{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:23GRXNCEZLA7CSVGHCSXUKW5QA","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":"4489d8842117347eecbab134d2c33cee2d784bf9eed70abc556d658b2e891fd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-10-21T11:16:05Z","title_canon_sha256":"9435af2bd802cdabfb9ccbff86437d20fff90900468c45b783b4ea507b44444c"},"schema_version":"1.0","source":{"id":"2510.18529","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.18529","created_at":"2026-06-19T16:11:14Z"},{"alias_kind":"arxiv_version","alias_value":"2510.18529v3","created_at":"2026-06-19T16:11:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.18529","created_at":"2026-06-19T16:11:14Z"},{"alias_kind":"pith_short_12","alias_value":"23GRXNCEZLA7","created_at":"2026-06-19T16:11:14Z"},{"alias_kind":"pith_short_16","alias_value":"23GRXNCEZLA7CSVG","created_at":"2026-06-19T16:11:14Z"},{"alias_kind":"pith_short_8","alias_value":"23GRXNCE","created_at":"2026-06-19T16:11:14Z"}],"graph_snapshots":[{"event_id":"sha256:dbd0278889b7a0e6b13dfa557dbc952de8ccff05da781b2f4ff6a753b6263725","target":"graph","created_at":"2026-06-19T16:11:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2510.18529/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We continue the study of Adin, Alon and Roichman [arXiv:2502.14398, 2025] on the number of steps required to sort $n$ labelled points on a circle by transpositions. Imagine that the vertices of a cycle of length $n$ are labelled by the elements $1,\\dots,n$. We are allowed to change this labelling by swapping the labels of any two vertices on the cycle. How many swaps are needed to obtain a labelling that has the elements $1,\\dots,n$ in clockwise order?\n  We provide evidence for their conjecture that at most $n-3$ transpositions are needed to sort a circular permutation when $n$ is not prime. W","authors_text":"Anurag Bishnoi, Carla Groenland, Dion Gijswijt, Paul Bastide, Rohinee Joshi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-10-21T11:16:05Z","title":"Circular sorting, strong complete mappings and wreath product constructions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.18529","kind":"arxiv","version":3},"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":"sha256:3ad0cfa18ed40a3ca294b60a8e4515692ac4974ebad16fed30de06315d4b0489","target":"record","created_at":"2026-06-19T16:11:14Z","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":"4489d8842117347eecbab134d2c33cee2d784bf9eed70abc556d658b2e891fd1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-10-21T11:16:05Z","title_canon_sha256":"9435af2bd802cdabfb9ccbff86437d20fff90900468c45b783b4ea507b44444c"},"schema_version":"1.0","source":{"id":"2510.18529","kind":"arxiv","version":3}},"canonical_sha256":"d6cd1bb444cac1f14aa638a57a2add800bf1f7412535461ef32206d7fb14a7d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d6cd1bb444cac1f14aa638a57a2add800bf1f7412535461ef32206d7fb14a7d8","first_computed_at":"2026-06-19T16:11:14.245685Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:11:14.245685Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2oDerlirvMqtDfNY9rFbyL761GF+TH3sMi4RXH3son9RmQpBMLTQSH8EEHkhI2l8haf+JW/VDjKaiDC7UTe+Aw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:11:14.246193Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.18529","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ad0cfa18ed40a3ca294b60a8e4515692ac4974ebad16fed30de06315d4b0489","sha256:dbd0278889b7a0e6b13dfa557dbc952de8ccff05da781b2f4ff6a753b6263725"],"state_sha256":"07207f3e57f0f5be52ce1c1c894040b673c5dd00255d6f25ce848ad859d5791e"}