{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:TSM4GTLV7PAH4JUCRMS77RUKV7","short_pith_number":"pith:TSM4GTLV","canonical_record":{"source":{"id":"1011.5104","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-23T14:08:10Z","cross_cats_sorted":[],"title_canon_sha256":"1b1e5eb61037150387c859e7a99bcd76aa306493c229a3f9ce6955a0fce51277","abstract_canon_sha256":"b5dccf6969236cd6276c6eb34b77289ac18b79a72a022e54aade0b6f0a5ac592"},"schema_version":"1.0"},"canonical_sha256":"9c99c34d75fbc07e26828b25ffc68aafc9eb4676792fb2651890a611ff9b5884","source":{"kind":"arxiv","id":"1011.5104","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5104","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5104v3","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5104","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"TSM4GTLV7PAH","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TSM4GTLV7PAH4JUC","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TSM4GTLV","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:TSM4GTLV7PAH4JUCRMS77RUKV7","target":"record","payload":{"canonical_record":{"source":{"id":"1011.5104","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-23T14:08:10Z","cross_cats_sorted":[],"title_canon_sha256":"1b1e5eb61037150387c859e7a99bcd76aa306493c229a3f9ce6955a0fce51277","abstract_canon_sha256":"b5dccf6969236cd6276c6eb34b77289ac18b79a72a022e54aade0b6f0a5ac592"},"schema_version":"1.0"},"canonical_sha256":"9c99c34d75fbc07e26828b25ffc68aafc9eb4676792fb2651890a611ff9b5884","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:34:01.224989Z","signature_b64":"6nanM/HloBiIE7e7+tGVo/qhiDuayRC49NbhW0+eGseTpmWE+8KJpj2LASXYjz6HO9zU3fhvxi1q+fVZjUH5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c99c34d75fbc07e26828b25ffc68aafc9eb4676792fb2651890a611ff9b5884","last_reissued_at":"2026-05-18T04:34:01.224585Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:34:01.224585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.5104","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":"2026-05-18T04:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"doW5J6vtBRJt2rn0RaL2MOPK4ua3wSU1L3tWraVBjJscJ0PnF1SMTTyjL4Oa6gnwRBc9KrGirX5JpliTrz4GCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:00:42.070549Z"},"content_sha256":"fb50b89ef4ebb6c4ce4afe9489a5fbb9e2917c815344c204f3bdf9f1a544bce6","schema_version":"1.0","event_id":"sha256:fb50b89ef4ebb6c4ce4afe9489a5fbb9e2917c815344c204f3bdf9f1a544bce6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:TSM4GTLV7PAH4JUCRMS77RUKV7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the superposition of heterogeneous traffic at large time scales","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Luis Lopez-Oliveros, Sidney I. Resnick","submitted_at":"2010-11-23T14:08:10Z","abstract_excerpt":"Various empirical and theoretical studies indicate that cumulative network traffic is a Gaussian process. However, depending on whether the intensity at which sessions are initiated is large or small relative to the session duration tail, Mikosch et al. (Ann Appl Probab, 12:23-68, 2002) and Kaj and Taqqu (Progress Probab, 60:383-427, 2008) have shown that traffic at large time scales can be approximated by either fractional Brownian motion (fBm) or stable Levy motion. We study distributional properties of cumulative traffic that consists of a finite number of independent streams and give an ex"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5104","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":"2026-05-18T04:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"u54liwxuaiExWDBdDbQP1Q/uJCW+8pas/pc5fV7O8toncxcBhWU4YQnG4q7cZY+o5EzMl0gvLY0Dk3NNbaPvCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:00:42.070883Z"},"content_sha256":"a77187a47080d2db2fe16d9f3dbf0ed1275a35caf5f1511b26de095bc4750808","schema_version":"1.0","event_id":"sha256:a77187a47080d2db2fe16d9f3dbf0ed1275a35caf5f1511b26de095bc4750808"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TSM4GTLV7PAH4JUCRMS77RUKV7/bundle.json","state_url":"https://pith.science/pith/TSM4GTLV7PAH4JUCRMS77RUKV7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TSM4GTLV7PAH4JUCRMS77RUKV7/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":"2026-06-26T23:00:42Z","links":{"resolver":"https://pith.science/pith/TSM4GTLV7PAH4JUCRMS77RUKV7","bundle":"https://pith.science/pith/TSM4GTLV7PAH4JUCRMS77RUKV7/bundle.json","state":"https://pith.science/pith/TSM4GTLV7PAH4JUCRMS77RUKV7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TSM4GTLV7PAH4JUCRMS77RUKV7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TSM4GTLV7PAH4JUCRMS77RUKV7","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":"b5dccf6969236cd6276c6eb34b77289ac18b79a72a022e54aade0b6f0a5ac592","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-23T14:08:10Z","title_canon_sha256":"1b1e5eb61037150387c859e7a99bcd76aa306493c229a3f9ce6955a0fce51277"},"schema_version":"1.0","source":{"id":"1011.5104","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.5104","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1011.5104v3","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.5104","created_at":"2026-05-18T04:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"TSM4GTLV7PAH","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TSM4GTLV7PAH4JUC","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TSM4GTLV","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:a77187a47080d2db2fe16d9f3dbf0ed1275a35caf5f1511b26de095bc4750808","target":"graph","created_at":"2026-05-18T04:34:01Z","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":"Various empirical and theoretical studies indicate that cumulative network traffic is a Gaussian process. However, depending on whether the intensity at which sessions are initiated is large or small relative to the session duration tail, Mikosch et al. (Ann Appl Probab, 12:23-68, 2002) and Kaj and Taqqu (Progress Probab, 60:383-427, 2008) have shown that traffic at large time scales can be approximated by either fractional Brownian motion (fBm) or stable Levy motion. We study distributional properties of cumulative traffic that consists of a finite number of independent streams and give an ex","authors_text":"Luis Lopez-Oliveros, Sidney I. Resnick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-23T14:08:10Z","title":"On the superposition of heterogeneous traffic at large time scales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5104","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:fb50b89ef4ebb6c4ce4afe9489a5fbb9e2917c815344c204f3bdf9f1a544bce6","target":"record","created_at":"2026-05-18T04:34:01Z","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":"b5dccf6969236cd6276c6eb34b77289ac18b79a72a022e54aade0b6f0a5ac592","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-11-23T14:08:10Z","title_canon_sha256":"1b1e5eb61037150387c859e7a99bcd76aa306493c229a3f9ce6955a0fce51277"},"schema_version":"1.0","source":{"id":"1011.5104","kind":"arxiv","version":3}},"canonical_sha256":"9c99c34d75fbc07e26828b25ffc68aafc9eb4676792fb2651890a611ff9b5884","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c99c34d75fbc07e26828b25ffc68aafc9eb4676792fb2651890a611ff9b5884","first_computed_at":"2026-05-18T04:34:01.224585Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:34:01.224585Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6nanM/HloBiIE7e7+tGVo/qhiDuayRC49NbhW0+eGseTpmWE+8KJpj2LASXYjz6HO9zU3fhvxi1q+fVZjUH5DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:34:01.224989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.5104","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb50b89ef4ebb6c4ce4afe9489a5fbb9e2917c815344c204f3bdf9f1a544bce6","sha256:a77187a47080d2db2fe16d9f3dbf0ed1275a35caf5f1511b26de095bc4750808"],"state_sha256":"2a3e1476e05e0068aaf799368be866b5ddc7023363ef14ab20d25dabdd42e4d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a1q8MS+eFPCfVt7koTvEoy1cWhz6nZufEkNywCnByKIoSr/j/mygCGwBtemygS+PMlmv/2RxSrt9Fpt0yK3RBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:00:42.073040Z","bundle_sha256":"ae7e2b86f90fc1879ca19cc10f89a2aa9cfd4b07e359c76cd35de7de1e7734e0"}}