Four-month visit in Spain from US for research

Question

My wife, a professor and anthropologist, is using her sabbatical in the fall 2023 semester to perform cultural research in Spain. I and our son are going along. Our son will attend school there and I will be vacationing.

Our stay will be four months, so the three-month tourist visa will not work. I was thinking that a research visa for my wife would do the trick, but one of the documents required for the visa is:

4. Residence permit. Original and a copy of the residence permit issued by the Large Companies and Strategic Groups Unit.

I'm not sure what this is, but it doesn't sound like something that a person can arbitrarily acquire. No other information is provided on the website to indicate what that is.

https://www.exteriores.gob.es/Consulados/boston/en/ServiciosConsulares/Paginas/Consular/Visado-para-investigadores.aspx

My primary question is: Is it required that her research be associated with an organization, or can a professor just go and perform research independently? If that is possible, what is this Residence Permit and how might I go about acquiring one?

P.S. We intend on travelling back and forth to the US as needed and also taking trains to different places in Europe from time to time.

EDIT: My wife has an invitation from the University of Cadiz, but the University isn't supporting her during our stay.

Answer 1

This visa seems to require being hosted by a local institution. Even before coming to specific documentary requirements, the website you found is quite explicit about that:

Visa to engage in training, research, development and innovation activities at public or private entities in the following cases:

• Research staff referred to in article 13 and additional provision one of Act 14/2011 of 1 June on Science, Technology and Innovation.
• Scientific and technical staff carrying out scientific research, development and technological innovation work at business entities or R&D&i centres established in Spain.
• Researchers hosted, in the framework of an agreement, by public or private research bodies.
• Teaching staff hired by universities, higher education and research bodies or centres, or business schools established in Spain.

Article 13 is broad but mostly covers research staff at Spanish universities and research institutions, the rest of the list extends the scope a little bit but only to researchers with some sort of link to a Spanish entity. This is quite typical, the visa is not designed to help (independent) researchers or let anybody engage in research, it's designed to support the needs of Spanish institutions.