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Coordinates

Abstract

Coordinates

This is the finite source-coordinate dependency of full corrected-field inversion. Arbitrary symmetric even integral lattices, rank zero, zero charge, empty supports and indefinite norms remain in scope. No positive energy, ground pairing or Jacobi premise is used.

Theorem 1.1 (sectorFlow_X).

Lean statement: D5/S3/VertexAlgebra/SourceMobius/Coordinates.sectorFlow_X

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/SourceMobius/Coordinates.sectorFlow_X (✓ std3). ∎

Citation. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The actual finite flow sends X(i,r) to the binomial sum plus the bilinear charge times u^(r+1). The proof calculates actual iterated lowering powers and their factorial cancellation.

Theorem 1.2 (sectorFlow_eq_aeval).

Lean statement: D5/S3/VertexAlgebra/SourceMobius/Coordinates.sectorFlow_eq_aeval

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/SourceMobius/Coordinates.sectorFlow_eq_aeval (✓ std3). ∎

Citation. Bojko Bakalov and Victor G. Kac (2004). Twisted Modules over Lattice Vertex Algebras. DOI: 10.1142/9789812702562_0001. URL: https://arxiv.org/abs/math/0402315v1.

Commentary.

The binomial variable formula determines the same algebra substitution on all finite oscillator polynomials. It is the closed coordinate form of the already proved actual factorial flow.

The imported Sugawara architecture retains Kalle Kytola attribution. No literature novelty is claimed. Full all-source corrected-field adjointness, the K_L/K_R coefficient law and the complete Monster, VOA, CFT, fusion, string-theory and AdS/CFT goal remain open.

References