{"id":"palomar/PALOMAR-2026-11-02-000018","url":"https://github.com/stalex444/arithmetic-of-time-reversible-units-degree-nine/tree/723197b0d1d48fbe12bf19e81683de0090c5ce5c","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-11-02-000018-v1.json","repo":"https://github.com/stalex444/arithmetic-of-time-reversible-units-degree-nine","tags":["math.NT","math.OA","math.RA","quant-ph","math-ph","physics.hist-ph","msc:11R27","msc:11R16","msc:11R06","msc:15B48"],"score":0,"title":"The Arithmetic of Time: reversible units of a degree-nine field. The units of K = LM (L, M cubic) with rank-one Hermitian symbol are exactly those of trivial relative norm to L and to M, a group of rank two, and exactly those whose Schur multipliers run both ways","trust":"high","domain":"math.NT","source":"palomar","authors":["Stephanie Alexander"],"reviews":0,"subject":"math.NT","summary":"Kernel-checked proofs, in Lean 4 + Mathlib, of ten statements. Let K be a number field of degree 9 containing a totally real cubic field L and a cubic field M with one real place. Then K = LM has signature (3, 3), and its nine embeddings are the pairs (lambda, mu). A slot assignment, fixed by a labelling of L's embeddings and a non-real embedding mu_1 of M, places the nine conjugates of x in K in a 3 x 3 Hermitian array, the symbol of x; the symbol of x^-1 is its entrywise (Hadamard) inverse. (1) For every finite index type, a positive semidefinite complex matrix with no zero entry has…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-11-02","reactions":{},"formalized":true}