{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5RIU2FDMFHJ36DC7OMCW4GKZU3","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a041de6ef7eceee185b71729616096574331a2c07288d038cc7f3f3d34d264d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-13T12:38:45Z","title_canon_sha256":"c5b96b7abdb1ec4eed96d263ad6a1d700943dde4fc8af18d81d3866999c11d25"},"schema_version":"1.0","source":{"id":"1806.04984","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.04984","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"arxiv_version","alias_value":"1806.04984v2","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.04984","created_at":"2026-05-18T00:00:08Z"},{"alias_kind":"pith_short_12","alias_value":"5RIU2FDMFHJ3","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5RIU2FDMFHJ36DC7","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5RIU2FDM","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:8f920d9292123a6d4972058bf70d2c916d0babced7db96dcebea898e9fff7146","target":"graph","created_at":"2026-05-18T00:00:08Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study the behaviour of the minimal slope of Euclidean lattices under tensor product. A general conjecture predicts that $\\mu_{min}(L \\otimes M) = \\mu_{min}(L)\\mu_{min}(M)$ for all Euclidean lattices $L$ and $M$. We prove that this is the case under the additional assumptions that $L$ and $M$ are acted on multiplicity-free by their automorphism group, such that one of them has at most $2$ irreducible components.","authors_text":"Gabriele Nebe, Renaud Coulangeon","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-13T12:38:45Z","title":"Slopes of Euclidean lattices, tensor product and group actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.04984","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:498c3b78a6a96a9bf85cfae92f4febe15cfe07aac59bbeb543a6f470236e1621","target":"record","created_at":"2026-05-18T00:00:08Z","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":"a041de6ef7eceee185b71729616096574331a2c07288d038cc7f3f3d34d264d2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-06-13T12:38:45Z","title_canon_sha256":"c5b96b7abdb1ec4eed96d263ad6a1d700943dde4fc8af18d81d3866999c11d25"},"schema_version":"1.0","source":{"id":"1806.04984","kind":"arxiv","version":2}},"canonical_sha256":"ec514d146c29d3bf0c5f73056e1959a6e363a7ec65f6399aae6fa0eea6817f2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec514d146c29d3bf0c5f73056e1959a6e363a7ec65f6399aae6fa0eea6817f2b","first_computed_at":"2026-05-18T00:00:08.475452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:08.475452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OReEnq5GZFUVvO9KfRuS7DyYwahGKsNvlJ0v7fOiQXrzbZUQNemDaWF3KtSx6R8G0sJPnnpQ9Q+1hA1opkYRDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:08.476057Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.04984","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:498c3b78a6a96a9bf85cfae92f4febe15cfe07aac59bbeb543a6f470236e1621","sha256:8f920d9292123a6d4972058bf70d2c916d0babced7db96dcebea898e9fff7146"],"state_sha256":"5499a2315dcbbcc6f300b853fd970dca87074abee7b7b93f10a90731fbe0e840"}