{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:KZIC4GJRNWTB4RRYOZL5OAXV5A","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":"f6164d252f6eb9bb8206cad1e621625a9a0bc205e4b02ae5eff1364b22e2f96f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-11T16:23:23Z","title_canon_sha256":"8c38a60860ecbfbd0197576e370c1abfb53a92412d03f02af1a4a82cd7ebf914"},"schema_version":"1.0","source":{"id":"1405.2547","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2547","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2547v1","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2547","created_at":"2026-05-18T02:52:05Z"},{"alias_kind":"pith_short_12","alias_value":"KZIC4GJRNWTB","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_16","alias_value":"KZIC4GJRNWTB4RRY","created_at":"2026-05-18T12:28:35Z"},{"alias_kind":"pith_short_8","alias_value":"KZIC4GJR","created_at":"2026-05-18T12:28:35Z"}],"graph_snapshots":[{"event_id":"sha256:809f4ec2294edd9d7c588f5d8e40e352163eee7c9ff33b07fdc2ccde730cae75","target":"graph","created_at":"2026-05-18T02:52:05Z","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":"Connection matrices for graph parameters with values in a field have been introduced by M. Freedman, L. Lov{\\'a}sz and A. Schrijver (2007). Graph parameters with connection matrices of finite rank can be computed in polynomial time on graph classes of bounded tree-width. We introduce join matrices, a generalization of connection matrices, and allow graph parameters to take values in the tropical rings (max-plus algebras) over the real numbers. We show that rank-finiteness of join matrices implies that these graph parameters can be computed in polynomial time on graph classes of bounded clique-","authors_text":"Johann A. Makowsky, Nadia Labai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-11T16:23:23Z","title":"Finiteness conditions for graph algebras over tropical semirings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2547","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":"sha256:101f294482541094210ae1bbdd587a9922cd71c471f9062bc79b2484131c07c3","target":"record","created_at":"2026-05-18T02:52:05Z","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":"f6164d252f6eb9bb8206cad1e621625a9a0bc205e4b02ae5eff1364b22e2f96f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-05-11T16:23:23Z","title_canon_sha256":"8c38a60860ecbfbd0197576e370c1abfb53a92412d03f02af1a4a82cd7ebf914"},"schema_version":"1.0","source":{"id":"1405.2547","kind":"arxiv","version":1}},"canonical_sha256":"56502e19316da61e46387657d702f5e83b0bac8d4d736fdaf30e7b3b749431db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56502e19316da61e46387657d702f5e83b0bac8d4d736fdaf30e7b3b749431db","first_computed_at":"2026-05-18T02:52:05.269792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:52:05.269792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SzENLV2oYS+KzENiuNW2Izy3rrUGBAi6vPg/OkP41hRWqrYUeG9o1N4SnMOEPDTZwpbxGtM9dcgUfpLF6mrzAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:52:05.270403Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2547","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:101f294482541094210ae1bbdd587a9922cd71c471f9062bc79b2484131c07c3","sha256:809f4ec2294edd9d7c588f5d8e40e352163eee7c9ff33b07fdc2ccde730cae75"],"state_sha256":"06bb15f9676ce169e7c322911f44e7f3f5c36e5054c32e06eba4e6abfb889dc2"}