@InProceedings{gokaj_et_al:LIPIcs.ITCS.2025.55, author = {Gokaj, Geri and K\"{u}nnemann, Marvin}, title = {{Completeness Theorems for k-SUM and Geometric Friends: Deciding Fragments of Linear Integer Arithmetic}}, booktitle = {16th Innovations in Theoretical Computer Science Conference (ITCS 2025)}, pages = {55:1--55:25}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-361-4}, ISSN = {1868-8969}, year = {2025}, volume = {325}, editor = {Meka, Raghu}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.55}, URN = {urn:nbn:de:0030-drops-226835}, doi = {10.4230/LIPIcs.ITCS.2025.55}, annote = {Keywords: fine-grained complexity theory, descriptive complexity, presburger arithmetic, completeness results, k-SUM} }