I am looking into this right now.
According to this Image URL Naming Scheme the "path hash" is generated from the sha1sum of the original uploaded file (not the resized _1280 one).
URL | Post ID
https://data.tumblr.com/20b42c7d2d3613dbd9450b5a506cfbd3/tumblr_inline_o52i3aUCp21s6b18b_raw.png 142356364280
https://data.tumblr.com/20b42c7d2d3613dbd9450b5a506cfbd3/tumblr_inline_o5p15wTJvV1s6b18b_raw.png 142862598358
https://data.tumblr.com/20b42c7d2d3613dbd9450b5a506cfbd3/tumblr_inline_o6krbiugVC1t8vyl1_raw.png 143764052781
https://data.tumblr.com/20b42c7d2d3613dbd9450b5a506cfbd3/tumblr_inline_o8b40w7wGg1t8vyl1_raw.png 145458898886
https://data.tumblr.com/20b42c7d2d3613dbd9450b5a506cfbd3/tumblr_inline_o8ze2tfKNF1t8vyl1_raw.png 146118662296
https://data.tumblr.com/20b42c7d2d3613dbd9450b5a506cfbd3/tumblr_inline_odemy29NAE1tnns90_raw.png 150330941101
https://data.tumblr.com/20b42c7d2d3613dbd9450b5a506cfbd3/tumblr_inline_oeca19dxFg1t8vyl1_raw.png 151163621951
https://data.tumblr.com/20b42c7d2d3613dbd9450b5a506cfbd3/tumblr_inline_oefltuWf7l1t8vyl1_raw.png 151247611726
https://data.tumblr.com/20b42c7d2d3613dbd9450b5a506cfbd3/tumblr_inline_ofvlu8QK0T1sjl8et_raw.png 152521367261
https://data.tumblr.com/20b42c7d2d3613dbd9450b5a506cfbd3/tumblr_inline_oio5kwLNvv1t8vyl1_raw.png 154875513091
https://data.tumblr.com/20b42c7d2d3613dbd9450b5a506cfbd3/tumblr_inline_p1brk7DTpU1tdsqfw_raw.png 168794714560
the Post ID is what you get in a typical tumblr API response.
Another proof that the original file's content is used for generation:
https://data.tumblr.com/20aa2775a98061db21f6f86ad46df399/tumblr_noafrk8hB41uowduuo1_r1_raw.png 118859314504
https://data.tumblr.com/20aa2775a98061db21f6f86ad46df399/tumblr_o87jds0wPW1uowduuo1_raw.png 145364317345
The r1 means revision number 1, the file has been altered by the original author, but the path hash and filename are kept the same.