Sharpened Dynamical Cobordism ties the allowed range of critical exponent δ to theory structure ξ, flagging obstructions from non-trivial cobordism charges that require new degrees of freedom.
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Explicit worldsheet constructions of 9d junctions joining several 10d string theories via generalized RG flow interpolations and closed tachyon condensation, providing dynamical realizations of multi-theory cobordisms.
In codimension-one warped compactifications with exponential potentials, the KK mass decay rate λ_KK is reduced by warping but still satisfies the Sharpened Distance Conjecture precisely when the higher-dimensional potential obeys the Strong de Sitter condition.
A duality web is proposed in which Z2 quotients of M-theory on S1 vee S1 and F-theory on (S1 vee S1) x S1 map to 0A/0B orientifolds and non-supersymmetric E-type and D-type heterotic strings, providing evidence for existing dualities.
Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.
A consistent set of rules from M-theory on S¹ ∨ S¹ combined with type I' enhancements reproduces the light spectra, gauge groups, and global structure of ten-dimensional heterotic string theories, with indications of junctions between them.