Usually it is the responsibility of the person asserting claims to provide proof (or at least evidence) of those claims. So what proof do you have that the MP was a sand sump? What proof do you have that there were multiple log platforms cut into niches*? What proof do you have that Kidd signed the map, or that the map is even old enough for Kidd to have signed it?
Conversely, what evidence would you consider sufficient to "prove" your assertions wrong? If a known historical expert on Kidd says the map signature is highly unlikely, is that enough? It is otherwise almost impossible to "prove" your assertions wrong (like proving unicorns don't exist), the best we can do is apply likelihoods to them. So your "bet" is probably safe, especially if it requires "proving"
all 3 assertions to be wrong.
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*The log platforms is one of those elements of the legend that has been inconsistent over the years. Which version is true?
- The boys discovered some logs at 10 feet
- The boys discovered a log platform at 10 feet
- The boys discovered log platforms every 10 feet
- The boys discovered oak plank platforms every 10 feet
- The boys discovered a log platform at 10 feet, then cuts in the wall of the pit every 10 feet beyond.
- The boys discovered a log platform at 10 feet, then charcoal/clay/coir every 10 feet beyond.
Anyone who wishes to claim any one of these is true, I'd like to see the "proof."