{"paper":{"title":"The Principle of Isomorphism: A Theory of Population Activity in Grid Cells and Beyond","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.NC","authors_text":"Bailu Si, Fei Song, Maoshen Xu, Shanshan Qin","submitted_at":"2025-10-03T09:42:32Z","abstract_excerpt":"Neural population activity organizes into low-dimensional manifolds embedded within high-dimensional state spaces, yet the principles governing the topology and geometry of these manifolds remain elusive. Here, we propose the Principle of Isomorphism (PIso), which posits that the topology of a neural manifold is constrained by the mathematical structure of the computational task it supports. We apply this framework to the mammalian grid cell system through two distinct theoretical lenses: an intrinsic neural metric, which requires a locally flat Riemannian structure, and path integration, whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.02853","kind":"arxiv","version":3},"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/2510.02853/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"}