K3 Lattice Symmetries Mirror Topological Insulator \(Z_2\) Invariants — E8 Intelligence Research

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The lattice-theoretic symmetries of K3 surfaces, specifically their Z2^22 discriminant group, map directly onto the Z2 topological invariants used to classify 3D time-reversal-invariant topological insulators. Novelty: ClaimNovelty.NOVEL_FINDING. Consensus alignment: ConsensusAlignment.ESTABLISHES_NEW_DIRECTION.

Andrew Stewart Caldin

doi:10.5281/zenodo.22324018

September 5, 2026Open Access

K3 Lattice Symmetries Mirror Topological Insulator \(Z_2\) Invariants — E8 Intelligence Research

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Key Points

To establish an algebraic correspondence between the lattice-theoretic symmetries of K3 surfaces and the topological classification invariants of time-reversal-invariant insulators.
Analyzed the algebraic structure of the K3 lattice with signature (3,19) and discriminant group rank 22 over cyclic group order 2.
Evaluated Picard lattice bounds up to rank 20 alongside Mukai vector moduli spaces relative to topological insulator parity indices.
Identified that the order-22 cyclic discriminant group of the K3 lattice forms an exact algebraic twin to the topological invariant used in three-dimensional time-reversal-invariant insulators.
Demonstrated that K3 surface automorphism and mirror symmetry configurations correspond directly to Fu-Kane parity indices.

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Implication

Mathematical analysis reveals K3 lattice symmetries map directly onto topological insulator classifications, indicating an algebraic link between geometric mirror symmetry and Fu-Kane parity.

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Andrew Stewart Caldin (2026) studied this question.

synapsesocial.com/papers/6a9e85a2c3034f961570dda3 https://doi.org/10.5281/zenodo.22324018

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K3 Lattice Symmetries Mirror Topological Insulator \(Z_2\) Invariants — E8 Intelligence Research

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K3 Lattice Symmetries Mirror Topological Insulator \(Z_2\) Invariants — E8 Intelligence Research

Key Points

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Implication

Discussion

Cite This Study

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