{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RUT6AE7IYIMVSPDMUX7P2SR6QK","short_pith_number":"pith:RUT6AE7I","canonical_record":{"source":{"id":"1410.3936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-15T06:07:14Z","cross_cats_sorted":[],"title_canon_sha256":"656274157da57aa6ef4b741d048fd0a30301d021de78dfebf675d804ebb1fcad","abstract_canon_sha256":"c8f067f2ebeb5ad2f8a56783bc548194ae3db36cf3c9b6dc714ed1a470f6e4ab"},"schema_version":"1.0"},"canonical_sha256":"8d27e013e8c219593c6ca5fefd4a3e82a171536eff81835161142e7ea5737b71","source":{"kind":"arxiv","id":"1410.3936","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3936","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3936v1","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3936","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"RUT6AE7IYIMV","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RUT6AE7IYIMVSPDM","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RUT6AE7I","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RUT6AE7IYIMVSPDMUX7P2SR6QK","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3936","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-15T06:07:14Z","cross_cats_sorted":[],"title_canon_sha256":"656274157da57aa6ef4b741d048fd0a30301d021de78dfebf675d804ebb1fcad","abstract_canon_sha256":"c8f067f2ebeb5ad2f8a56783bc548194ae3db36cf3c9b6dc714ed1a470f6e4ab"},"schema_version":"1.0"},"canonical_sha256":"8d27e013e8c219593c6ca5fefd4a3e82a171536eff81835161142e7ea5737b71","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:03.600949Z","signature_b64":"lGVXCdI1lzMSMS370Iu36WwBRzEoGEfv+gCGQtdQ//sVaB1VyBv/T9KgHGrWgt1rEodLN3kEBc1bmvCoFOmAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d27e013e8c219593c6ca5fefd4a3e82a171536eff81835161142e7ea5737b71","last_reissued_at":"2026-05-18T02:40:03.600403Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:03.600403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3936","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":"2026-05-18T02:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1V3Y9niEFNBz9cHGYkgOI3Cd7m5G5kdwHtoGuRn7eC0l4twEq6I5ZUOSH0Wz1VuKyEznz8omlssb5rw+zEG9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T10:17:36.330152Z"},"content_sha256":"74baf3169bc11e468d1a94aa89b51466d3597454290c743c612e1287b8de4e55","schema_version":"1.0","event_id":"sha256:74baf3169bc11e468d1a94aa89b51466d3597454290c743c612e1287b8de4e55"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RUT6AE7IYIMVSPDMUX7P2SR6QK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Harnack Inequality and Applications for Infinite-Dimensional GEM Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Feng-Yu Wang, Shui Feng","submitted_at":"2014-10-15T06:07:14Z","abstract_excerpt":"The dimension-free Harnack inequality and uniform heat kernel upper/lower bounds are derived for a class of infinite-dimensional GEM processes, which was introduced in \\cite{FW} to simulate the two-parameter GEM distributions. In particular, the associated Dirichlet form satisfies the super log-Sobolev inequality which strengthens the log-Sobolev inequality derived in \\cite{FW}. To prove the main results, explicit Harnack inequality and super Poincar\\'e inequality are established for the one-dimensional Wright-Fisher diffusion processes. The main tool of the study is the coupling by change of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3936","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":""},"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":"2026-05-18T02:40:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZfqDZQnB6+myHP0pUnZBPbsGKgNPmYcJ4g/c9kvKQhTqThMnKRG2Vs0p70OCHcVylbI3tiBiI9m+snGO3TODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T10:17:36.330935Z"},"content_sha256":"38a6b8664e1735326ca6ef18cdbea71c0dbfa7f4dec0c03618c1d1999e31a707","schema_version":"1.0","event_id":"sha256:38a6b8664e1735326ca6ef18cdbea71c0dbfa7f4dec0c03618c1d1999e31a707"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RUT6AE7IYIMVSPDMUX7P2SR6QK/bundle.json","state_url":"https://pith.science/pith/RUT6AE7IYIMVSPDMUX7P2SR6QK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RUT6AE7IYIMVSPDMUX7P2SR6QK/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":"2026-05-23T10:17:36Z","links":{"resolver":"https://pith.science/pith/RUT6AE7IYIMVSPDMUX7P2SR6QK","bundle":"https://pith.science/pith/RUT6AE7IYIMVSPDMUX7P2SR6QK/bundle.json","state":"https://pith.science/pith/RUT6AE7IYIMVSPDMUX7P2SR6QK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RUT6AE7IYIMVSPDMUX7P2SR6QK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RUT6AE7IYIMVSPDMUX7P2SR6QK","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":"c8f067f2ebeb5ad2f8a56783bc548194ae3db36cf3c9b6dc714ed1a470f6e4ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-15T06:07:14Z","title_canon_sha256":"656274157da57aa6ef4b741d048fd0a30301d021de78dfebf675d804ebb1fcad"},"schema_version":"1.0","source":{"id":"1410.3936","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3936","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3936v1","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3936","created_at":"2026-05-18T02:40:03Z"},{"alias_kind":"pith_short_12","alias_value":"RUT6AE7IYIMV","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RUT6AE7IYIMVSPDM","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RUT6AE7I","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:38a6b8664e1735326ca6ef18cdbea71c0dbfa7f4dec0c03618c1d1999e31a707","target":"graph","created_at":"2026-05-18T02:40:03Z","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":"The dimension-free Harnack inequality and uniform heat kernel upper/lower bounds are derived for a class of infinite-dimensional GEM processes, which was introduced in \\cite{FW} to simulate the two-parameter GEM distributions. In particular, the associated Dirichlet form satisfies the super log-Sobolev inequality which strengthens the log-Sobolev inequality derived in \\cite{FW}. To prove the main results, explicit Harnack inequality and super Poincar\\'e inequality are established for the one-dimensional Wright-Fisher diffusion processes. The main tool of the study is the coupling by change of ","authors_text":"Feng-Yu Wang, Shui Feng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-15T06:07:14Z","title":"Harnack Inequality and Applications for Infinite-Dimensional GEM Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3936","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":"sha256:74baf3169bc11e468d1a94aa89b51466d3597454290c743c612e1287b8de4e55","target":"record","created_at":"2026-05-18T02:40:03Z","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":"c8f067f2ebeb5ad2f8a56783bc548194ae3db36cf3c9b6dc714ed1a470f6e4ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-10-15T06:07:14Z","title_canon_sha256":"656274157da57aa6ef4b741d048fd0a30301d021de78dfebf675d804ebb1fcad"},"schema_version":"1.0","source":{"id":"1410.3936","kind":"arxiv","version":1}},"canonical_sha256":"8d27e013e8c219593c6ca5fefd4a3e82a171536eff81835161142e7ea5737b71","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d27e013e8c219593c6ca5fefd4a3e82a171536eff81835161142e7ea5737b71","first_computed_at":"2026-05-18T02:40:03.600403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:03.600403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lGVXCdI1lzMSMS370Iu36WwBRzEoGEfv+gCGQtdQ//sVaB1VyBv/T9KgHGrWgt1rEodLN3kEBc1bmvCoFOmAAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:03.600949Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3936","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74baf3169bc11e468d1a94aa89b51466d3597454290c743c612e1287b8de4e55","sha256:38a6b8664e1735326ca6ef18cdbea71c0dbfa7f4dec0c03618c1d1999e31a707"],"state_sha256":"309e649b36f88733caad12e87c98e164def24411ea419a1be7c913104330999d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"28X1W/34SdYvIxettsnuoYn5H75aD8ysKqV5xNPfPxgCOlhMG5323a6BEztfnIr5ww3SrnrFax2JvNeQpxO+Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T10:17:36.334438Z","bundle_sha256":"57b402db2c88d88bd352c23ce4823458d877a982458ff7173d34f7ed0c60a740"}}