{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:722DU7KTJOGTS7CXET4EJU2IRY","short_pith_number":"pith:722DU7KT","canonical_record":{"source":{"id":"2505.22828","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T20:11:03Z","cross_cats_sorted":[],"title_canon_sha256":"0d0743bf9944590ff9a4e2cdb24b6634f7b612276506ce417eb7d181bfd22a58","abstract_canon_sha256":"252229d076b7d4d788bdfcb0a84e2f4fffb59d8e4a36f2adfaca8e62018fb3d9"},"schema_version":"1.0"},"canonical_sha256":"feb43a7d534b8d397c5724f844d3488e1723af2a17fe01a9a3dfc9018aeab632","source":{"kind":"arxiv","id":"2505.22828","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22828","created_at":"2026-07-05T11:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22828v1","created_at":"2026-07-05T11:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22828","created_at":"2026-07-05T11:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"722DU7KTJOGT","created_at":"2026-07-05T11:11:50Z"},{"alias_kind":"pith_short_16","alias_value":"722DU7KTJOGTS7CX","created_at":"2026-07-05T11:11:50Z"},{"alias_kind":"pith_short_8","alias_value":"722DU7KT","created_at":"2026-07-05T11:11:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:722DU7KTJOGTS7CXET4EJU2IRY","target":"record","payload":{"canonical_record":{"source":{"id":"2505.22828","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T20:11:03Z","cross_cats_sorted":[],"title_canon_sha256":"0d0743bf9944590ff9a4e2cdb24b6634f7b612276506ce417eb7d181bfd22a58","abstract_canon_sha256":"252229d076b7d4d788bdfcb0a84e2f4fffb59d8e4a36f2adfaca8e62018fb3d9"},"schema_version":"1.0"},"canonical_sha256":"feb43a7d534b8d397c5724f844d3488e1723af2a17fe01a9a3dfc9018aeab632","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:50.492588Z","signature_b64":"J8ehvQb6lYx/uWvLjSwisGWMx4sxatBr4Qvi1rrnrMljKULfvqCmNZlNNm1IryNiPbsPre5jlexPw9MzJMr1Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"feb43a7d534b8d397c5724f844d3488e1723af2a17fe01a9a3dfc9018aeab632","last_reissued_at":"2026-07-05T11:11:50.492106Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:50.492106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2505.22828","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EAxlx2Rpr/zMUKtF3UYgXilSUoys01UWiwu8EupjY5fFl9ohVCJCBnm/uXuWWAq5GwjiM5NCEojmC4R9TRi4Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:16:38.510049Z"},"content_sha256":"e40ebbf3f57ea0a8143a6db4dcd80df285b49ac957a5dfb376ae137cbc1b1aa8","schema_version":"1.0","event_id":"sha256:e40ebbf3f57ea0a8143a6db4dcd80df285b49ac957a5dfb376ae137cbc1b1aa8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:722DU7KTJOGTS7CXET4EJU2IRY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The range of the des statistic for conjugacy classes in $S_n$","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yisca Kares","submitted_at":"2025-05-28T20:11:03Z","abstract_excerpt":"We determine the range of the des statistic on every conjugacy class in the symmetric group $S_n$, prove that the minimum is $1$ (except for the identity class), and show that every intermediate value from $1$ to the maximum value is attained. We also demonstrate a constructive method to achieve every value in the range and discuss its combinatorial implications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22828","kind":"arxiv","version":1},"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/2505.22828/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CwEHl9gWCVY5k+94JMoyLtZAq5zpc7TWm/NdfziMmQZEIboOBwidslw6VYQOSxx7vSYxH4TdD2FYgyfcO2RtBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:16:38.510632Z"},"content_sha256":"146204120ff427b231aad4219cc120c624e33cbed6cbcf31066b37f0bb0b3123","schema_version":"1.0","event_id":"sha256:146204120ff427b231aad4219cc120c624e33cbed6cbcf31066b37f0bb0b3123"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/722DU7KTJOGTS7CXET4EJU2IRY/bundle.json","state_url":"https://pith.science/pith/722DU7KTJOGTS7CXET4EJU2IRY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/722DU7KTJOGTS7CXET4EJU2IRY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-08T16:16:38Z","links":{"resolver":"https://pith.science/pith/722DU7KTJOGTS7CXET4EJU2IRY","bundle":"https://pith.science/pith/722DU7KTJOGTS7CXET4EJU2IRY/bundle.json","state":"https://pith.science/pith/722DU7KTJOGTS7CXET4EJU2IRY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/722DU7KTJOGTS7CXET4EJU2IRY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:722DU7KTJOGTS7CXET4EJU2IRY","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":"252229d076b7d4d788bdfcb0a84e2f4fffb59d8e4a36f2adfaca8e62018fb3d9","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T20:11:03Z","title_canon_sha256":"0d0743bf9944590ff9a4e2cdb24b6634f7b612276506ce417eb7d181bfd22a58"},"schema_version":"1.0","source":{"id":"2505.22828","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.22828","created_at":"2026-07-05T11:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"2505.22828v1","created_at":"2026-07-05T11:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.22828","created_at":"2026-07-05T11:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"722DU7KTJOGT","created_at":"2026-07-05T11:11:50Z"},{"alias_kind":"pith_short_16","alias_value":"722DU7KTJOGTS7CX","created_at":"2026-07-05T11:11:50Z"},{"alias_kind":"pith_short_8","alias_value":"722DU7KT","created_at":"2026-07-05T11:11:50Z"}],"graph_snapshots":[{"event_id":"sha256:146204120ff427b231aad4219cc120c624e33cbed6cbcf31066b37f0bb0b3123","target":"graph","created_at":"2026-07-05T11:11:50Z","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/2505.22828/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the range of the des statistic on every conjugacy class in the symmetric group $S_n$, prove that the minimum is $1$ (except for the identity class), and show that every intermediate value from $1$ to the maximum value is attained. We also demonstrate a constructive method to achieve every value in the range and discuss its combinatorial implications.","authors_text":"Yisca Kares","cross_cats":[],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T20:11:03Z","title":"The range of the des statistic for conjugacy classes in $S_n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.22828","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:e40ebbf3f57ea0a8143a6db4dcd80df285b49ac957a5dfb376ae137cbc1b1aa8","target":"record","created_at":"2026-07-05T11:11:50Z","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":"252229d076b7d4d788bdfcb0a84e2f4fffb59d8e4a36f2adfaca8e62018fb3d9","cross_cats_sorted":[],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.CO","submitted_at":"2025-05-28T20:11:03Z","title_canon_sha256":"0d0743bf9944590ff9a4e2cdb24b6634f7b612276506ce417eb7d181bfd22a58"},"schema_version":"1.0","source":{"id":"2505.22828","kind":"arxiv","version":1}},"canonical_sha256":"feb43a7d534b8d397c5724f844d3488e1723af2a17fe01a9a3dfc9018aeab632","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"feb43a7d534b8d397c5724f844d3488e1723af2a17fe01a9a3dfc9018aeab632","first_computed_at":"2026-07-05T11:11:50.492106Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:50.492106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J8ehvQb6lYx/uWvLjSwisGWMx4sxatBr4Qvi1rrnrMljKULfvqCmNZlNNm1IryNiPbsPre5jlexPw9MzJMr1Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:50.492588Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.22828","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e40ebbf3f57ea0a8143a6db4dcd80df285b49ac957a5dfb376ae137cbc1b1aa8","sha256:146204120ff427b231aad4219cc120c624e33cbed6cbcf31066b37f0bb0b3123"],"state_sha256":"4301705d1a44f463de262463311efd56b3cd6f72ce49d2a89c46074a52b03b89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eSPVC0RMv8SEi6qW5nKsE7im53yxNqV056F/YhV969pMPZ3G615G8qXgRSrGtwZb/jovasN9krtv07zE9vneCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T16:16:38.515066Z","bundle_sha256":"eebb6920eb165b77c9a299fee4618bc71485a4fd4e0ab4072c5f88ec89aa3599"}}