Original matter/ghost unrestricted integer iterate
Abstract
Original matter/ghost unrestricted integer iterate
The finite-support constructions and residue telescope retain the Scott Carnahan vertexAlg Apache-2.0 attribution of their existing suppliers. The signed proof calculations adapt the actual bc ghost supplier to arbitrary complex modules, while reusing the existing generic PairSpace cancellation kernel and delta-binomial identity. This is classical Dong locality and creative reconstruction, with no literature novelty claim. Original stateField_parity determines the parity of the actual mode product. Signed all-integer residue locality, original creation and original translation feed the existing tensor creative_unique theorem. Four actual even and odd components then give the unrestricted identity. The full three-integer Borcherds identity, induced quotient identities, cohomology, fusion, Monster identification, string realization and AdS/CFT remain open.
Theorem 1.1 (All original states and all integer modes).
Lean statement: D5/S3/VertexAlgebra/Lattice/LatticeMatterGhostStateFieldIterate.stateField_iterate
Proof. Machine-checked in Lean as D5/S3/VertexAlgebra/Lattice/LatticeMatterGhostStateFieldIterate.stateField_iterate (✓ std3). ∎
Source. Repository-derived.
Commentary.
For every original LatticeData D, all original tensor states a,b,c and all integers r,n, the theorem proves finite support of all three action families and the exact signed iterate identity. Set a0=(a+Pa)/2 and a1=(a-Pa)/2. The reverse braiding is the sum with field pair (b,a0) and field pair (Pb,a1), multiplied by (-1)^r. No homogeneity, rank, Gram-inverse, charge, Jacobi or reconstruction hypothesis is imposed.