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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","authors_text":"Aur\\'elie Lagoutte, Kevin Hendrey, Louis Esperet, Margaux Marseloo, Raphael Steiner, Sergey Norin","cross_cats":["cs.DM"],"headline":"All nowhere-zero Z_2^8-flows on every 2-edge-connected graph are connected by sequences differing on single cycles.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-12-19T08:34:36Z","title":"Nowhere-zero flow reconfiguration"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.17342","kind":"arxiv","version":4},"verdict":{"created_at":"2026-05-16T21:13:45.395009Z","id":"2fb4fabf-fb98-4597-bba0-f28a01724102","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"All nowhere-zero Z_2^8-flows on every 2-edge-connected graph are connected by sequences differing on single cycles.","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.","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."}},"verdict_id":"2fb4fabf-fb98-4597-bba0-f28a01724102"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7af4b719cfdf9b3230573c8ca4387505230c9c48e2720a4bebf57f1e2adc0fa2","target":"record","created_at":"2026-07-07T01:16:02Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fe1836a759056c7858926812fd5ba2677908d642fe6aad21c9e2cc17de08aa5f","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-12-19T08:34:36Z","title_canon_sha256":"be5e0895ca3721c0c10d7ce054bea574b3d141a0593ac659ad62d61dec272e42"},"schema_version":"1.0","source":{"id":"2512.17342","kind":"arxiv","version":4}},"canonical_sha256":"391d94c2383e54fd5473abeaef4dd1b6bb1313db1fd74c59340051e8c910eec8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"391d94c2383e54fd5473abeaef4dd1b6bb1313db1fd74c59340051e8c910eec8","first_computed_at":"2026-07-07T01:16:02.434298Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-07T01:16:02.434298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q6iTokL9xjflOBkgo04nsOsvUXKkDtjhuuD9MjOPuGwBtm0GP6iVPYBcjdKhdA+AGOvTf+cfL5P+/FuLBNMBBg==","signature_status":"signed_v1","signed_at":"2026-07-07T01:16:02.435241Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.17342","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7af4b719cfdf9b3230573c8ca4387505230c9c48e2720a4bebf57f1e2adc0fa2","sha256:2e22eb89229ce6a58ba69b1623408490120b243d5a67c914c9d73f1356f2948a"],"state_sha256":"011546a5fd8176b993ae2c795d34a06ba767ddf06a9f60bfd58412f51fd4dfdb"}