{"paper":{"title":"Nowhere-zero flow reconfiguration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"All nowhere-zero Z_2^8-flows on every 2-edge-connected graph are connected by sequences differing on single cycles.","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Aur\\'elie Lagoutte, Kevin Hendrey, Louis Esperet, Margaux Marseloo, Raphael Steiner, Sergey Norin","submitted_at":"2025-12-19T08:34:36Z","abstract_excerpt":"We initiate the study of nowhere-zero flow reconfiguration. The natural question is whether any two nowhere-zero $k$-flows of a given graph $G$ are connected by a sequence of nowhere-zero $k$-flows of $G$, such that any two consecutive flows in the sequence differ only on a cycle of $G$.\n  We study this problem in the setting of integer flows and group flows, and prove a number of positive and negative results.\n  * The natural reconfiguration variant of Tutte's 5-flow conjecture, stating that any two nowhere-zero 5-flows in any 2-edge-connected graph are connected, is false in the group and in"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"All nowhere-zero Z_2^8-flows of every 2-edge-connected graph are connected and for every sufficiently large abelian group A, all nowhere-zero A-flows of every 2-edge-connected graph are connected.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The graph is 2-edge-connected, which is required for the existence and reconfiguration properties of nowhere-zero flows to hold in the stated forms.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Nowhere-zero flows on 2-edge-connected graphs can be reconfigured via successive cycle changes for Z_2^8-flows and sufficiently large groups, but the 5-flow reconfiguration conjecture is false, with group structure mattering unlike existence.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"All nowhere-zero Z_2^8-flows on every 2-edge-connected graph are connected by sequences differing on single cycles.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"3b787aacbf614c927fb4e06cf2423afc0ae50781964fa6526a362bce776c1153"},"source":{"id":"2512.17342","kind":"arxiv","version":4},"verdict":{"id":"2fb4fabf-fb98-4597-bba0-f28a01724102","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T21:13:45.395009Z","strongest_claim":"All nowhere-zero Z_2^8-flows of every 2-edge-connected graph are connected and for every sufficiently large abelian group A, all nowhere-zero A-flows of every 2-edge-connected graph are connected.","one_line_summary":"Nowhere-zero flows on 2-edge-connected graphs can be reconfigured via successive cycle changes for Z_2^8-flows and sufficiently large groups, but the 5-flow reconfiguration conjecture is false, with group structure mattering unlike existence.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The graph is 2-edge-connected, which is required for the existence and reconfiguration properties of nowhere-zero flows to hold in the stated forms.","pith_extraction_headline":"All nowhere-zero Z_2^8-flows on every 2-edge-connected graph are connected by sequences differing on single cycles."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.17342/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"}