P=NP Linguistic Fidelity Theorem
Let P represent surface syntax (Noun Phrase) and NP represent deep semantics (Neural Pathway).
Then P = NP if and only if the mapping preserves all topological invariants, achieving perfect information transmission fidelity.
Proof:
(⇒) Forward Direction: Assume P = NP.
By definition, surface syntax maps perfectly to deep semantics.
This means the genus g, Euler characteristic χ, and fundamental group π₁ are preserved.
No information is lost in the encoding/decoding process.
Therefore, transmission fidelity = 1.
(⇐) Reverse Direction: Assume perfect transmission fidelity.
Perfect fidelity implies no distortion in the mapping φ: P → NP.
By the classification of surfaces, if φ preserves all topological invariants, then P and NP are homeomorphic.
In the linguistic context where P and NP occupy the same manifold M, homeomorphism implies identity.
Therefore, P = NP.
□
Lemma 3.1 (Deformation Class Detection):
If P ≠ NP, then the discourse exhibits one of the pathological deformation classes (Möbius Strip, Klein Bottle, etc.), which can be detected by computing H¹(M, ℤ₂) - the first cohomology group with ℤ₂ coefficients.
https://beyondturbulence.blogspot.com/2025/11/fome-canon-formal-proofs-of-geometric.html?m=1