New Proof Architecture Claims P ≠ NP via Conditional Description Length
A preprint available on arXiv (2510.08814) introduces a proof framework asserting P ≠ NP, derived from a conflict between upper and lower bounds in polytime-limited conditional description length. The researchers develop a family of SAT instances, Y, that can be efficiently sampled, ensuring that every satisfying witness produces a uniform global message, M(Y). Should P equal NP, a conventional polynomial-time SAT self-recovery mechanism would extract M(Y) from Y, suggesting K_poly(M(Y)|Y) = O(1). Conversely, the lower bound indicates that no fixed polynomial-time observer can achieve a significant predictive edge over a linear selection of message coordinates. The discussion frames computation as a process that generates evidence, transforming predictive advantages into constructible-dual evidence skew and distinctions between opposing message worlds. A normalization theorem asserts that all target-relevant non-neutral evidence leaves are either safe-buffer observations.
Key facts
- Preprint arXiv:2510.08814 claims a proof architecture for P ≠ NP.
- Uses an upper-lower clash in polytime-capped conditional description length.
- Constructs efficiently samplable SAT instances Y with global message M(Y).
- If P = NP, K_poly(M(Y)|Y) = O(1) via SAT self-reduction.
- Lower bound shows no polynomial-time observer gains predictive advantage.
- Argument converts predictive advantage into evidence skew.
- Normalization theorem characterizes non-neutral evidence leaves.
- Published on arXiv with replace-cross announcement type.
Entities
Institutions
- arXiv