{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:TTJB3Z2KMS6QQ5LPCX2XYSHK7M","short_pith_number":"pith:TTJB3Z2K","canonical_record":{"source":{"id":"1801.00542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-02T03:55:22Z","cross_cats_sorted":[],"title_canon_sha256":"99a77ee28d3e1bbec2ccf0dc3b0e493e66c9752acba22910933d43f14a123da3","abstract_canon_sha256":"7c554bbead9689803044b49b82fcd166943641f35eea11dccc5a42d9492c1ec8"},"schema_version":"1.0"},"canonical_sha256":"9cd21de74a64bd08756f15f57c48eafb2d98b2a17328ac7932f81599955722e6","source":{"kind":"arxiv","id":"1801.00542","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00542","created_at":"2026-05-18T00:01:09Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00542v2","created_at":"2026-05-18T00:01:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00542","created_at":"2026-05-18T00:01:09Z"},{"alias_kind":"pith_short_12","alias_value":"TTJB3Z2KMS6Q","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TTJB3Z2KMS6QQ5LP","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TTJB3Z2K","created_at":"2026-05-18T12:32:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:TTJB3Z2KMS6QQ5LPCX2XYSHK7M","target":"record","payload":{"canonical_record":{"source":{"id":"1801.00542","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-02T03:55:22Z","cross_cats_sorted":[],"title_canon_sha256":"99a77ee28d3e1bbec2ccf0dc3b0e493e66c9752acba22910933d43f14a123da3","abstract_canon_sha256":"7c554bbead9689803044b49b82fcd166943641f35eea11dccc5a42d9492c1ec8"},"schema_version":"1.0"},"canonical_sha256":"9cd21de74a64bd08756f15f57c48eafb2d98b2a17328ac7932f81599955722e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:09.956231Z","signature_b64":"NNS1cAzz6yetdNmjhpsjU6G61U4BlFSBJH4XdxoRH9atDNCby64tp1JDH2UR7wMLfX5OisQnX77aWnJhPWkpBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cd21de74a64bd08756f15f57c48eafb2d98b2a17328ac7932f81599955722e6","last_reissued_at":"2026-05-18T00:01:09.955634Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:09.955634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.00542","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":"2026-05-18T00:01:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qzvqOv5zjllWMp6eBdTxYT4Uofd2jaeW5UXu83bU50+ysgO+pn+4JOCOiOW5/k3zT1G/8HBx+ZQ5m0eChlIXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:52:37.984512Z"},"content_sha256":"69629db5db3e59f04d8a6594247b710b311a3dd8c7f6e916034fe0865a4e706f","schema_version":"1.0","event_id":"sha256:69629db5db3e59f04d8a6594247b710b311a3dd8c7f6e916034fe0865a4e706f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:TTJB3Z2KMS6QQ5LPCX2XYSHK7M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Normal approximations for discrete-time occupancy processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Liam Hodgkinson, Philip K. Pollett, Ross McVinish","submitted_at":"2018-01-02T03:55:22Z","abstract_excerpt":"We study normal approximations for a class of discrete-time occupancy processes, namely, Markov chains with transition kernels of product Bernoulli form. This class encompasses numerous models which appear in the complex networks literature, including stochastic patch occupancy models in ecology, network models in epidemiology, and a variety of dynamic random graph models. Bounds on the rate of convergence for a central limit theorem are obtained using Stein's method and moment inequalities on the deviation from an analogous deterministic model. As a consequence, our work also implies a unifor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00542","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":"2026-05-18T00:01:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r6S+KrF9rM6ZUDU+8Q3nh+0UP+TnP7Gmb5SFA+mV9B886J4z36i/IfmMSx+/VptlTIJtNEKwBIFrkvmu9mHdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:52:37.984887Z"},"content_sha256":"3f95fd0cd2b3a3d118a0d63f6a7ef033f4b7527cb8d9e7c0061bdccc0b3d371b","schema_version":"1.0","event_id":"sha256:3f95fd0cd2b3a3d118a0d63f6a7ef033f4b7527cb8d9e7c0061bdccc0b3d371b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TTJB3Z2KMS6QQ5LPCX2XYSHK7M/bundle.json","state_url":"https://pith.science/pith/TTJB3Z2KMS6QQ5LPCX2XYSHK7M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TTJB3Z2KMS6QQ5LPCX2XYSHK7M/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":"2026-06-06T19:52:37Z","links":{"resolver":"https://pith.science/pith/TTJB3Z2KMS6QQ5LPCX2XYSHK7M","bundle":"https://pith.science/pith/TTJB3Z2KMS6QQ5LPCX2XYSHK7M/bundle.json","state":"https://pith.science/pith/TTJB3Z2KMS6QQ5LPCX2XYSHK7M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TTJB3Z2KMS6QQ5LPCX2XYSHK7M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:TTJB3Z2KMS6QQ5LPCX2XYSHK7M","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":"7c554bbead9689803044b49b82fcd166943641f35eea11dccc5a42d9492c1ec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-02T03:55:22Z","title_canon_sha256":"99a77ee28d3e1bbec2ccf0dc3b0e493e66c9752acba22910933d43f14a123da3"},"schema_version":"1.0","source":{"id":"1801.00542","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.00542","created_at":"2026-05-18T00:01:09Z"},{"alias_kind":"arxiv_version","alias_value":"1801.00542v2","created_at":"2026-05-18T00:01:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.00542","created_at":"2026-05-18T00:01:09Z"},{"alias_kind":"pith_short_12","alias_value":"TTJB3Z2KMS6Q","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_16","alias_value":"TTJB3Z2KMS6QQ5LP","created_at":"2026-05-18T12:32:56Z"},{"alias_kind":"pith_short_8","alias_value":"TTJB3Z2K","created_at":"2026-05-18T12:32:56Z"}],"graph_snapshots":[{"event_id":"sha256:3f95fd0cd2b3a3d118a0d63f6a7ef033f4b7527cb8d9e7c0061bdccc0b3d371b","target":"graph","created_at":"2026-05-18T00:01:09Z","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 study normal approximations for a class of discrete-time occupancy processes, namely, Markov chains with transition kernels of product Bernoulli form. This class encompasses numerous models which appear in the complex networks literature, including stochastic patch occupancy models in ecology, network models in epidemiology, and a variety of dynamic random graph models. Bounds on the rate of convergence for a central limit theorem are obtained using Stein's method and moment inequalities on the deviation from an analogous deterministic model. As a consequence, our work also implies a unifor","authors_text":"Liam Hodgkinson, Philip K. Pollett, Ross McVinish","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-02T03:55:22Z","title":"Normal approximations for discrete-time occupancy processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.00542","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":"sha256:69629db5db3e59f04d8a6594247b710b311a3dd8c7f6e916034fe0865a4e706f","target":"record","created_at":"2026-05-18T00:01:09Z","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":"7c554bbead9689803044b49b82fcd166943641f35eea11dccc5a42d9492c1ec8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-02T03:55:22Z","title_canon_sha256":"99a77ee28d3e1bbec2ccf0dc3b0e493e66c9752acba22910933d43f14a123da3"},"schema_version":"1.0","source":{"id":"1801.00542","kind":"arxiv","version":2}},"canonical_sha256":"9cd21de74a64bd08756f15f57c48eafb2d98b2a17328ac7932f81599955722e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cd21de74a64bd08756f15f57c48eafb2d98b2a17328ac7932f81599955722e6","first_computed_at":"2026-05-18T00:01:09.955634Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:09.955634Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NNS1cAzz6yetdNmjhpsjU6G61U4BlFSBJH4XdxoRH9atDNCby64tp1JDH2UR7wMLfX5OisQnX77aWnJhPWkpBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:09.956231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.00542","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69629db5db3e59f04d8a6594247b710b311a3dd8c7f6e916034fe0865a4e706f","sha256:3f95fd0cd2b3a3d118a0d63f6a7ef033f4b7527cb8d9e7c0061bdccc0b3d371b"],"state_sha256":"bbb88b5eeb689d974f3ef206e80cded8d227e4ed7584ba446a2959203e854901"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1TK61Dc32ELWPAvGjKojZZdHDds4a/+TbxVrC8vXQsg6L/Q5klspLYLVeZUG373NTGJEBrcTPFodMTEMD7qABA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:52:37.988094Z","bundle_sha256":"a146d712a9375ccd3f5f61c2266cf327a3d712b016c316e3aedc39d59a4dd961"}}