O(1) Thouless Time from Primon Gas and Prime-Restricted SFF Ramp Slope

This hypothesis sits at a strange and beautiful crossroads: the abstract mathematics of prime numbers and the physics of black holes. Prime numbers are the indivisible building blocks of all integers — 2, 3, 5, 7, 11, and so on forever — and mathematicians have spent centuries trying to understand their seemingly random distribution. Black holes, meanwhile, are regions of space so gravitationally intense that not even light escapes, and physicists are wrestling with a deep puzzle: what happens to information about matter that falls in? Does it disappear forever, or does the black hole eventually leak it back out? The connecting thread here is a mathematical object called the Riemann zeta function, which encodes deep patterns in prime number distribution. A concept called the 'primon gas' treats primes like quantum particles in a thermodynamic system, and its partition function — a kind of statistical fingerprint — turns out to equal the zeta function. This hypothesis proposes using that connection to compute something called the Spectral Form Factor (SFF), essentially a signal that physicists use to track how quantum systems scramble and release information over time. The key claim is that restricting this calculation to prime numbers introduces a correction factor — specifically a slowly decaying '1/log(t)' term familiar from the Prime Number Theorem — that predicts an unusually fast 'Thouless time': the moment a chaotic system begins revealing its quantum fingerprint. In plain terms: the hypothesis suggests that the mathematical skeleton of prime numbers may impose a detectable signature on how black holes process and eventually return information. If true, the famous randomness of primes and the famous mystery of black hole information loss would be secretly speaking the same language.

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