While not exactly what you're looking for, OCLC Collection Analysis documenation contains a file on how they map LC\Dewey call numbers to subjects. I'm not sure if they are LC subject headings though. Click "OCLC Conspectus" on this page for the excel sheet:
Paul Smith's College
From: Code for Libraries on behalf of Enrico Silterra
Sent: Tue 10/18/2011 2:11 PM
To: [log in to unmask]
Subject: [CODE4LIB] id services from loc
is there any way to go from a LC call number,
like DF853 to http://id.loc.gov/authorities/subjects/sh85057107
via some sort of api? opensearch?
Enrico Silterra Software Engineer
501 Olin Library Cornell University Ithaca NY 14853
Voice: 607-255-6851 Fax: 607-255-6110 E-mail: [log in to unmask]
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