"palpable proof" is correct and usable in written English.
It is often used to describe tangible, physical evidence that is hard to dispute. For example, "The witness presented palpable proof of the defendant's guilt in the form of the murder weapon."
Even absent palpable proof, like a nuclear test, Iran's steady progress toward nuclear weapons has long been evident.
In presenting the plan, he described emigration as "the most palpable proof of the political, economic and social disaster" of his predecessors.
On Again! is often cited as misogynist, and it's difficult to argue against that charge with an opening line like: "I love a good bum on a woman, it makes my day"; (he then follows it up with a clever Latin pun: "To me it is palpable proof of God's existence, a posteriori").
If life were a movie directed by Frank Capra, then the Baileys of the world would become billionaires and lo and behold, there is Buffett and his $33.2 billion pile, palpable proof that nice guys do not always finish last.
All one has to do is stroll through a drug store, department store, watch television, or read mass-market publications, and the blizzard of ads gives palpable proof of the Kline and Co. finding that cosmetics in the U.S. is a $30-billion-a-year 30-billion-a-year 30-billion-a-year 30-billion-a-year business
The chilly temperature in my bedroom was palpable proof that my choice to become a freelancer, after 11 years as a teacher, was a poor one at least in my head, where I was momentarily ignoring any professional achievements over the past half-decade, of which there've been plenty.
Patti and Robert's need to find their creative voice within their interdependence is palpable and moving and proof that an artistic path is chosen for some before they are born.
At the same time, Ejiofor has the modern actor's ability to isolate key phrases so that his insatiate demand for "the ocular proof" of infidelity becomes a palpable sign of dementia.
Senator Shaheen is proof that women in office make a palpable difference.
In an interview with Charlie Rose about the McQueen exhibit, style journalist Suzy Menkes pointed to the wild popularity of these exhibitions as proof that the public connection with fashion is deeply palpable.
The author shows that while there was no firm proof of a slave conspiracy, whites' fears of such an apocalypse were palpable.
