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In other words, we show that the Beardwood, Halton and Hammersley theorem does not extend from the case of independent uniformly distributed random variables to the case of stationary ergodic sequences with uniform marginal distributions."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1307.0221","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-30T16:56:56Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"c1d7d9106173e0405f4807cb81810bea0167a842ed29e35993b11a7e599a406d","abstract_canon_sha256":"33e0f563edb0853db8417348a10e6c1fec39de7b0e2c5d9bfd93494b4fefb47f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:24.857175Z","signature_b64":"iqhhSZQJA7hwgQAbEqjqSreloyzRbTx1k1Qen+uuEaAdeEsC/PT6FImPIwA8hSTFyY04tPH7QouhxZ0x+8yaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24b30f9e3f23bf16270bdda9ea7cd72ca58911d0f54c2f09e12669514745bfab","last_reissued_at":"2026-05-18T01:06:24.856681Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:24.856681Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Beardwood-Halton-Hammersley Theorem for Stationary Ergodic Sequences: a Counterexample","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"math.PR","authors_text":"Alessandro Arlotto, J. 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