{"paper":{"title":"On Trajectory-Based Stability Analysis for $1$-bit Sigma-Delta Quantization and its Application to the Second-Order Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Alessandro Lupoli, Felix Krahmer, Rohan Joy","submitted_at":"2026-05-16T19:12:14Z","abstract_excerpt":"A state-of-the-art strategy for digitally representing a bandlimited signal $f$ is $\\Sigma\\Delta$ quantization. $\\Sigma\\Delta$ quantization schemes choose a bit sequence $(q_n)$ representing the samples $(y_n)$ of $f$ sequentially based on a state sequence $(u_n)$ defined via a recurrence relation of the form \\begin{equation*}\n  u_n = (h*u)_n + y_n - q_n, \\end{equation*} where $h_j = 0$ for $j\\le 0.$ The effectiveness of a quantization scheme crucially depends on the fact that it is stable, i.e. , the state variable remains uniformly bounded in a given class of signals. Thus, a common strategy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.17127","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.17127/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-19T22:33:23.779876Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T22:01:58.026866Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"7e8ab00d18445ca91faf75c149361dfa8d5a541be5a6110914886cd2d6da33d5"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}