P vs NP — Complete Proof

P vs NP — Complete Proof A complete proof manuscript of P ≠ NP, organized as a modular, node-based corpus (Nodes 00–20). The document builds a fully checkable proof chain under a fixed representation lock (one immutable input/promise/metric format) and a pointwise stopping rule that avoids reliance on probabilistic “tails” or non-adaptive assumptions. The internal core develops a corridor-style protocol (MU-certification, forbidden-set avoidance, and wave/remote-point “handcuffs”), and then connects to the final separation via external bridges documented with precise bibliographic “passports” (hardness magnification and range-avoidance/remote-point results). The manuscript is designed for peer verification: each node compiles standalone, includes self-checks for placeholders/inconsistencies, and adheres to a consistent interface across the full proof.