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OriginalCarrier

Abstract

OriginalCarrier

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 (actual_sugawara_one_monomial_bound).

Lean statement: D5/S3/VertexAlgebra/SourceMobius/OriginalCarrier.actual_sugawara_one_monomial_bound

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/SourceMobius/OriginalCarrier.actual_sugawara_one_monomial_bound (✓ 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 original integer determinant-unit assumption supplies H = inverse(gramComplex D) by determinant mapping, retaining the sharp actual-weight monomial bound.

Theorem 1.2 (actual_sourceFlow_eq_sum).

Lean statement: D5/S3/VertexAlgebra/SourceMobius/OriginalCarrier.actual_sourceFlow_eq_sum

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/SourceMobius/OriginalCarrier.actual_sourceFlow_eq_sum (✓ 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 sourceFlow operation uses the closed binomial coordinate substitution. Its bridge to the algebra flow consumes the coordinate formula; true finite charge support supplies a uniform cutoff for its equality to the finite factorial sum of the existing Sugawara mode 1.

Theorem 1.3 (actual_sugawara_one_bound).

Lean statement: D5/S3/VertexAlgebra/SourceMobius/OriginalCarrier.actual_sugawara_one_bound

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/SourceMobius/OriginalCarrier.actual_sugawara_one_bound (✓ 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 same maximum original oscillator weighted degree plus one kills every original Carrier source. The proof consumes the integer-hypothesis monomial bound through the actual finite charge and monomial supports.

Theorem 1.4 (sourceFlow_add).

Lean statement: D5/S3/VertexAlgebra/SourceMobius/OriginalCarrier.sourceFlow_add

Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/SourceMobius/OriginalCarrier.sourceFlow_add (✓ 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 charge-sector algebra composition law extends to additive parameter composition on the original finite charge direct sum.

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