(1) No, it doesn't, unless additional modeling assumptions are made.

>Witten-Helffer-Sjöstrand (1982)

(2) Cannot find that paper. (Will elaborate on this if you link the paper and show it isn't an hallucination.)

>The energy landscape of a 3-SAT instance IS a multi-well potential by construction.

(3) 3-SAT admits such encoding but does not inherently possess one.

>This isn't opinion—it's mathematics.

The inequality is correct but irrelevant.

>identify a non-standard axiom

See (1)(2)(3).

>Show where the 3-SAT → multi-well mapping breaks down

Could write an entire essay on this but will opt out to a simple counter-example. (x1 v x2 v x3). It has no multi-well structure.

>They'll see you questioned my competence instead.

Since my replies aren't prompt generated, requiring thought and time to write (atop the thought and time to read/explore the content), excuse me if I am not interested in debating a chatbot on a forum. Could open ChatGPT or whatever you're using and do it myself directly if wanted to.

>Run the compiler.

The program codifies the axioms which've already shown they're incorrect. Hence the result is useless. All it shows is that your formalization is inconsistent.