100% proof of conspiracy was presented by Michael Baden of the HSCA and James Humes in his WC testimony.
<emphasis added>
Michael Baden, Head of the HSCA Medical Panel
"In [JFK's] jacket and the underlying shirt there is a perforation of the fabric that corresponds directly with the location of the perforation of the skin of the right upper back that, the panel concluded, was an entrance gunshot perforation that entered the back of the President. This is correspondingly seen in the shirt underneath."
https://history-matters.com/archive/jfk/hsca/reportvols/vol1/html/HSCA_Vol1_0100b.htm
The WC testimony of Commander James Humes pg 364-5
https://www.aarclibrary.org/publib/jfk/wc/wcvols/wh2/pdf/WH2_Humes.pdf
<emphasis added>
Mr. SPECTOR: Have you had an opportunity to examine the clothing which has been identified for you as being that worn by the President on the day of the assassination?
Commander HUMES: Yes; yesterday, just shortly before the Commission hearing today was begun, Mr. Chief Justice, we had opportunity for the first time to examine the clothing worn by the late President. In private conversation among ourselves before this opportunity, we predicted we would find defects in the clothing corresponding with the defects which were found, of course, on the body of the late President. ..
Mr. SPECTOR: …Doctor Humes, will you describe for the record what hole, if any, is observable in the back of that garment which would be at or about the spot you have described as being the point of entry on the President’s back or lower neck.
Commander HUMES. Yes, sir. This exhibit is a grey suit coat stated to have been worn by the President on the day of his death. Situated to the right of the midline high in the back portion of the coat is a defect, one margin of which is semicircular. Situated above it just below the collar is an additional defect. It is our opinion that the lower of these defects corresponds essentially with the point of entrance of the missile at Point C on Exhibit 385.
Mr. SPECTER. Would it be accurate to state that the hole which you have identified as being the point of entry is approximately 6 inches below the top of the collar, and 2 inches to the right of the middle seam of the coat?
Commander HUMES. That is approximately correct, sir. This defect, I might say, continues on through the material. </q>
The bullet holes in the clothes match the back wound -- too low to associate with the throat wound.