{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:X47KMPL6TFVEEZUPD6SY5OFGKU","short_pith_number":"pith:X47KMPL6","canonical_record":{"source":{"id":"cond-mat/0609671","kind":"arxiv","version":7},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-09-26T18:10:10Z","cross_cats_sorted":[],"title_canon_sha256":"5f2440209e68a58247a43074b86495647ae53ed0db7996d8aa3b22c02a039ffa","abstract_canon_sha256":"9b087a3688b0d05ac092fc711aa1942e8ebb352401f058e5f9b5f512dffa28bb"},"schema_version":"1.0"},"canonical_sha256":"bf3ea63d7e996a42668f1fa58eb8a6551b8b6d9bd47780d0c8b7bdcf7b3e3e80","source":{"kind":"arxiv","id":"cond-mat/0609671","version":7},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0609671","created_at":"2026-05-18T01:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0609671v7","created_at":"2026-05-18T01:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0609671","created_at":"2026-05-18T01:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"X47KMPL6TFVE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"X47KMPL6TFVEEZUP","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"X47KMPL6","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:X47KMPL6TFVEEZUPD6SY5OFGKU","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0609671","kind":"arxiv","version":7},"metadata":{"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-09-26T18:10:10Z","cross_cats_sorted":[],"title_canon_sha256":"5f2440209e68a58247a43074b86495647ae53ed0db7996d8aa3b22c02a039ffa","abstract_canon_sha256":"9b087a3688b0d05ac092fc711aa1942e8ebb352401f058e5f9b5f512dffa28bb"},"schema_version":"1.0"},"canonical_sha256":"bf3ea63d7e996a42668f1fa58eb8a6551b8b6d9bd47780d0c8b7bdcf7b3e3e80","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:42.978245Z","signature_b64":"Wh53R/5PHd+7QbqAyPtH3LpN5QuM5nz2Wfygewi42AC16dcl4IaGZ7aeDIJWODnv1ANkej8hd3ycACIiUri2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf3ea63d7e996a42668f1fa58eb8a6551b8b6d9bd47780d0c8b7bdcf7b3e3e80","last_reissued_at":"2026-05-18T01:39:42.977619Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:42.977619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0609671","source_version":7,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OwtjzNOTeUzGHc7F/8fsLRjUBUVyzXTJVmvXmU4bHMSdRcyvgnpD8q9zoDhepZx4cgJmdHmP7aKqlvJA8bIyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:37:43.497205Z"},"content_sha256":"78e869dfbc4977bb3ba5b72c37f67b6f87a4bcbfe02fe5d2c182d1e805fbca10","schema_version":"1.0","event_id":"sha256:78e869dfbc4977bb3ba5b72c37f67b6f87a4bcbfe02fe5d2c182d1e805fbca10"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:X47KMPL6TFVEEZUPD6SY5OFGKU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hurst Exponents, Markov Processes, and Fractional Brownian motion","license":"","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Gemunu H. Gunaratne, Joseph L. McCauley, Kevin E. Bassler","submitted_at":"2006-09-26T18:10:10Z","abstract_excerpt":"There is much confusion in the literature over Hurst exponents. Recently, we took a step in the direction of eliminating some of the confusion. One purpose of this paper is to illustrate the difference between fBm on the one hand and Gaussian Markov processes where H not equal to 1/2 on the other. The difference lies in the increments, which are stationary and correlated in one case and nonstationary and uncorrelated in the other. The two- and one-point densities of fBm are constructed explicitly. The two-point density doesn't scale. The one-point density is identical with that for a Markov pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0609671","kind":"arxiv","version":7},"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":"2026-05-18T01:39:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q6iDZAnW+TKWL/ZT2Ek9dPL7vGhgmtDKdTWRkgxv7Y0678nUqA/58lI/L3lvB/T8aOZspf7LcGZsrd3LLIcDBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:37:43.497565Z"},"content_sha256":"8e1ac7070615493c34de3cfda3717212320d8e538d08040d3a83bac476e16451","schema_version":"1.0","event_id":"sha256:8e1ac7070615493c34de3cfda3717212320d8e538d08040d3a83bac476e16451"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X47KMPL6TFVEEZUPD6SY5OFGKU/bundle.json","state_url":"https://pith.science/pith/X47KMPL6TFVEEZUPD6SY5OFGKU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X47KMPL6TFVEEZUPD6SY5OFGKU/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":"2026-06-02T04:37:43Z","links":{"resolver":"https://pith.science/pith/X47KMPL6TFVEEZUPD6SY5OFGKU","bundle":"https://pith.science/pith/X47KMPL6TFVEEZUPD6SY5OFGKU/bundle.json","state":"https://pith.science/pith/X47KMPL6TFVEEZUPD6SY5OFGKU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X47KMPL6TFVEEZUPD6SY5OFGKU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:X47KMPL6TFVEEZUPD6SY5OFGKU","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":"9b087a3688b0d05ac092fc711aa1942e8ebb352401f058e5f9b5f512dffa28bb","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-09-26T18:10:10Z","title_canon_sha256":"5f2440209e68a58247a43074b86495647ae53ed0db7996d8aa3b22c02a039ffa"},"schema_version":"1.0","source":{"id":"cond-mat/0609671","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0609671","created_at":"2026-05-18T01:39:42Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0609671v7","created_at":"2026-05-18T01:39:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0609671","created_at":"2026-05-18T01:39:42Z"},{"alias_kind":"pith_short_12","alias_value":"X47KMPL6TFVE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"X47KMPL6TFVEEZUP","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"X47KMPL6","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:8e1ac7070615493c34de3cfda3717212320d8e538d08040d3a83bac476e16451","target":"graph","created_at":"2026-05-18T01:39:42Z","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":"There is much confusion in the literature over Hurst exponents. Recently, we took a step in the direction of eliminating some of the confusion. One purpose of this paper is to illustrate the difference between fBm on the one hand and Gaussian Markov processes where H not equal to 1/2 on the other. The difference lies in the increments, which are stationary and correlated in one case and nonstationary and uncorrelated in the other. The two- and one-point densities of fBm are constructed explicitly. The two-point density doesn't scale. The one-point density is identical with that for a Markov pr","authors_text":"Gemunu H. Gunaratne, Joseph L. McCauley, Kevin E. Bassler","cross_cats":[],"headline":"","license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-09-26T18:10:10Z","title":"Hurst Exponents, Markov Processes, and Fractional Brownian motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0609671","kind":"arxiv","version":7},"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":"sha256:78e869dfbc4977bb3ba5b72c37f67b6f87a4bcbfe02fe5d2c182d1e805fbca10","target":"record","created_at":"2026-05-18T01:39:42Z","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":"9b087a3688b0d05ac092fc711aa1942e8ebb352401f058e5f9b5f512dffa28bb","cross_cats_sorted":[],"license":"","primary_cat":"cond-mat.stat-mech","submitted_at":"2006-09-26T18:10:10Z","title_canon_sha256":"5f2440209e68a58247a43074b86495647ae53ed0db7996d8aa3b22c02a039ffa"},"schema_version":"1.0","source":{"id":"cond-mat/0609671","kind":"arxiv","version":7}},"canonical_sha256":"bf3ea63d7e996a42668f1fa58eb8a6551b8b6d9bd47780d0c8b7bdcf7b3e3e80","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf3ea63d7e996a42668f1fa58eb8a6551b8b6d9bd47780d0c8b7bdcf7b3e3e80","first_computed_at":"2026-05-18T01:39:42.977619Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:42.977619Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wh53R/5PHd+7QbqAyPtH3LpN5QuM5nz2Wfygewi42AC16dcl4IaGZ7aeDIJWODnv1ANkej8hd3ycACIiUri2AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:42.978245Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0609671","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:78e869dfbc4977bb3ba5b72c37f67b6f87a4bcbfe02fe5d2c182d1e805fbca10","sha256:8e1ac7070615493c34de3cfda3717212320d8e538d08040d3a83bac476e16451"],"state_sha256":"c8ca704797f0d24b18bcbc2113522d6ff90101eda81c6a65f01c82de17a4b0c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2d+0ZP9nrpB0Yhhc1XKuMR9ETnWIyohUzyTt64jkag2jm4gFEUmxfG02goA0Xak8JFJx+R/Va1hF+p1lOGwxAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:37:43.499512Z","bundle_sha256":"a59a162bce9a490de1a446a15de32a6f6af6f18e5bf8be29bcd3b152951776fc"}}