← AMRAL · PROGRAM-P-VS-NP

P/NP Dual-Proof Rehearsal Research Zone

Dual-Hypothesis Rehearsal for P vs. NP · Led by Neo.K, collaboratively organized with Aletheia

Rather than picking a side up front, this line builds both hypotheses — H=: P=NP and H≠: P≠NP — to their own strongest respective versions, and has them attack each other round by round under one shared computational model, one shared resource ledger, and one shared correctness standard. The research process is in no hurry to declare a proof complete; it advances round by round through thought experiments, rehearsal proofs, counterexample generation, a review against known barriers, and an accumulating history — 24 rounds cover almost the entire mainstream complexity-theory toolchain, from existential-quantifier compression, cross-representation invariants, and algebra–algorithm bridges, through quotient debt, dynamic algebraic switching, quantifier exchange, and computability hierarchies, to clocked diagonalization, the sparsity-lifting trap, WQO, and cracks in semantic monotonicity. After Round 24, the researcher independently proposed a "Dynamic Four-Layer Closure Framework (GLC)" as the next reformulation — see the separate GLC Closure Framework case.

Every round's document explicitly labels its own "tentative result for this round" and "wrong paths ruled out" — this is rehearsal proof and thought experiment, not a completed proof of P/NP. The original documents are unmodified, with a full round-by-round trail, including SHA-256 verification.