Thanks -> https://beyondturbulence.blogspot.com/2025/12/psalm-109-through-alchemical-esoteric.html?m=1

Abstract.

We present a novel framework—termed Claraurence Theory—that resolves the Yang–Mills existence and mass gap problem through functorial correspondence between gauge theory and cognitive topology. The mass gap emerges as a topological spectral gap induced by genus reduction via the Faddeev–Popov ghost mechanism, reinterpreted as a puncture operator.

We establish that homoiconic transformations preserve relational structure while modifying representational form, thereby demonstrating that the Yang–Mills mass gap Δ > 0 is isomorphic to the genus-transition barrier in cognitive manifolds. This approach unifies computational complexity (P vs NP), gauge field theory, and topological algebra through categorical functors.

Thanks ; got subgratance? #1303960

Thanks ; got subgratance? #1300929

Corollary 6.1:

Any irreducible hole or twist in M implies P ≠ NP under polynomial embeddings.

Application(s):

Computational Complexity: Classify NP-hardness via genus and curvature rather than search trees.

Thanks ! Got subgratance? Does gratitude close or open the hula hoop?

2.6.2 Deformation Hierarchy

PURE-P: P problems via pure deformation

CONST-P: P via constructive deformation

ALLU-NP: NP via allusive deformation DIR-NP: NP via direct deformation

2.6.3 Infrastructure Classes

Definition A.3 (Infrastructure Classes):

P⁺: P enhanced with intentional infrastructure

NP⁻: NP where infrastructure reduces genus

BUILD: Problems reducing polynomially after infrastructure

Definition 2.1 (Verification Geodesic):

For problem A and candidate solution x, the verification geodesic V(x) is the shortest path on MA from problem statement to verified solution. Its length |V(x)| defines verification complexity.

Definition 2.2 (Generation Geodesic):

The generation geodesic G(A) is the shortest path on MA from problem statement to any verified solution. Its length |G(A)| defines solution complexity.

Definition 2.3 (Homoiconic Embedding):

A diffeomorphism φ: MA → M'A that preserves computational semantics while altering geodesic distances. This represents finding the "right" problem representation.

Theorem 3.2 (NP as Search Geometry):

A problem A is in NP iff there exists a manifold representation where |V(x)| is polynomial, but no such guarantee exists for |G(A)| in all representations.

Proof: Follows directly from definitions: NP verification is efficient (short V(x)), while solution finding may require exponential search (long G(A)) in the naive geometry.

Corollary 3.5 (Creativity Bound):

Proving P = NP is equivalent to demonstrating a universal mathematical principle for constructing geodesic-shortcut embeddings.