Signs and signatures in SL(2) x R+ exceptional field theory: Hull's starred theories from a non-Euclidean generalised metric

We determine, with every sign kept, which eleven- and ten-dimensional theories the SL(2) x R+ exceptional field theory of Berman, Blair, Malek and Rudolph describes when its generalised metric is not positive definite, for external signatures (8,1) and (9,0). For all twelve sign cells we derive the signature, the character of the circle, and the signs of the form-field kinetic terms on both sections. The three-form sign on the M-theory section is lambda = epsilon sigma, the IIB circle is spacelike or timelike according to tau = epsilon, and the IIB axion and four-form signs equal sigma. The ExFT duality relation gives a real (anti-)self-dual five-form exactly when epsilon (-1)^t9 = -1, which on the M-theory section reads lambda = -(-1)^t11. This agrees with Hull's three-form sign in the signatures (10,1) and (9,2) reached here, but it is a parity rule, not specific to Hull's theories: the two other cells that meet the condition give eleven-dimensional theories, (8,3) and (11,0), in the Weyl orbit that Keurentjes found to contain the signatures not allowed by eleven-dimensional supersymmetry. The four cells that pair Hull theories match the four shrinking two-torus limits of Hull in this range, with their circle characters. The table entries are checked numerically at quadratic order around constant backgrounds against eleven- and ten-dimensional supergravity, with the curvature computed from its definition; the check also finds, at that order, two probable misprints in the internal-derivative part of the scalar potential as printed in arXiv:1512.06115v2. A short methods note: the nine-dimensional coset SL(2,R)/SO(1,1) x R+ is Hull's, and the mechanism is known for SL(5) and E6(6). Version 2 changes only the text, after an independent post-publication review (summary in REVIEW_POSTPUB.md); no computation or number changed. See the Note on versions in the paper. Version 1 (doi:10.5281/zenodo.23028881) stays available. The source archive contains the LaTeX source, all scripts (run_all.sh reproduces every table entry and number), the output of the longest run (m2_output.txt), the plan written before the computation, and the review summary.