{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LNKLZSDR2SK5M24NIKZ42L2LLW","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":"35079164ff0432e513bbd8111238b0a00ea471f5420bdf9855d77e7207d2b6eb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-04T20:42:19Z","title_canon_sha256":"53ef1850dd089d90c5948183e1bc81524fc9f5a7d52b5e11bd45a18600c0ee54"},"schema_version":"1.0","source":{"id":"1705.02008","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02008","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02008v1","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02008","created_at":"2026-05-18T00:45:00Z"},{"alias_kind":"pith_short_12","alias_value":"LNKLZSDR2SK5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LNKLZSDR2SK5M24N","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LNKLZSDR","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:32205d40b704cb3554e60d7a62936c73f833578f30514619913c5719e2b3fbeb","target":"graph","created_at":"2026-05-18T00:45:00Z","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 present several results describing the interplay between the max algebraic joint spectral radius (JSR) for compact sets of matrices and suitably defined matrix norms. In particular, we extend a classical result for the conventional algebra, showing that the JSR can be described in terms of induced norms of the matrices in the set. We also show that for a set generating an irreducible semigroup (in a cone-theoretic sense), a monotone Barabanov norm always exists. This fact is then used to show that the max algebraic JSR is locally Lipschitz continuous on the space of compact irreducible sets","authors_text":"Fabian Wirth, Nicola Guglielmi, Oliver Mason","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-04T20:42:19Z","title":"Barabanov norms, Lipschitz continuity and monotonicity for the max algebraic joint spectral radius"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02008","kind":"arxiv","version":1},"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":"sha256:52a7db370b704c6a4684b179441946cf93e285c35df4060b351ad19b14a35f73","target":"record","created_at":"2026-05-18T00:45:00Z","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":"35079164ff0432e513bbd8111238b0a00ea471f5420bdf9855d77e7207d2b6eb","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2017-05-04T20:42:19Z","title_canon_sha256":"53ef1850dd089d90c5948183e1bc81524fc9f5a7d52b5e11bd45a18600c0ee54"},"schema_version":"1.0","source":{"id":"1705.02008","kind":"arxiv","version":1}},"canonical_sha256":"5b54bcc871d495d66b8d42b3cd2f4b5da0028eba249904a41dd59092a2c4bfab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b54bcc871d495d66b8d42b3cd2f4b5da0028eba249904a41dd59092a2c4bfab","first_computed_at":"2026-05-18T00:45:00.871210Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:00.871210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b6jBDIoCmcTbkAXXOOtlbg/zY6hpG5eDOb5x2U9BHZEHGIDSyMtOA/P3psnybVNdG99UXOTm8P9CuGp/Hhc7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:00.871615Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02008","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52a7db370b704c6a4684b179441946cf93e285c35df4060b351ad19b14a35f73","sha256:32205d40b704cb3554e60d7a62936c73f833578f30514619913c5719e2b3fbeb"],"state_sha256":"9b65cfb819fd99f44fdfe873432ab828dbb512a1191c6869dab728139150cdc3"}