{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BEJT6JHJHHRGK2YYQ5MI6TMWKB","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":"1194917981902dc74f282ddaf789c7a060df3bdfc79239ad0825e010c3b2612a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-14T23:19:17Z","title_canon_sha256":"72d61609df82114ab26f177b2fe6d3622bbc76138a3340cab508237f1364fa11"},"schema_version":"1.0","source":{"id":"1508.03674","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.03674","created_at":"2026-05-18T01:35:15Z"},{"alias_kind":"arxiv_version","alias_value":"1508.03674v1","created_at":"2026-05-18T01:35:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.03674","created_at":"2026-05-18T01:35:15Z"},{"alias_kind":"pith_short_12","alias_value":"BEJT6JHJHHRG","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BEJT6JHJHHRGK2YY","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BEJT6JHJ","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:ff3de0fb12dd839ae152a78e37939cc3b90e94c374108032d51451d8cbe65351","target":"graph","created_at":"2026-05-18T01:35:15Z","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":"Consider a finite sequence of permutations of the elements 1,...,n, with the property that each element changes its position by at most 1 from any permutation to the next. We call such a sequence a tangle, and we define a move of element i to be a maximal subsequence of at least two consecutive permutations during which its positions form an arithmetic progression of common difference +1 or -1. We prove that for any initial and final permutations, there is a tangle connecting them in which each element makes at most 5 moves, and another in which the total number of moves is at most 4n. On the ","authors_text":"Alexander E. Holroyd, Lev Nachmanson, Sergey Bereg, Sergey Pupyrev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-14T23:19:17Z","title":"Representing Permutations with Few Moves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.03674","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":"sha256:0957717fc42e645c86a2ff950903c3000cfec7981f88b03899e2676de717dc90","target":"record","created_at":"2026-05-18T01:35:15Z","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":"1194917981902dc74f282ddaf789c7a060df3bdfc79239ad0825e010c3b2612a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-14T23:19:17Z","title_canon_sha256":"72d61609df82114ab26f177b2fe6d3622bbc76138a3340cab508237f1364fa11"},"schema_version":"1.0","source":{"id":"1508.03674","kind":"arxiv","version":1}},"canonical_sha256":"09133f24e939e2656b1887588f4d96505a926f07be459eecf3718080c66abc16","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09133f24e939e2656b1887588f4d96505a926f07be459eecf3718080c66abc16","first_computed_at":"2026-05-18T01:35:15.458342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:15.458342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"F/kuJBrAb8j00WQvvLSOQLYn0Ap46I091fYHgT1J+CAet2Ui3Nnwf9CM1P80QvZQjEpi9wBNmVdQMds7AugtCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:15.458753Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.03674","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0957717fc42e645c86a2ff950903c3000cfec7981f88b03899e2676de717dc90","sha256:ff3de0fb12dd839ae152a78e37939cc3b90e94c374108032d51451d8cbe65351"],"state_sha256":"3f78da603caf4ab9cd712d44027ffe115289922d78a4497afd452f65b6e8f30c"}