{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PHD4SOEZ23U3H2DTH6UG7OGFME","short_pith_number":"pith:PHD4SOEZ","canonical_record":{"source":{"id":"1403.5822","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-24T00:33:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"07bc2b2a75929ba9e574e7ed7e2755083c55b1e8bb6ad7ba7f132b112f5db1d1","abstract_canon_sha256":"780e0b7b7f7e1394f3cb31347096c018b42a8ad7c843cfa5ca5c09986df88005"},"schema_version":"1.0"},"canonical_sha256":"79c7c93899d6e9b3e8733fa86fb8c5612c9bc600fc6f77010adf54aa79dc86f0","source":{"kind":"arxiv","id":"1403.5822","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5822","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5822v3","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5822","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"PHD4SOEZ23U3","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PHD4SOEZ23U3H2DT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PHD4SOEZ","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PHD4SOEZ23U3H2DTH6UG7OGFME","target":"record","payload":{"canonical_record":{"source":{"id":"1403.5822","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-24T00:33:19Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"07bc2b2a75929ba9e574e7ed7e2755083c55b1e8bb6ad7ba7f132b112f5db1d1","abstract_canon_sha256":"780e0b7b7f7e1394f3cb31347096c018b42a8ad7c843cfa5ca5c09986df88005"},"schema_version":"1.0"},"canonical_sha256":"79c7c93899d6e9b3e8733fa86fb8c5612c9bc600fc6f77010adf54aa79dc86f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:55.302262Z","signature_b64":"SYAKCxowAVDPBbaeLQCNe9MhI++t47C+NBMr3z7IcU958xcegdBGVfcBqNC2CTGZcT3pknzdRFy3/IB5zFQDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79c7c93899d6e9b3e8733fa86fb8c5612c9bc600fc6f77010adf54aa79dc86f0","last_reissued_at":"2026-05-18T00:48:55.301636Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:55.301636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.5822","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dYkY6oLDonQtF0/zRT8Jg6oOISefbGw4LIYPihRGEfOOZAP0+lX3cZN/uTjMqebJvAJtDhf5iF37UwbTzP/MDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:55:59.310301Z"},"content_sha256":"d13abb7ae75b9fd266a8247d75151251821fe0707630fa1604717a05303cfbe5","schema_version":"1.0","event_id":"sha256:d13abb7ae75b9fd266a8247d75151251821fe0707630fa1604717a05303cfbe5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PHD4SOEZ23U3H2DTH6UG7OGFME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalization of carries process and riffle shuffles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Fumihiko Nakano, Taizo Sadahiro","submitted_at":"2014-03-24T00:33:19Z","abstract_excerpt":"As a continuation to our previous work, we consider a generalization of carries process. Our results are : (i) right eigenvectors of the transition probability matrix, (ii) correlation of carries between different steps, and (iii) generalized riffle shuffle having the same distribution as that of the generalized carries process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5822","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:48:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y8qV2njiVhbYFmbi8llctSVe/zAo8FW1h1WPdJXjDW21GVfLHnblCn/VsUE1K/Lpd9tIOa3D8WAwZVXoPkbBCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:55:59.310985Z"},"content_sha256":"8d8a218ac619e495d5aa218409e2e29f46d4ba79e64eab5361ebaa9c91f7ee8f","schema_version":"1.0","event_id":"sha256:8d8a218ac619e495d5aa218409e2e29f46d4ba79e64eab5361ebaa9c91f7ee8f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PHD4SOEZ23U3H2DTH6UG7OGFME/bundle.json","state_url":"https://pith.science/pith/PHD4SOEZ23U3H2DTH6UG7OGFME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PHD4SOEZ23U3H2DTH6UG7OGFME/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":"2026-06-10T22:55:59Z","links":{"resolver":"https://pith.science/pith/PHD4SOEZ23U3H2DTH6UG7OGFME","bundle":"https://pith.science/pith/PHD4SOEZ23U3H2DTH6UG7OGFME/bundle.json","state":"https://pith.science/pith/PHD4SOEZ23U3H2DTH6UG7OGFME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PHD4SOEZ23U3H2DTH6UG7OGFME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PHD4SOEZ23U3H2DTH6UG7OGFME","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":"780e0b7b7f7e1394f3cb31347096c018b42a8ad7c843cfa5ca5c09986df88005","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-24T00:33:19Z","title_canon_sha256":"07bc2b2a75929ba9e574e7ed7e2755083c55b1e8bb6ad7ba7f132b112f5db1d1"},"schema_version":"1.0","source":{"id":"1403.5822","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.5822","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"1403.5822v3","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.5822","created_at":"2026-05-18T00:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"PHD4SOEZ23U3","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PHD4SOEZ23U3H2DT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PHD4SOEZ","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:8d8a218ac619e495d5aa218409e2e29f46d4ba79e64eab5361ebaa9c91f7ee8f","target":"graph","created_at":"2026-05-18T00:48:55Z","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":"As a continuation to our previous work, we consider a generalization of carries process. Our results are : (i) right eigenvectors of the transition probability matrix, (ii) correlation of carries between different steps, and (iii) generalized riffle shuffle having the same distribution as that of the generalized carries process.","authors_text":"Fumihiko Nakano, Taizo Sadahiro","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-24T00:33:19Z","title":"A generalization of carries process and riffle shuffles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.5822","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:d13abb7ae75b9fd266a8247d75151251821fe0707630fa1604717a05303cfbe5","target":"record","created_at":"2026-05-18T00:48:55Z","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":"780e0b7b7f7e1394f3cb31347096c018b42a8ad7c843cfa5ca5c09986df88005","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-03-24T00:33:19Z","title_canon_sha256":"07bc2b2a75929ba9e574e7ed7e2755083c55b1e8bb6ad7ba7f132b112f5db1d1"},"schema_version":"1.0","source":{"id":"1403.5822","kind":"arxiv","version":3}},"canonical_sha256":"79c7c93899d6e9b3e8733fa86fb8c5612c9bc600fc6f77010adf54aa79dc86f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79c7c93899d6e9b3e8733fa86fb8c5612c9bc600fc6f77010adf54aa79dc86f0","first_computed_at":"2026-05-18T00:48:55.301636Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:55.301636Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SYAKCxowAVDPBbaeLQCNe9MhI++t47C+NBMr3z7IcU958xcegdBGVfcBqNC2CTGZcT3pknzdRFy3/IB5zFQDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:55.302262Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.5822","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d13abb7ae75b9fd266a8247d75151251821fe0707630fa1604717a05303cfbe5","sha256:8d8a218ac619e495d5aa218409e2e29f46d4ba79e64eab5361ebaa9c91f7ee8f"],"state_sha256":"c5217fc34c4bc1cdc3acdbead71155843c0fd443ce396b04eb2d7b94c383eba2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M6GF6he6kXYCckO3nssaOHphnxpW4/+gt0NjgPGwJsJ/t0g0fTw72RRkN/fPipWVjLxtA+gTCM+o1MXz/etrCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:55:59.314231Z","bundle_sha256":"c9d667d33498d072fd982e8f67a75b5fa2d6355229a3d73abc9ca64b9dbfb431"}}