{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:I63QAVGMGFG5JY5JICYWVPCALU","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":"4f0627f134dbd0cda27a6688adfb6218eb9ca8a07c25afabc2d614fbc84a9d03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-11-07T09:50:36Z","title_canon_sha256":"f3a8cfa0202040323c2e39b5fd3603b47c51c12187d864f21add805ffb5c3782"},"schema_version":"1.0","source":{"id":"2311.03844","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.03844","created_at":"2026-06-19T16:12:12Z"},{"alias_kind":"arxiv_version","alias_value":"2311.03844v2","created_at":"2026-06-19T16:12:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.03844","created_at":"2026-06-19T16:12:12Z"},{"alias_kind":"pith_short_12","alias_value":"I63QAVGMGFG5","created_at":"2026-06-19T16:12:12Z"},{"alias_kind":"pith_short_16","alias_value":"I63QAVGMGFG5JY5J","created_at":"2026-06-19T16:12:12Z"},{"alias_kind":"pith_short_8","alias_value":"I63QAVGM","created_at":"2026-06-19T16:12:12Z"}],"graph_snapshots":[{"event_id":"sha256:d3226bd9e0f007ea6d0812425bef46559a9ba5ce47d2f3593057352574b1aa49","target":"graph","created_at":"2026-06-19T16:12:12Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2311.03844/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Max-plus algebra is a semiring with addition $a\\oplus b = \\max(a,b)$ and multiplication $a\\otimes b = a+b$. It is applied in cases, such as combinatorial optimization and discrete event systems. We consider the power of max-plus square matrices, which is equivalent to obtaining the all-pair maximum weight paths with a fixed length in the corresponding weighted digraph. Each $n$-by-$n$ matrix admits the CSR expansion that decomposes the matrix into a sum of at most $n$ periodic terms after $O(n^{2})$ times of powers. In this study, we propose an $O(n(m+n \\log n))$ time algorithm for the CSR exp","authors_text":"Yuki Nishida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-11-07T09:50:36Z","title":"Algorithm for the CSR expansion of max-plus matrices using the characteristic polynomial"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.03844","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":"sha256:4df25863da702b9959a557285ef862ae076e2a034b82e11f285c6f109802d6c6","target":"record","created_at":"2026-06-19T16:12:12Z","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":"4f0627f134dbd0cda27a6688adfb6218eb9ca8a07c25afabc2d614fbc84a9d03","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2023-11-07T09:50:36Z","title_canon_sha256":"f3a8cfa0202040323c2e39b5fd3603b47c51c12187d864f21add805ffb5c3782"},"schema_version":"1.0","source":{"id":"2311.03844","kind":"arxiv","version":2}},"canonical_sha256":"47b70054cc314dd4e3a940b16abc405d0bcd39355b19902de5318c2442f8fdfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47b70054cc314dd4e3a940b16abc405d0bcd39355b19902de5318c2442f8fdfb","first_computed_at":"2026-06-19T16:12:12.440798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:12:12.440798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nSTMkWzvM3qjJAaoIo/L9EtOtye+IOr5KHkG74OLC5KtDj9U3N38++i1ZA3ye6noo2KVdW307btzWCtf6reQBA==","signature_status":"signed_v1","signed_at":"2026-06-19T16:12:12.441214Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.03844","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4df25863da702b9959a557285ef862ae076e2a034b82e11f285c6f109802d6c6","sha256:d3226bd9e0f007ea6d0812425bef46559a9ba5ce47d2f3593057352574b1aa49"],"state_sha256":"493531427995b8076d5775aa3494c52cab0fafae6f79b1d769a4ef731bebe7f7"}