{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:D5O4253ZDBZG7WUOHJGDFMVQRR","short_pith_number":"pith:D5O4253Z","canonical_record":{"source":{"id":"1001.0895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-06T13:39:43Z","cross_cats_sorted":[],"title_canon_sha256":"1aeedf09a4e7bbc5ac5773d65cc3665940f6b6219f7900bf75702acd7219b368","abstract_canon_sha256":"17dfee4cba7b57873183de20f5aab56643c909625258fc076e30eadac10b8b17"},"schema_version":"1.0"},"canonical_sha256":"1f5dcd777918726fda8e3a4c32b2b08c5a9eeadd0c9ca0f5489c74a64b0258a6","source":{"kind":"arxiv","id":"1001.0895","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0895","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0895v2","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0895","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"pith_short_12","alias_value":"D5O4253ZDBZG","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D5O4253ZDBZG7WUO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D5O4253Z","created_at":"2026-05-18T12:26:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:D5O4253ZDBZG7WUOHJGDFMVQRR","target":"record","payload":{"canonical_record":{"source":{"id":"1001.0895","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-06T13:39:43Z","cross_cats_sorted":[],"title_canon_sha256":"1aeedf09a4e7bbc5ac5773d65cc3665940f6b6219f7900bf75702acd7219b368","abstract_canon_sha256":"17dfee4cba7b57873183de20f5aab56643c909625258fc076e30eadac10b8b17"},"schema_version":"1.0"},"canonical_sha256":"1f5dcd777918726fda8e3a4c32b2b08c5a9eeadd0c9ca0f5489c74a64b0258a6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:07.239706Z","signature_b64":"yrKRy7THgHQxARP8a4bQ2rKNPOftN6wKcah68W4SJNKBKjNxlm2zskUQ9LmTVCvwN7odx3eAZDU3XoIWFWsnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f5dcd777918726fda8e3a4c32b2b08c5a9eeadd0c9ca0f5489c74a64b0258a6","last_reissued_at":"2026-05-18T03:31:07.239173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:07.239173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1001.0895","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":"2026-05-18T03:31:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/OdE3mdrlHI+YOmazt8VSBywqphHz5wLkOv6r+BmrAoybyL7Z1LaiU/ujN6Jb5Ws2grUGCW/cxdu4kflNw7aDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:22:50.393129Z"},"content_sha256":"8c4ff0f0c79d264bf190e57697b90e512b3f6878862432ffc28e105221ffc77b","schema_version":"1.0","event_id":"sha256:8c4ff0f0c79d264bf190e57697b90e512b3f6878862432ffc28e105221ffc77b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:D5O4253ZDBZG7WUOHJGDFMVQRR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Averaging over fast variables in the fluid limit for Markov chains: Application to the supermarket model with memory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"J. R. Norris, M. J. Luczak","submitted_at":"2010-01-06T13:39:43Z","abstract_excerpt":"We set out a general procedure which allows the approximation of certain Markov chains by the solutions of differential equations. The chains considered have some components which oscillate rapidly and randomly, while others are close to deterministic. The limiting dynamics are obtained by averaging the drift of the latter with respect to a local equilibrium distribution of the former. Some general estimates are proved under a uniform mixing condition on the fast variable which give explicit error probabilities for the fluid approximation. Mitzenmacher, Prabhakar and Shah [In Proc. 43rd Ann. S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0895","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":"2026-05-18T03:31:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jKKrI+uu8CyUOPZEm6QhNZ8sC2iBvDvWfRc7OcareEawT8vH4R3DSp3tscxpBdgR6lv2PSavBPV2jdWx96VcDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:22:50.393851Z"},"content_sha256":"b6bc738201a120a2eb324e65e394d12507008a01493298c22a151b77a2fba8e6","schema_version":"1.0","event_id":"sha256:b6bc738201a120a2eb324e65e394d12507008a01493298c22a151b77a2fba8e6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D5O4253ZDBZG7WUOHJGDFMVQRR/bundle.json","state_url":"https://pith.science/pith/D5O4253ZDBZG7WUOHJGDFMVQRR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D5O4253ZDBZG7WUOHJGDFMVQRR/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":"2026-06-06T23:22:50Z","links":{"resolver":"https://pith.science/pith/D5O4253ZDBZG7WUOHJGDFMVQRR","bundle":"https://pith.science/pith/D5O4253ZDBZG7WUOHJGDFMVQRR/bundle.json","state":"https://pith.science/pith/D5O4253ZDBZG7WUOHJGDFMVQRR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D5O4253ZDBZG7WUOHJGDFMVQRR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:D5O4253ZDBZG7WUOHJGDFMVQRR","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":"17dfee4cba7b57873183de20f5aab56643c909625258fc076e30eadac10b8b17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-06T13:39:43Z","title_canon_sha256":"1aeedf09a4e7bbc5ac5773d65cc3665940f6b6219f7900bf75702acd7219b368"},"schema_version":"1.0","source":{"id":"1001.0895","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.0895","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"arxiv_version","alias_value":"1001.0895v2","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.0895","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"pith_short_12","alias_value":"D5O4253ZDBZG","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"D5O4253ZDBZG7WUO","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"D5O4253Z","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:b6bc738201a120a2eb324e65e394d12507008a01493298c22a151b77a2fba8e6","target":"graph","created_at":"2026-05-18T03:31:07Z","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":"We set out a general procedure which allows the approximation of certain Markov chains by the solutions of differential equations. The chains considered have some components which oscillate rapidly and randomly, while others are close to deterministic. The limiting dynamics are obtained by averaging the drift of the latter with respect to a local equilibrium distribution of the former. Some general estimates are proved under a uniform mixing condition on the fast variable which give explicit error probabilities for the fluid approximation. Mitzenmacher, Prabhakar and Shah [In Proc. 43rd Ann. S","authors_text":"J. R. Norris, M. J. Luczak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-06T13:39:43Z","title":"Averaging over fast variables in the fluid limit for Markov chains: Application to the supermarket model with memory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.0895","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":"sha256:8c4ff0f0c79d264bf190e57697b90e512b3f6878862432ffc28e105221ffc77b","target":"record","created_at":"2026-05-18T03:31:07Z","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":"17dfee4cba7b57873183de20f5aab56643c909625258fc076e30eadac10b8b17","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-06T13:39:43Z","title_canon_sha256":"1aeedf09a4e7bbc5ac5773d65cc3665940f6b6219f7900bf75702acd7219b368"},"schema_version":"1.0","source":{"id":"1001.0895","kind":"arxiv","version":2}},"canonical_sha256":"1f5dcd777918726fda8e3a4c32b2b08c5a9eeadd0c9ca0f5489c74a64b0258a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f5dcd777918726fda8e3a4c32b2b08c5a9eeadd0c9ca0f5489c74a64b0258a6","first_computed_at":"2026-05-18T03:31:07.239173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:07.239173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yrKRy7THgHQxARP8a4bQ2rKNPOftN6wKcah68W4SJNKBKjNxlm2zskUQ9LmTVCvwN7odx3eAZDU3XoIWFWsnCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:07.239706Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.0895","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c4ff0f0c79d264bf190e57697b90e512b3f6878862432ffc28e105221ffc77b","sha256:b6bc738201a120a2eb324e65e394d12507008a01493298c22a151b77a2fba8e6"],"state_sha256":"5099f97201ed4c289b6ad75391acc839ef2866f0a396cf9235ba9b59cee5dbf2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a2A4LREC42sYhV/vV2AgtruSUv0Y+p5iDZINGYeiBnWyb9me2GeFWSew0jqmdC45mPBLWm7nSGqCNyqiNRfYDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T23:22:50.397708Z","bundle_sha256":"6cee2800b67742c3689f2cbc523050c40401dda088439173dc514b28c3409c1e"}}