{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UZDFCLPDNPF3764COK2RIDRXMT","short_pith_number":"pith:UZDFCLPD","canonical_record":{"source":{"id":"1603.02625","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-08T19:10:26Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"15c0f42479fc56ddbfc985e9eff1a334519051d6ffaae4d3f232878268e35b71","abstract_canon_sha256":"ca07689eef545b8dec9fcd7b75b489b3775c279009ade10442a5862e9376ef75"},"schema_version":"1.0"},"canonical_sha256":"a646512de36bcbbffb8272b5140e3764f39bdc2ad2a2055bf567159da93fd853","source":{"kind":"arxiv","id":"1603.02625","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02625","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02625v3","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02625","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"UZDFCLPDNPF3","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UZDFCLPDNPF3764C","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UZDFCLPD","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UZDFCLPDNPF3764COK2RIDRXMT","target":"record","payload":{"canonical_record":{"source":{"id":"1603.02625","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-08T19:10:26Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"15c0f42479fc56ddbfc985e9eff1a334519051d6ffaae4d3f232878268e35b71","abstract_canon_sha256":"ca07689eef545b8dec9fcd7b75b489b3775c279009ade10442a5862e9376ef75"},"schema_version":"1.0"},"canonical_sha256":"a646512de36bcbbffb8272b5140e3764f39bdc2ad2a2055bf567159da93fd853","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:06.859703Z","signature_b64":"9FWE+4z71QrucHgcwaOVTz+zW+7T1FfqwnN13AGlhv5fuoC2uKuCdLaJ8qdECBXvYvtxdXH/SNUX0cjbn9+PDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a646512de36bcbbffb8272b5140e3764f39bdc2ad2a2055bf567159da93fd853","last_reissued_at":"2026-05-18T00:49:06.859111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:06.859111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.02625","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":"2026-05-18T00:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxKHny1KyeNTrWrqU92DviKjY6gG2DaJzU61EAk5T4W9pfDwSZroCjFI+wW0fcSqzlUifZ63d8vpOnxdOGgdCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:51.596475Z"},"content_sha256":"a3a9bfb9f472affe0cd1c86fb7ba07dd077ea35eedabba9fe27d09ba8867fba6","schema_version":"1.0","event_id":"sha256:a3a9bfb9f472affe0cd1c86fb7ba07dd077ea35eedabba9fe27d09ba8867fba6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UZDFCLPDNPF3764COK2RIDRXMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Asymptotic Normality of Estimating the Affine Preferential Attachment Network Models with Random Initial Degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Aad van der Vaart, Fengnan Gao","submitted_at":"2016-03-08T19:10:26Z","abstract_excerpt":"We consider the estimation of the affine parameter (and power-law exponent) in the preferential attachment model with random initial degrees. We derive the likelihood, and show that the maximum likelihood estimator (MLE) is asymptotically normal and efficient. We also propose a quasi-maximum-likelihood estimator (QMLE) to overcome the MLE's dependence on the history of the initial degrees. To demonstrate the power of our idea, we present numerical simulations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02625","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":"2026-05-18T00:49:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L8/x3/rlH5VyR8fR2Pgb0+cGoCqLQ7bJ0Do1LUlzWo47vw+PnaF9HALNneL5vxyFdigkNrpSGG9zY7gDMUI9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:38:51.597148Z"},"content_sha256":"bf345ba53455025f34cb8a83b4cb5be97d018445494f491fd5701a0cf0d33fe7","schema_version":"1.0","event_id":"sha256:bf345ba53455025f34cb8a83b4cb5be97d018445494f491fd5701a0cf0d33fe7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UZDFCLPDNPF3764COK2RIDRXMT/bundle.json","state_url":"https://pith.science/pith/UZDFCLPDNPF3764COK2RIDRXMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UZDFCLPDNPF3764COK2RIDRXMT/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":"2026-05-31T08:38:51Z","links":{"resolver":"https://pith.science/pith/UZDFCLPDNPF3764COK2RIDRXMT","bundle":"https://pith.science/pith/UZDFCLPDNPF3764COK2RIDRXMT/bundle.json","state":"https://pith.science/pith/UZDFCLPDNPF3764COK2RIDRXMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UZDFCLPDNPF3764COK2RIDRXMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UZDFCLPDNPF3764COK2RIDRXMT","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":"ca07689eef545b8dec9fcd7b75b489b3775c279009ade10442a5862e9376ef75","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-08T19:10:26Z","title_canon_sha256":"15c0f42479fc56ddbfc985e9eff1a334519051d6ffaae4d3f232878268e35b71"},"schema_version":"1.0","source":{"id":"1603.02625","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.02625","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"arxiv_version","alias_value":"1603.02625v3","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.02625","created_at":"2026-05-18T00:49:06Z"},{"alias_kind":"pith_short_12","alias_value":"UZDFCLPDNPF3","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UZDFCLPDNPF3764C","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UZDFCLPD","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:bf345ba53455025f34cb8a83b4cb5be97d018445494f491fd5701a0cf0d33fe7","target":"graph","created_at":"2026-05-18T00:49:06Z","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 consider the estimation of the affine parameter (and power-law exponent) in the preferential attachment model with random initial degrees. We derive the likelihood, and show that the maximum likelihood estimator (MLE) is asymptotically normal and efficient. We also propose a quasi-maximum-likelihood estimator (QMLE) to overcome the MLE's dependence on the history of the initial degrees. To demonstrate the power of our idea, we present numerical simulations.","authors_text":"Aad van der Vaart, Fengnan Gao","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-08T19:10:26Z","title":"On the Asymptotic Normality of Estimating the Affine Preferential Attachment Network Models with Random Initial Degrees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.02625","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:a3a9bfb9f472affe0cd1c86fb7ba07dd077ea35eedabba9fe27d09ba8867fba6","target":"record","created_at":"2026-05-18T00:49:06Z","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":"ca07689eef545b8dec9fcd7b75b489b3775c279009ade10442a5862e9376ef75","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-03-08T19:10:26Z","title_canon_sha256":"15c0f42479fc56ddbfc985e9eff1a334519051d6ffaae4d3f232878268e35b71"},"schema_version":"1.0","source":{"id":"1603.02625","kind":"arxiv","version":3}},"canonical_sha256":"a646512de36bcbbffb8272b5140e3764f39bdc2ad2a2055bf567159da93fd853","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a646512de36bcbbffb8272b5140e3764f39bdc2ad2a2055bf567159da93fd853","first_computed_at":"2026-05-18T00:49:06.859111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:06.859111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9FWE+4z71QrucHgcwaOVTz+zW+7T1FfqwnN13AGlhv5fuoC2uKuCdLaJ8qdECBXvYvtxdXH/SNUX0cjbn9+PDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:06.859703Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.02625","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3a9bfb9f472affe0cd1c86fb7ba07dd077ea35eedabba9fe27d09ba8867fba6","sha256:bf345ba53455025f34cb8a83b4cb5be97d018445494f491fd5701a0cf0d33fe7"],"state_sha256":"50cd2e0482f6d788b6b3225c6361a08930b6a371ad110261b2e81b8db3926b8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jWogWweo6RetxfVarQt6/Jrnl+/U1DVv11UlYKSd/WY5YPPNOUtQ3+BgozsP6WMqbePjamF4k5SNsp4UPFK/AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:38:51.601330Z","bundle_sha256":"ebe0633777b01c1633ffc786f0d27b966f4fdda5ffff5234c9c31b2ad6aeadf1"}}