators and giant graviton expansion.JHEP, 06:088,.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Schur line defect correlators and giant graviton expansion.JHEP, 06:088,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:19:42.706697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 69da866e-9c8a-4f82-b757-28e1a1588bee · outbound

This paper cites Giant graviton expansion for general Wilson line operator indices.JHEP, 09:202, 2024.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Giant graviton expansion for general Wilson line operator indices.JHEP, 09:202, 2024

Reference 29

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.172196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9d0a866a-cab7-400e-8a45-f7ae1d41a52b · outbound

This paper cites The exact Schur index ofN = 4SYM.JHEP, 11:210, 2015.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM The exact Schur index ofN = 4SYM.JHEP, 11:210, 2015

Reference 30

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.156260Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 77f98349-f61b-4aac-95c0-16a631689925 · outbound

This paper cites Deformed Schur indices and Macdonald polynomials.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Deformed Schur indices and Macdonald polynomials

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-15T15:19:42.012577Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fc2c2054-5327-40c1-88b7-97ce0765510e · outbound

This paper cites Superconformal index forN = 4Super Yang–Mills and elliptic Macdonald polynomials.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Superconformal index forN = 4Super Yang–Mills and elliptic Macdonald polynomials

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T15:19:42.017900Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 00bb0b41-c9fe-4679-b5c0-70b998fd588d · outbound

This paper cites an unresolved cited work.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Unresolved cited work

Reference 33

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.141600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c11454fe-abbf-417f-b6bd-8e75ce84497e · outbound

This paper cites Unitary matrix models, quantized symmetric functions and spin chain.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Unitary matrix models, quantized symmetric functions and spin chain

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:19:42.690563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4087132d-ad99-4947-88f4-2a34e2576b87 · outbound

This paper cites Correlation function of Schur process with application to local geometry of a random three-dimensional Young diagram.J.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Correlation function of Schur process with application to local geometry of a random three-dimensional Young diagram.J

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-15T15:19:42.033621Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06140f91-f508-47a0-b1b5-60a3021cd3a0 · outbound

This paper cites Macdonald processes.Probab.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Macdonald processes.Probab

Reference 36

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.110691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 02b0bd1c-27e8-483d-a3f0-83a55f7df893 · outbound

This paper cites Correlation functions of the Schur process through Macdonald difference operators.J.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Correlation functions of the Schur process through Macdonald difference operators.J

Reference 37

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.094407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 29b6f266-4c84-4f9c-b5aa-41a6f846fc64 · outbound

This paper cites A determinant of the Chudnovskys generalizing the elliptic Frobenius–Stickelberger–Cauchy determinantal identity.Electron.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM A determinant of the Chudnovskys generalizing the elliptic Frobenius–Stickelberger–Cauchy determinantal identity.Electron

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:19:42.674541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8f449f86-4009-4db1-9d6b-0d6c98f9b3a1 · outbound

This paper cites Kronecker theta function and a decomposition theorem for theta functions I.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Kronecker theta function and a decomposition theorem for theta functions I

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:19:42.659967Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 75c23e38-c46e-4bb4-bc31-fbaa71ae397b · outbound

This paper cites Equal-charge projection of the $\mathcal{N}=4$ index: exact large-$N$ formula and finite-rank $U(3)$ coefficients.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Equal-charge projection of the $\mathcal{N}=4$ index: exact large-$N$ formula and finite-rank $U(3)$ coefficients

Reference 40

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:19:42.449778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8b2fd058-9232-4282-8550-c16a3a57d6dd · outbound

This paper cites an unresolved cited work.

Exact Finite-$N$ eRS Surface-Defect Indices and Giant-Graviton Corrections in $\mathcal N=4$ SYM Unresolved cited work

Reference 2024

Resolution: verified exact; doi, observed 2026-08-15T15:19:42.188035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

No inbound Pith citation observations are available.