{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:P2LFHX73IFQIFW4OUMKETXFYVN","short_pith_number":"pith:P2LFHX73","canonical_record":{"source":{"id":"1701.02397","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T00:05:52Z","cross_cats_sorted":[],"title_canon_sha256":"ed84da85ea2f51858703ab63b65e432e58faefad2e63fe65c2032251ef1c1527","abstract_canon_sha256":"87779a8035f8939903c560bdeefe76bdbe739afedf4d4e8173ea32d3c31c2e74"},"schema_version":"1.0"},"canonical_sha256":"7e9653dffb416082db8ea31449dcb8ab69cc049af9ed2beb54ffb47578fa9222","source":{"kind":"arxiv","id":"1701.02397","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02397","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02397v1","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02397","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"pith_short_12","alias_value":"P2LFHX73IFQI","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P2LFHX73IFQIFW4O","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P2LFHX73","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:P2LFHX73IFQIFW4OUMKETXFYVN","target":"record","payload":{"canonical_record":{"source":{"id":"1701.02397","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T00:05:52Z","cross_cats_sorted":[],"title_canon_sha256":"ed84da85ea2f51858703ab63b65e432e58faefad2e63fe65c2032251ef1c1527","abstract_canon_sha256":"87779a8035f8939903c560bdeefe76bdbe739afedf4d4e8173ea32d3c31c2e74"},"schema_version":"1.0"},"canonical_sha256":"7e9653dffb416082db8ea31449dcb8ab69cc049af9ed2beb54ffb47578fa9222","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:04.342164Z","signature_b64":"i+IJrq34YtoR/mDtHkHOa1Y5zkHbrM7BVSqGsdqYlLHHq2Pb5/UyahVqYCQrMhrLBIW/V5HB3e03atE5EQpPCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e9653dffb416082db8ea31449dcb8ab69cc049af9ed2beb54ffb47578fa9222","last_reissued_at":"2026-05-18T00:53:04.341481Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:04.341481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.02397","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":"2026-05-18T00:53:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z7oLAjt98rUKfEPTWP/5O2Xwxg/xliFEWzZvm8WVwp20sI/KQWclpVF9Fk/52biXIEOu6HfgMgBzp2P1mjXWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:13:08.693820Z"},"content_sha256":"99a31f55cbae0b862d3146af68e64a554cd2df6b87e5cc1bd39d2e71a939e657","schema_version":"1.0","event_id":"sha256:99a31f55cbae0b862d3146af68e64a554cd2df6b87e5cc1bd39d2e71a939e657"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:P2LFHX73IFQIFW4OUMKETXFYVN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dependence between Path-length and Size in Random Digital Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hsien-Kuei Hwang, Michael Fuchs","submitted_at":"2017-01-10T00:05:52Z","abstract_excerpt":"We study the size and the external path length of random tries and show that they are asymptotically independent in the asymmetric case but strongly dependent with small periodic fluctuations in the symmetric case. Such an unexpected behavior is in sharp contrast to the previously known results on random tries that the size is totally positively correlated to the internal path length and that both tend to the same normal limit law. These two dependence examples provide concrete instances of bivariate normal distributions (as limit laws) whose correlation is $0$, $1$ and periodically oscillatin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02397","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":"2026-05-18T00:53:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kuS+nbogcbesFqA3PUt7xpY7zMVHghDDBDfczQy4hPT+jj3ky9x6w73FpstBOHqAKCgIsJSq5b5eu+EvFhNYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:13:08.694369Z"},"content_sha256":"42f9d06b79858bc34264e5f11f6a630a91bbcd4751feedb71e65bd4ddc015bec","schema_version":"1.0","event_id":"sha256:42f9d06b79858bc34264e5f11f6a630a91bbcd4751feedb71e65bd4ddc015bec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P2LFHX73IFQIFW4OUMKETXFYVN/bundle.json","state_url":"https://pith.science/pith/P2LFHX73IFQIFW4OUMKETXFYVN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P2LFHX73IFQIFW4OUMKETXFYVN/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":"2026-06-06T17:13:08Z","links":{"resolver":"https://pith.science/pith/P2LFHX73IFQIFW4OUMKETXFYVN","bundle":"https://pith.science/pith/P2LFHX73IFQIFW4OUMKETXFYVN/bundle.json","state":"https://pith.science/pith/P2LFHX73IFQIFW4OUMKETXFYVN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P2LFHX73IFQIFW4OUMKETXFYVN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P2LFHX73IFQIFW4OUMKETXFYVN","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":"87779a8035f8939903c560bdeefe76bdbe739afedf4d4e8173ea32d3c31c2e74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T00:05:52Z","title_canon_sha256":"ed84da85ea2f51858703ab63b65e432e58faefad2e63fe65c2032251ef1c1527"},"schema_version":"1.0","source":{"id":"1701.02397","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02397","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02397v1","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02397","created_at":"2026-05-18T00:53:04Z"},{"alias_kind":"pith_short_12","alias_value":"P2LFHX73IFQI","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P2LFHX73IFQIFW4O","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P2LFHX73","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:42f9d06b79858bc34264e5f11f6a630a91bbcd4751feedb71e65bd4ddc015bec","target":"graph","created_at":"2026-05-18T00:53:04Z","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 the size and the external path length of random tries and show that they are asymptotically independent in the asymmetric case but strongly dependent with small periodic fluctuations in the symmetric case. Such an unexpected behavior is in sharp contrast to the previously known results on random tries that the size is totally positively correlated to the internal path length and that both tend to the same normal limit law. These two dependence examples provide concrete instances of bivariate normal distributions (as limit laws) whose correlation is $0$, $1$ and periodically oscillatin","authors_text":"Hsien-Kuei Hwang, Michael Fuchs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T00:05:52Z","title":"Dependence between Path-length and Size in Random Digital Trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02397","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":"sha256:99a31f55cbae0b862d3146af68e64a554cd2df6b87e5cc1bd39d2e71a939e657","target":"record","created_at":"2026-05-18T00:53:04Z","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":"87779a8035f8939903c560bdeefe76bdbe739afedf4d4e8173ea32d3c31c2e74","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-10T00:05:52Z","title_canon_sha256":"ed84da85ea2f51858703ab63b65e432e58faefad2e63fe65c2032251ef1c1527"},"schema_version":"1.0","source":{"id":"1701.02397","kind":"arxiv","version":1}},"canonical_sha256":"7e9653dffb416082db8ea31449dcb8ab69cc049af9ed2beb54ffb47578fa9222","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e9653dffb416082db8ea31449dcb8ab69cc049af9ed2beb54ffb47578fa9222","first_computed_at":"2026-05-18T00:53:04.341481Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:04.341481Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i+IJrq34YtoR/mDtHkHOa1Y5zkHbrM7BVSqGsdqYlLHHq2Pb5/UyahVqYCQrMhrLBIW/V5HB3e03atE5EQpPCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:04.342164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02397","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99a31f55cbae0b862d3146af68e64a554cd2df6b87e5cc1bd39d2e71a939e657","sha256:42f9d06b79858bc34264e5f11f6a630a91bbcd4751feedb71e65bd4ddc015bec"],"state_sha256":"dab30c5e188dca9ca3ac7dc205fa769dda8a97a6f70f6287a472ad80db0fcb6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8T8pc+fsytGVwX7iMBHhP4haJ2ujPqTpfqIjGQDF9qovMQNaWJ441OOEfQHC2MAqGfYdANBr75l7YZZtY0ZBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T17:13:08.696690Z","bundle_sha256":"52aa434d4755856605943bea2baba7d603b3ec0a3f9ec6302d822fbc3bee2c24"}}