[YubiaoWang]

1. Add optional THnSparse QA filled with the jet, rho and fluctuation, to check the jet sample, the two background-density definitions and the fluctuation input offline.
2. Add TH2 QA of the background density versus centrality, separately for in-plane and out-of-plane jets and for both density definitions, to check the azimuthal dependence of the background.
3. Make the sparse binning configurable to reduce the filling rate for large productions.

[github-actions]

O2 linter results: ❌ 0 errors, ⚠️ 2 warnings, 🔕 0 disabled

[alibuild]

Error while checking build/O2Physics/code-check for 139241c at 2026-10-27 06:37:

## sw/BUILD/O2Physics-code-check-latest/log
--
========== List of issues found ==========
++ echo 'To reproduce the results below locally, run: '\''aliBuild build O2Physics-code-check -e ALIBUILD_BASE_HASH=upstream/master'\''.'
To reproduce the results below locally, run: 'aliBuild build O2Physics-code-check -e ALIBUILD_BASE_HASH=upstream/master'.
++ echo 'To apply all automatic fixes, add the '\''-e O2PHYSICS_CHECKER_FIX=1'\'' option.'
To apply all automatic fixes, add the '-e O2PHYSICS_CHECKER_FIX=1' option.
++ echo 'See the documentation for more details at: <https://aliceo2group.github.io/analysis-framework/docs/tools/#running-with-o2physics-code-check>.'
See the documentation for more details at: <https://aliceo2group.github.io/analysis-framework/docs/tools/#running-with-o2physics-code-check>.
++ echo 'Found 1 errors and 10 warnings.'
Found 1 errors and 10 warnings.
++ [[ 1 -gt 0 ]]
++ cat /sw/BUILD/0d6308c0510fe35428954fffab67c1211b6f7806/O2Physics-code-check/errors.txt
PWGJE/Tasks/jetChargedV2.cxx:135:8: error: no header providing "std::shared_ptr" is directly included [misc-include-cleaner,-warnings-as-errors]
++ [[ 10 -gt 0 ]]
++ cat /sw/BUILD/0d6308c0510fe35428954fffab67c1211b6f7806/O2Physics-code-check/warnings.txt
PWGJE/Tasks/jetChargedV2.cxx:1840:19: warning: do not declare C-style arrays, use 'std::array' instead [modernize-avoid-c-arrays]
PWGJE/Tasks/jetChargedV2.cxx:1841:26: warning: do not implicitly decay an array into a pointer; consider using gsl::array_view or an explicit cast instead [cppcoreguidelines-pro-bounds-array-to-pointer-decay]
PWGJE/Tasks/jetChargedV2.cxx:1842:19: warning: do not declare C-style arrays, use 'std::array' instead [modernize-avoid-c-arrays]
PWGJE/Tasks/jetChargedV2.cxx:1843:30: warning: do not implicitly decay an array into a pointer; consider using gsl::array_view or an explicit cast instead [cppcoreguidelines-pro-bounds-array-to-pointer-decay]
PWGJE/Tasks/jetChargedV2.cxx:1844:19: warning: do not declare C-style arrays, use 'std::array' instead [modernize-avoid-c-arrays]
PWGJE/Tasks/jetChargedV2.cxx:1845:29: warning: do not implicitly decay an array into a pointer; consider using gsl::array_view or an explicit cast instead [cppcoreguidelines-pro-bounds-array-to-pointer-decay]
PWGJE/Tasks/jetChargedV2.cxx:1960:19: warning: do not declare C-style arrays, use 'std::array' instead [modernize-avoid-c-arrays]
PWGJE/Tasks/jetChargedV2.cxx:1963:28: warning: do not implicitly decay an array into a pointer; consider using gsl::array_view or an explicit cast instead [cppcoreguidelines-pro-bounds-array-to-pointer-decay]
PWGJE/Tasks/jetChargedV2.cxx:2021:17: warning: do not declare C-style arrays, use 'std::array' instead [modernize-avoid-c-arrays]
PWGJE/Tasks/jetChargedV2.cxx:2024:38: warning: do not implicitly decay an array into a pointer; consider using gsl::array_view or an explicit cast instead [cppcoreguidelines-pro-bounds-array-to-pointer-decay]
++ [[ 1 -gt 0 ]]
++ exit 1
--

Full log here.