{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:N3QRWQT3MGKBCJVENKZSLRXBZL","short_pith_number":"pith:N3QRWQT3","schema_version":"1.0","canonical_sha256":"6ee11b427b61941126a46ab325c6e1cad4c415137b2ce0e5d94f11f761d12b8e","source":{"kind":"arxiv","id":"2512.07349","version":2},"attestation_state":"computed","paper":{"title":"Symmetries in Sorting","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Vikraman Choudhury, Wind Wong","submitted_at":"2025-12-08T09:41:47Z","abstract_excerpt":"Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions, they are functions on lists that perform combinatorial operations on the representation of the input list. In this paper, we study sorting algorithms conceptually as abstract sorting functions.\n  There is a canonical surjection from the free monoid on a set (lists of elements) to the free commutative monoid on the same set (multisets of elements). We show th"},"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":"2512.07349","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"cs.LO","submitted_at":"2025-12-08T09:41:47Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"2a4ab979864cd7289ee6a6918bf20ba29997f5b9a3d51efb3d307ea387526afd","abstract_canon_sha256":"2fb419980c79a13ed5da139bfbea23d42d392bf59abd8fd4a4ab97c3171240ed"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T02:04:49.408157Z","signature_b64":"q2N3htaX3bus24gdvjPTGl/3PJjjRQC50AJJUz/6RwPhIUupVDpyC+oslRaMZojTN18DSP4XDJCkcf3G3SsJBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ee11b427b61941126a46ab325c6e1cad4c415137b2ce0e5d94f11f761d12b8e","last_reissued_at":"2026-06-02T02:04:49.407651Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T02:04:49.407651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Symmetries in Sorting","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Vikraman Choudhury, Wind Wong","submitted_at":"2025-12-08T09:41:47Z","abstract_excerpt":"Sorting algorithms are fundamental to computer science, and their correctness criteria are well understood as rearranging elements of a list according to a specified total order on the underlying set of elements. As mathematical functions, they are functions on lists that perform combinatorial operations on the representation of the input list. In this paper, we study sorting algorithms conceptually as abstract sorting functions.\n  There is a canonical surjection from the free monoid on a set (lists of elements) to the free commutative monoid on the same set (multisets of elements). We show th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.07349","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2512.07349/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2512.07349","created_at":"2026-06-02T02:04:49.407711+00:00"},{"alias_kind":"arxiv_version","alias_value":"2512.07349v2","created_at":"2026-06-02T02:04:49.407711+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.07349","created_at":"2026-06-02T02:04:49.407711+00:00"},{"alias_kind":"pith_short_12","alias_value":"N3QRWQT3MGKB","created_at":"2026-06-02T02:04:49.407711+00:00"},{"alias_kind":"pith_short_16","alias_value":"N3QRWQT3MGKBCJVE","created_at":"2026-06-02T02:04:49.407711+00:00"},{"alias_kind":"pith_short_8","alias_value":"N3QRWQT3","created_at":"2026-06-02T02:04:49.407711+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N3QRWQT3MGKBCJVENKZSLRXBZL","json":"https://pith.science/pith/N3QRWQT3MGKBCJVENKZSLRXBZL.json","graph_json":"https://pith.science/api/pith-number/N3QRWQT3MGKBCJVENKZSLRXBZL/graph.json","events_json":"https://pith.science/api/pith-number/N3QRWQT3MGKBCJVENKZSLRXBZL/events.json","paper":"https://pith.science/paper/N3QRWQT3"},"agent_actions":{"view_html":"https://pith.science/pith/N3QRWQT3MGKBCJVENKZSLRXBZL","download_json":"https://pith.science/pith/N3QRWQT3MGKBCJVENKZSLRXBZL.json","view_paper":"https://pith.science/paper/N3QRWQT3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2512.07349&json=true","fetch_graph":"https://pith.science/api/pith-number/N3QRWQT3MGKBCJVENKZSLRXBZL/graph.json","fetch_events":"https://pith.science/api/pith-number/N3QRWQT3MGKBCJVENKZSLRXBZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N3QRWQT3MGKBCJVENKZSLRXBZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N3QRWQT3MGKBCJVENKZSLRXBZL/action/storage_attestation","attest_author":"https://pith.science/pith/N3QRWQT3MGKBCJVENKZSLRXBZL/action/author_attestation","sign_citation":"https://pith.science/pith/N3QRWQT3MGKBCJVENKZSLRXBZL/action/citation_signature","submit_replication":"https://pith.science/pith/N3QRWQT3MGKBCJVENKZSLRXBZL/action/replication_record"}},"created_at":"2026-06-02T02:04:49.407711+00:00","updated_at":"2026-06-02T02:04:49.407711+00:00"}