What question did this study set out to answer?

This research aims to present the BCT Superfluid Lattice Model as a physical realization of bosonic string theory on the D4 root lattice.

March 15, 2026Open Access

BCT Letter 37: Ramanujan's Vacuum — The BCT Superfluid Lattice as the Physical Realisation of the Bosonic String on the D4 Root Lattice

Key Points

This research aims to present the BCT Superfluid Lattice Model as a physical realization of bosonic string theory on the D4 root lattice.
Analyzed the properties of the D4 kissing number in relation to string modes.
Evaluated the BCT instanton action and its connection to the Ramanujan discriminant.
Identified corrections in the mass hierarchy formula linked to string amplitudes.
Established an equivalence between the D4 kissing number and transverse bosonic string modes.
Found that the BCT instanton action matches the Ramanujan discriminant at a specific point.
Determined that the mass hierarchy formula's residual relates to string amplitude corrections.

Abstract

We demonstrate that the BCT Superfluid Lattice Model is the unique physical realisation of the critical bosonic string theory compactified on the D4 root lattice. Three independent lines of evidence converge: (i) the D4 kissing number 24 is identical to the number of transverse bosonic string modes, (ii) the BCT instanton action SD4 = π5/6 is the evaluation of the Ramanujan discriminant at the modular CM point τ = i, and (iii) the 0. 075% residual in the BCT mass hierarchy formula is identified as the genus-1 string amplitude correction. BCT resolves the non-determinism of general relativity: GR emerges from a fully deterministic superfluid substrate. The Ramanujan tau function τ (n) is reinterpreted as the degeneracy spectrum of the quantum vacuum.

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