{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DLVJO6UKNKQTCF74WLTMDHOISW","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":"a454fc42e071ac99bd144143c8686e32d88652d60ece58d92cb4736d3514db4b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-11-22T17:48:34Z","title_canon_sha256":"0cbf31b89cbf6cdfad53a8228ea7e63ccd00003763c7d224d7cbc19ea987c932"},"schema_version":"1.0","source":{"id":"1311.5832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.5832","created_at":"2026-05-18T03:06:23Z"},{"alias_kind":"arxiv_version","alias_value":"1311.5832v1","created_at":"2026-05-18T03:06:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.5832","created_at":"2026-05-18T03:06:23Z"},{"alias_kind":"pith_short_12","alias_value":"DLVJO6UKNKQT","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DLVJO6UKNKQTCF74","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DLVJO6UK","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:c751ead671aa27f80f9f34a07f473960c8c5701bded77295b6b1cc50a3e670fd","target":"graph","created_at":"2026-05-18T03:06:23Z","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 give the maximal distance between a copula and itself when the argument is permuted for arbitrary dimension, generalizing a result for dimension two by Nelsen (2007), Klement and Mesiar (2006). Furthermore, we establish a subset of $[0,1]^d$ in which this bound might be attained. For each point in this subset we present a copula and a permutation, for which the distance in this point is maximal. In the process, we see that this subset depends on the dimension being even or odd.","authors_text":"Michael Harder, Ulrich Stadtm\\\"uller","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-11-22T17:48:34Z","title":"Maximal Non-Exchangeability in Dimension d"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5832","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:e3eaec92cd262bd4e30410e423410c0017c9fa95b3c84f1d5393a493f1b07398","target":"record","created_at":"2026-05-18T03:06:23Z","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":"a454fc42e071ac99bd144143c8686e32d88652d60ece58d92cb4736d3514db4b","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-11-22T17:48:34Z","title_canon_sha256":"0cbf31b89cbf6cdfad53a8228ea7e63ccd00003763c7d224d7cbc19ea987c932"},"schema_version":"1.0","source":{"id":"1311.5832","kind":"arxiv","version":1}},"canonical_sha256":"1aea977a8a6aa13117fcb2e6c19dc895b6cd86b1f669e0292551da77fc9c7bdf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1aea977a8a6aa13117fcb2e6c19dc895b6cd86b1f669e0292551da77fc9c7bdf","first_computed_at":"2026-05-18T03:06:23.135643Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:23.135643Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7BChe4zA8EpraXZIr8n+JslncoGV+E8eh5Y9Ul5xaddtME9+jCzWBbGysWk1hKTGSApyt5klg1+h3dyD6aMjDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:23.136060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.5832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3eaec92cd262bd4e30410e423410c0017c9fa95b3c84f1d5393a493f1b07398","sha256:c751ead671aa27f80f9f34a07f473960c8c5701bded77295b6b1cc50a3e670fd"],"state_sha256":"e3ec8de692cde7a9168dd7d1609d05f01767326589adf3d31ffb9ca3d0e02425"}