Using the Search box within the App Guide Web version (http://cern.ch/geant4-userdoc/UsersGuides/ForApplicationDeveloper/html/index.html), the returned search results cause 404 Errors. The problem is that the generated URLs are malformed; for instance, searching for "G4ParticleGun" (http://geant4-userdoc.web.cern.ch/geant4-userdoc/UsersGuides/ForApplicationDeveloper/html/search.html?q=G4ParticleGun&check_keywords=yes&area=default) returns several results, the top two of which are "Geant4 General Particle Source": http://geant4-userdoc.web.cern.ch/geant4-userdoc/UsersGuides/ForApplicationDeveloper/html/GettingStarted/generalParticleSourceundefined?highlight=g4particlegun "How to Generate a Primary Event": http://geant4-userdoc.web.cern.ch/geant4-userdoc/UsersGuides/ForApplicationDeveloper/html/GettingStarted/eventDefundefined?highlight=g4particlegun Replacing the "undefined" string just before the question mark with ".html" produces a valid URL to the right part of the App Guide.
This was an issue with sphinx v3 being incompatible with the sphinx_rtd_theme. Should now be fixed. Thanks for identifying it!