{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SSC55T6LRZL4US2TNUKNFMWKZS","short_pith_number":"pith:SSC55T6L","canonical_record":{"source":{"id":"1509.07248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-24T06:06:21Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6acc28622e1807ee6c23f8a256c49154ec3670de12a64d1c6df9f16e20ef82c3","abstract_canon_sha256":"b3f4bcca00d07ea86910e2d16cbf82788e2b0ebbd119367a4892dd561dc2eb5e"},"schema_version":"1.0"},"canonical_sha256":"9485decfcb8e57ca4b536d14d2b2cacc983288ca8cd1ac448f9dd50dfc95ebea","source":{"kind":"arxiv","id":"1509.07248","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07248","created_at":"2026-05-18T01:22:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07248v2","created_at":"2026-05-18T01:22:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07248","created_at":"2026-05-18T01:22:50Z"},{"alias_kind":"pith_short_12","alias_value":"SSC55T6LRZL4","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SSC55T6LRZL4US2T","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SSC55T6L","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SSC55T6LRZL4US2TNUKNFMWKZS","target":"record","payload":{"canonical_record":{"source":{"id":"1509.07248","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-24T06:06:21Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6acc28622e1807ee6c23f8a256c49154ec3670de12a64d1c6df9f16e20ef82c3","abstract_canon_sha256":"b3f4bcca00d07ea86910e2d16cbf82788e2b0ebbd119367a4892dd561dc2eb5e"},"schema_version":"1.0"},"canonical_sha256":"9485decfcb8e57ca4b536d14d2b2cacc983288ca8cd1ac448f9dd50dfc95ebea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:50.417850Z","signature_b64":"k2NwsswsKhHuzQfwSERarK1D4ommfVsHPvHIdKK2b5H7MXkMK90xFE2eiyvke2ReWxD2Z/xHMYoqz1XFv9IPCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9485decfcb8e57ca4b536d14d2b2cacc983288ca8cd1ac448f9dd50dfc95ebea","last_reissued_at":"2026-05-18T01:22:50.417254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:50.417254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.07248","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":"2026-05-18T01:22:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"49jCyc9LwRdq5F0IfgeLSh1n/rixcmY6VrMt5ABQ+rVtETPazK3KnYj91pRG3p4zXNihpJnef9yOgwIdCwBNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:47:47.234401Z"},"content_sha256":"3c1151cf6c612d8880e2eb777cbfe5d1cf37869341421fcda4ed8491e61fe1dd","schema_version":"1.0","event_id":"sha256:3c1151cf6c612d8880e2eb777cbfe5d1cf37869341421fcda4ed8491e61fe1dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SSC55T6LRZL4US2TNUKNFMWKZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interactions between Ehrenfest's urns arising from group actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.PR","authors_text":"Hiroshi Mizukawa","submitted_at":"2015-09-24T06:06:21Z","abstract_excerpt":"Ehrenfest's diffusion model is a well-known classical physical model consisting of two urns and n balls. A group theoretical interpretation of the model by using the Gelfand pair (Z/2Zwr S_{n},S_{n}) is provided by Diaconis-Shahshahani. This interpretation remains valid for an r-urns generalization, in which case, the corresponding Gelfand pair is (S_{r}wr S_{n},S_{r-1}wr S_{n}). In these models, there are no restrictions for ball movements, i.e., each balls can freely move to any urn. This paper introduces interactions between urns arising from actions of finite groups. The degree of freedom "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07248","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":""},"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":"2026-05-18T01:22:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gCrNIbHjiHr9HtLJV+zxZI1EvLjBljd2O8wlUI5cSFkPJ4FE6SQumdNCRL+6YRPU05DmieGVCR5Bu/VD/O5wCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T17:47:47.235202Z"},"content_sha256":"00dfaad12871aeffa65874784ecd594e29e9f217141826508a51a54a480e38e9","schema_version":"1.0","event_id":"sha256:00dfaad12871aeffa65874784ecd594e29e9f217141826508a51a54a480e38e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SSC55T6LRZL4US2TNUKNFMWKZS/bundle.json","state_url":"https://pith.science/pith/SSC55T6LRZL4US2TNUKNFMWKZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SSC55T6LRZL4US2TNUKNFMWKZS/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":"2026-05-31T17:47:47Z","links":{"resolver":"https://pith.science/pith/SSC55T6LRZL4US2TNUKNFMWKZS","bundle":"https://pith.science/pith/SSC55T6LRZL4US2TNUKNFMWKZS/bundle.json","state":"https://pith.science/pith/SSC55T6LRZL4US2TNUKNFMWKZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SSC55T6LRZL4US2TNUKNFMWKZS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SSC55T6LRZL4US2TNUKNFMWKZS","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":"b3f4bcca00d07ea86910e2d16cbf82788e2b0ebbd119367a4892dd561dc2eb5e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-24T06:06:21Z","title_canon_sha256":"6acc28622e1807ee6c23f8a256c49154ec3670de12a64d1c6df9f16e20ef82c3"},"schema_version":"1.0","source":{"id":"1509.07248","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.07248","created_at":"2026-05-18T01:22:50Z"},{"alias_kind":"arxiv_version","alias_value":"1509.07248v2","created_at":"2026-05-18T01:22:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.07248","created_at":"2026-05-18T01:22:50Z"},{"alias_kind":"pith_short_12","alias_value":"SSC55T6LRZL4","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SSC55T6LRZL4US2T","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SSC55T6L","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:00dfaad12871aeffa65874784ecd594e29e9f217141826508a51a54a480e38e9","target":"graph","created_at":"2026-05-18T01:22:50Z","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"},"paper":{"abstract_excerpt":"Ehrenfest's diffusion model is a well-known classical physical model consisting of two urns and n balls. A group theoretical interpretation of the model by using the Gelfand pair (Z/2Zwr S_{n},S_{n}) is provided by Diaconis-Shahshahani. This interpretation remains valid for an r-urns generalization, in which case, the corresponding Gelfand pair is (S_{r}wr S_{n},S_{r-1}wr S_{n}). In these models, there are no restrictions for ball movements, i.e., each balls can freely move to any urn. This paper introduces interactions between urns arising from actions of finite groups. The degree of freedom ","authors_text":"Hiroshi Mizukawa","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-24T06:06:21Z","title":"Interactions between Ehrenfest's urns arising from group actions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.07248","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":"sha256:3c1151cf6c612d8880e2eb777cbfe5d1cf37869341421fcda4ed8491e61fe1dd","target":"record","created_at":"2026-05-18T01:22:50Z","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":"b3f4bcca00d07ea86910e2d16cbf82788e2b0ebbd119367a4892dd561dc2eb5e","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-24T06:06:21Z","title_canon_sha256":"6acc28622e1807ee6c23f8a256c49154ec3670de12a64d1c6df9f16e20ef82c3"},"schema_version":"1.0","source":{"id":"1509.07248","kind":"arxiv","version":2}},"canonical_sha256":"9485decfcb8e57ca4b536d14d2b2cacc983288ca8cd1ac448f9dd50dfc95ebea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9485decfcb8e57ca4b536d14d2b2cacc983288ca8cd1ac448f9dd50dfc95ebea","first_computed_at":"2026-05-18T01:22:50.417254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:50.417254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"k2NwsswsKhHuzQfwSERarK1D4ommfVsHPvHIdKK2b5H7MXkMK90xFE2eiyvke2ReWxD2Z/xHMYoqz1XFv9IPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:50.417850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.07248","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c1151cf6c612d8880e2eb777cbfe5d1cf37869341421fcda4ed8491e61fe1dd","sha256:00dfaad12871aeffa65874784ecd594e29e9f217141826508a51a54a480e38e9"],"state_sha256":"d1123192c573fb8f778ea87eeeeeae675a1216b9bc3b5d87b6b8e89cfade11b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3prPVyvlxnfDPiMctXG6YL/z3pl5kEBqZEpRKE9kP/fsgofiZNvKeBG4J+1Kc5KCsfEPOoe6/fbyWsSb73QYDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T17:47:47.238861Z","bundle_sha256":"698976135f68fc1d8bf197890e798c4eb2d8053b1b36f361ca9e1113b4cf2a2d"}}