{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EWLS3LXKPNF5NFKRORHJJ3LQR4","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":"8d5f925bb3b49c5e835266b4eaaa4462f4fe8ae90f8a448587379f3f9af47cf0","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-07-10T14:26:26Z","title_canon_sha256":"5c359a385c4aee4fb101c573e0fb158e4de591049e65a56c07e167217fb6f5f5"},"schema_version":"1.0","source":{"id":"1407.2801","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.2801","created_at":"2026-05-18T02:31:20Z"},{"alias_kind":"arxiv_version","alias_value":"1407.2801v2","created_at":"2026-05-18T02:31:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.2801","created_at":"2026-05-18T02:31:20Z"},{"alias_kind":"pith_short_12","alias_value":"EWLS3LXKPNF5","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"EWLS3LXKPNF5NFKR","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"EWLS3LXK","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:eaf89e78e96525d49b1f01a8508dd73c354a218c7ff40aa6dd1f07b589b8b7f7","target":"graph","created_at":"2026-05-18T02:31:20Z","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 a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form $QAP(A,B)$, by showing that the identity permutation is optimal when $A$ and $B$ are respectively a Robinson similarity and dissimilarity matrix and one of $A$ or $B$ is a Toeplitz matrix. A Robinson (dis)similarity matrix is a symmetric matrix whose entries (increase) decrease monotonically along rows and columns when moving away from the diagonal, and such matrices arise in the classical seriation problem.","authors_text":"Matteo Seminaroti, Monique Laurent","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-07-10T14:26:26Z","title":"The quadratic assignment problem is easy for Robinsonian matrices with Toeplitz structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2801","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:ec70ed3ab5433705dc6049d12d2882128c25c10f6251a0ab9e7b44078c9cc275","target":"record","created_at":"2026-05-18T02:31:20Z","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":"8d5f925bb3b49c5e835266b4eaaa4462f4fe8ae90f8a448587379f3f9af47cf0","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-07-10T14:26:26Z","title_canon_sha256":"5c359a385c4aee4fb101c573e0fb158e4de591049e65a56c07e167217fb6f5f5"},"schema_version":"1.0","source":{"id":"1407.2801","kind":"arxiv","version":2}},"canonical_sha256":"25972daeea7b4bd69551744e94ed708f096451425e2f85c3fb7ebf663b077e35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25972daeea7b4bd69551744e94ed708f096451425e2f85c3fb7ebf663b077e35","first_computed_at":"2026-05-18T02:31:20.871102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:20.871102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fXxT826sZffch0hHZPAO/uc5c/rKlWmBilW5ZPb2WsJRNNZer4sByRcRBjQ2Msg3mPJgkxWRCbc6EEYnWEg5CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:20.871827Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.2801","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec70ed3ab5433705dc6049d12d2882128c25c10f6251a0ab9e7b44078c9cc275","sha256:eaf89e78e96525d49b1f01a8508dd73c354a218c7ff40aa6dd1f07b589b8b7f7"],"state_sha256":"710c32f3210c1b98490c2e1e7493985a0f2ead5007a3de0362494e43da770931"}