{"paper":{"title":"Square-Annular Dynamics and Coalescence Frontiers for $n+\\tau(n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.NT","authors_text":"Eric Li (Trinity College, University of Cambridge)","submitted_at":"2026-06-16T13:38:26Z","abstract_excerpt":"Let $T(n)=n+\\tau(n)$, where $\\tau$ is the divisor function. We study the Erdos-Graham coalescence problem by encoding finite-level obstructions in the divisor-successor graph and in square-annular transfer maps. Coalescence is equivalent both to connectedness of this graph and to synchronization along an infinite non-autonomous sequence of finite annular systems. The basic identities are \\[\n  \\operatorname{im}(\\mathcal A_k)=E_{k+1},\n  \\qquad\n  \\mathcal F_{k^2}=k^2+E_k, \\] where $E_k$ is the set of square-crossing overshoots from below $k^2$. We prove a transfer parity law, dynamic frontier bou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.17926","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/2606.17926/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}