{"id":"palomar/PALOMAR-2026-10-28-000026","url":"https://github.com/sthubbar/goldbach-lean/tree/12f09bfeca2ae00988fa039e2e82c6de4d147108/entries/halupczok2012","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-10-28-000026-v1.json","repo":"https://github.com/sthubbar/goldbach-lean","tags":["math.NT","msc:11P32","msc:11N13","msc:11P55"],"score":0,"title":"CONDITIONAL on Perelli-Pintz-Salerno 1984 and Perelli-Pintz 1993: Halupczok's ternary Goldbach mean value theorem with primes in progressions and short intervals, repaired","trust":"high","domain":"math.NT","source":"palomar","authors":["Steve Hubbard"],"reviews":0,"subject":"math.NT","summary":"CONDITIONAL on two cited results, both taken as explicit hypotheses of the theorems and never as axioms: PPS1984Remark, the printed Remark on p. 530 of A. Perelli, J. Pintz and S. Salerno, Bombieri's theorem in short intervals, 1984, and PP1993Goldbach, the Goldbach analogue of Theorem 3 of A. Perelli and J. Pintz, On the exceptional set for Goldbach's problem in short intervals, 1993, established in its sections 3 to 5 but not printed as a numbered theorem. These are the inputs that the paper's own proof quotes as its Theorems 2.1 and 2.3. PP1993Goldbach is therefore a weaker citation than…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-10-28","reactions":{},"formalized":true,"formalizes":[{"title":"Goldbach's problem with primes in arithmetic progressions and in short intervals","identifier":"arXiv:1212.4406","relationship":"adapts"}]}