{"paper":{"title":"Anti-Periodic Positional Encoding: M\\\"obius Boundary Conditions Make In-Context Retrieval Reliable","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CL","authors_text":"Ji Ho Bae","submitted_at":"2026-07-23T15:04:44Z","abstract_excerpt":"M\\\"obius RoPE is a rotary positional encoding built on the anti-periodic frequency ladder $\\theta_i=\\pi(2i+1)/N$: every rotation plane advances by an odd multiple of $\\pi$ across the training context, so the positional holonomy is $-1$ and the two ends of the sequence are deterministically coupled through a closed-form Dirichlet \"dipole\"; to our knowledge this is the first anti-periodic boundary condition in positional encoding. We verify the theory numerically to $\\sim 10^{-6}$ and pretrain 48 models spanning six 160M-class and three 410M-class arms (2B FineWeb-Edu tokens each; the hybrid arm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.21405","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/2607.21405/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"}