Block/Delayed Diagonalization: Density Escape, Stage Control, and Conditional Progress

Since single-point diagonalization falls into the sparsity upward-separation trap, try switching to length blocks, stages, and delay instead. But it's immediately provable that the exponential asymmetry at a given input scale doesn't disappear just by “waiting a bit longer” (Same-Input Exponent Invariance) — a mathematical fact so obvious it sounds trivial, yet it precisely rules out the route of “deferring the simulation to a larger input of the same length.” Blowing up a single diagonal bit to fill an entire block doesn't make it any cheaper either — it just moves the cost from “per input” to “the block controller” (Amplification Knowledge Debt). The real Ladner-style delayed-diagonalization trick isn't brute-force simulating further into the future — it's a stage controller that advances one step only once it has actually found finite counterexample evidence. But this is where this round's most important double-edged sword shows up: if the controller gets permanently stuck on some candidate machine, unable to find a counterexample, that may be exactly because that machine really does equal SAT — the Freeze-or-Separate Principle. So the Ladner-theorem-style guarantee that “the controller always keeps advancing” already presupposes P≠NP, and can't be turned around into an unconditional proof of P≠NP.