{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QR64NTU27YLKLNMZHVOARHINTM","short_pith_number":"pith:QR64NTU2","canonical_record":{"source":{"id":"2510.00343","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-09-30T23:06:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"65517c8f0f56c7089ff3735e339b25ce8ec1adc447882e68029fdfd94f662e83","abstract_canon_sha256":"68f8743c95a8433b30fc9995aa637acbf9a114c55fff5b06d7ecafe4653d6a28"},"schema_version":"1.0"},"canonical_sha256":"847dc6ce9afe16a5b5993d5c089d0d9b3c8ed2212acc1eda9e0189b5c4358157","source":{"kind":"arxiv","id":"2510.00343","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.00343","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"arxiv_version","alias_value":"2510.00343v2","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.00343","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_12","alias_value":"QR64NTU27YLK","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_16","alias_value":"QR64NTU27YLKLNMZ","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_8","alias_value":"QR64NTU2","created_at":"2026-06-19T16:10:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QR64NTU27YLKLNMZHVOARHINTM","target":"record","payload":{"canonical_record":{"source":{"id":"2510.00343","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-09-30T23:06:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"65517c8f0f56c7089ff3735e339b25ce8ec1adc447882e68029fdfd94f662e83","abstract_canon_sha256":"68f8743c95a8433b30fc9995aa637acbf9a114c55fff5b06d7ecafe4653d6a28"},"schema_version":"1.0"},"canonical_sha256":"847dc6ce9afe16a5b5993d5c089d0d9b3c8ed2212acc1eda9e0189b5c4358157","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:10:31.501838Z","signature_b64":"VeoT/BOJG5azLe07j7Av3JSrgeZUJI608ofZtznsPikxDX4UaxB/+KZMU66HVqbHGwcYQPhDZFVV17Qj8ceKBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"847dc6ce9afe16a5b5993d5c089d0d9b3c8ed2212acc1eda9e0189b5c4358157","last_reissued_at":"2026-06-19T16:10:31.501353Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:10:31.501353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2510.00343","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-19T16:10:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J9nPV6LqNy6hukZhWm8z49sjAAOduU13/+FmIPvYRqpY07Nydr4l+0Nku4V3O6g7Reb5bMImzhSnyH4nctzhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T09:48:58.179301Z"},"content_sha256":"2e18da197caebf08120208e669940a28b998a71e93942cc771c6580125bc4d3a","schema_version":"1.0","event_id":"sha256:2e18da197caebf08120208e669940a28b998a71e93942cc771c6580125bc4d3a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QR64NTU27YLKLNMZHVOARHINTM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit theorems for descents and inversions of shelf-shuffles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Alexander Clay","submitted_at":"2025-09-30T23:06:17Z","abstract_excerpt":"We prove central limit theorems for the number of descents and inversions of permutations produced by shelf-shuffles. These are a model for casino card shuffling machines. We show the asymptotic normality of the number of descents in two limiting regimes depending on the ratio of cards to shelves. On the other hand, we study the inversions by employing a modification of the techniques from Islak's analysis of the statistics of riffle shuffles. In particular, we obtain a bound for the rate of convergence for inversions that is independent of the number of shelves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.00343","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/2510.00343/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":"2026-06-19T16:10:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SWUnE+QWYhigrR4QEeP4kOeLR6QK5wU8mmT1ijmwIQUzAAiinTFy/7YeZT6azl9lzJbL0vHPVh4OazvGM6vjCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T09:48:58.179693Z"},"content_sha256":"3a3df6a130caff9a26db928b261969594f95c1ab43ccaf0ad5e516016ebfc123","schema_version":"1.0","event_id":"sha256:3a3df6a130caff9a26db928b261969594f95c1ab43ccaf0ad5e516016ebfc123"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QR64NTU27YLKLNMZHVOARHINTM/bundle.json","state_url":"https://pith.science/pith/QR64NTU27YLKLNMZHVOARHINTM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QR64NTU27YLKLNMZHVOARHINTM/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":"2026-07-04T09:48:58Z","links":{"resolver":"https://pith.science/pith/QR64NTU27YLKLNMZHVOARHINTM","bundle":"https://pith.science/pith/QR64NTU27YLKLNMZHVOARHINTM/bundle.json","state":"https://pith.science/pith/QR64NTU27YLKLNMZHVOARHINTM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QR64NTU27YLKLNMZHVOARHINTM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QR64NTU27YLKLNMZHVOARHINTM","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":"68f8743c95a8433b30fc9995aa637acbf9a114c55fff5b06d7ecafe4653d6a28","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-09-30T23:06:17Z","title_canon_sha256":"65517c8f0f56c7089ff3735e339b25ce8ec1adc447882e68029fdfd94f662e83"},"schema_version":"1.0","source":{"id":"2510.00343","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.00343","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"arxiv_version","alias_value":"2510.00343v2","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.00343","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_12","alias_value":"QR64NTU27YLK","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_16","alias_value":"QR64NTU27YLKLNMZ","created_at":"2026-06-19T16:10:31Z"},{"alias_kind":"pith_short_8","alias_value":"QR64NTU2","created_at":"2026-06-19T16:10:31Z"}],"graph_snapshots":[{"event_id":"sha256:3a3df6a130caff9a26db928b261969594f95c1ab43ccaf0ad5e516016ebfc123","target":"graph","created_at":"2026-06-19T16:10:31Z","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/2510.00343/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove central limit theorems for the number of descents and inversions of permutations produced by shelf-shuffles. These are a model for casino card shuffling machines. We show the asymptotic normality of the number of descents in two limiting regimes depending on the ratio of cards to shelves. On the other hand, we study the inversions by employing a modification of the techniques from Islak's analysis of the statistics of riffle shuffles. In particular, we obtain a bound for the rate of convergence for inversions that is independent of the number of shelves.","authors_text":"Alexander Clay","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-09-30T23:06:17Z","title":"Limit theorems for descents and inversions of shelf-shuffles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.00343","kind":"arxiv","version":2},"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":"sha256:2e18da197caebf08120208e669940a28b998a71e93942cc771c6580125bc4d3a","target":"record","created_at":"2026-06-19T16:10:31Z","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":"68f8743c95a8433b30fc9995aa637acbf9a114c55fff5b06d7ecafe4653d6a28","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-09-30T23:06:17Z","title_canon_sha256":"65517c8f0f56c7089ff3735e339b25ce8ec1adc447882e68029fdfd94f662e83"},"schema_version":"1.0","source":{"id":"2510.00343","kind":"arxiv","version":2}},"canonical_sha256":"847dc6ce9afe16a5b5993d5c089d0d9b3c8ed2212acc1eda9e0189b5c4358157","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"847dc6ce9afe16a5b5993d5c089d0d9b3c8ed2212acc1eda9e0189b5c4358157","first_computed_at":"2026-06-19T16:10:31.501353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:31.501353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VeoT/BOJG5azLe07j7Av3JSrgeZUJI608ofZtznsPikxDX4UaxB/+KZMU66HVqbHGwcYQPhDZFVV17Qj8ceKBQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:31.501838Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.00343","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e18da197caebf08120208e669940a28b998a71e93942cc771c6580125bc4d3a","sha256:3a3df6a130caff9a26db928b261969594f95c1ab43ccaf0ad5e516016ebfc123"],"state_sha256":"4b2295a16abb3f32548444ecc741171adbf52544f7e84ca5910db8c4afe3201f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2NxSKu+sQatZJwwezvy8v+pi5JiarSon8N2IGCiKm9bni0FB2gtlOXgnm0Msyem53duMV3dAmcjTDIKSTHe9BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T09:48:58.181702Z","bundle_sha256":"6c08f0e8216704ef6891e5490541861ff7a41db83f6019dfed8955cd3a2c32f0"}}