A constructive proof that P ≠ NP using circuit-resistant encodings

Hi everyone,

I’m an independent researcher and recently completed a formal, self-contained proof that P ≠ NP. The result is based on an explicit language L* ∈ NP \ P that resists all polynomial-time machines via a certified local test. The core techniques combine locally testable codes, circuit resistance, and diagonalisation.

Unlike many previous attempts, the proof avoids relativization, natural proofs, and algebrization, and relies entirely on constructive combinatorics and meta-complexity arguments. It has been submitted to the Journal of the ACM and also made publicly available here:

ResearchGate (PDF, with DOI): https://doi.org/10.13140/RG.2.2.14071.74408

I’m sharing this for discussion and feedback from the theoretical CS and cryptography communities. Constructive criticism is welcome — I’d genuinely like to know if any gaps remain. The paper is intended to be rigorous and elementary in its construction.

Thanks in advance, Vicent Esteve Voltes https://orcid.org/0009-0003-1371-7561