{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:Z5YW3BPGKOE5P2BOK7XUAFRZ3C","short_pith_number":"pith:Z5YW3BPG","canonical_record":{"source":{"id":"1407.3395","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-07-12T14:58:35Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"c244e044b986a790d3fc3b894c483424dc6e9b14f46d7b5184a8575221a083f8","abstract_canon_sha256":"f92d27d9145fe672bc51bae457c8397ad6d97dbc0f803cf0e952ba24231c6935"},"schema_version":"1.0"},"canonical_sha256":"cf716d85e65389d7e82e57ef401639d8a77f6cf63b329df5a9d190fe1f50b33d","source":{"kind":"arxiv","id":"1407.3395","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3395","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3395v2","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3395","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"Z5YW3BPGKOE5","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z5YW3BPGKOE5P2BO","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z5YW3BPG","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:Z5YW3BPGKOE5P2BOK7XUAFRZ3C","target":"record","payload":{"canonical_record":{"source":{"id":"1407.3395","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-07-12T14:58:35Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"c244e044b986a790d3fc3b894c483424dc6e9b14f46d7b5184a8575221a083f8","abstract_canon_sha256":"f92d27d9145fe672bc51bae457c8397ad6d97dbc0f803cf0e952ba24231c6935"},"schema_version":"1.0"},"canonical_sha256":"cf716d85e65389d7e82e57ef401639d8a77f6cf63b329df5a9d190fe1f50b33d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:58.970946Z","signature_b64":"RrlN42UUZjpaZghzY/Fhr1G/xbYyWzVx6SGTZaU3A6tAPL1RNSyScREytNQnqXMnRnpAuhzqk0+cywL/dMtjBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf716d85e65389d7e82e57ef401639d8a77f6cf63b329df5a9d190fe1f50b33d","last_reissued_at":"2026-05-18T02:00:58.970305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:58.970305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.3395","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":"2026-05-18T02:00:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sfFkIWgmLUBE2cZ2qBzfIKYdsdKi0viPPHstvcZUlzGqGTOvLcGt1US+eRS+xGSOgkkxbHtT1ET9AeiY6AaMDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:42:23.878468Z"},"content_sha256":"3949f746a2474514b089a4eb6c4de6c1f32d4d43c3c45c3c0170756f6e71bd68","schema_version":"1.0","event_id":"sha256:3949f746a2474514b089a4eb6c4de6c1f32d4d43c3c45c3c0170756f6e71bd68"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:Z5YW3BPGKOE5P2BOK7XUAFRZ3C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniformly and strongly consistent estimation for the Hurst function of a Linear Multifractional Stable Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Antoine Ayache, Julien Hamonier","submitted_at":"2014-07-12T14:58:35Z","abstract_excerpt":"Since the middle of the 90's, multifractional processes have been introduced for overcoming some limitations of the classical Fractional Brownian Motion model. In their context, the Hurst parameter becomes a Holder continuous function H(?) of the time variable t. Linear Multifractional Stable Motion (LMSM) is the most known one of them with heavy-tailed distributions. Generally speaking, global and local sample path roughness of a multifractional process are determined by values of its parameter $H(\\cdot)$; therefore, since about two decades, several authors have been interested in their stat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3395","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":"2026-05-18T02:00:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4K/y2NWxZnj5eIOq3COHSsZXgeDmxAuPphY+DOCF/FWnHbQkhf3EDMQ+0RrZlQ6a3cK6S1ie3U38wrf6FS11BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T11:42:23.878829Z"},"content_sha256":"e7b4716ecd8775fecd559c9077e89e7130b8fe6dd80daa303536ecb63a1f05c9","schema_version":"1.0","event_id":"sha256:e7b4716ecd8775fecd559c9077e89e7130b8fe6dd80daa303536ecb63a1f05c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z5YW3BPGKOE5P2BOK7XUAFRZ3C/bundle.json","state_url":"https://pith.science/pith/Z5YW3BPGKOE5P2BOK7XUAFRZ3C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z5YW3BPGKOE5P2BOK7XUAFRZ3C/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":"2026-06-26T11:42:23Z","links":{"resolver":"https://pith.science/pith/Z5YW3BPGKOE5P2BOK7XUAFRZ3C","bundle":"https://pith.science/pith/Z5YW3BPGKOE5P2BOK7XUAFRZ3C/bundle.json","state":"https://pith.science/pith/Z5YW3BPGKOE5P2BOK7XUAFRZ3C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z5YW3BPGKOE5P2BOK7XUAFRZ3C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:Z5YW3BPGKOE5P2BOK7XUAFRZ3C","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":"f92d27d9145fe672bc51bae457c8397ad6d97dbc0f803cf0e952ba24231c6935","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-07-12T14:58:35Z","title_canon_sha256":"c244e044b986a790d3fc3b894c483424dc6e9b14f46d7b5184a8575221a083f8"},"schema_version":"1.0","source":{"id":"1407.3395","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.3395","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"arxiv_version","alias_value":"1407.3395v2","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3395","created_at":"2026-05-18T02:00:58Z"},{"alias_kind":"pith_short_12","alias_value":"Z5YW3BPGKOE5","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z5YW3BPGKOE5P2BO","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z5YW3BPG","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:e7b4716ecd8775fecd559c9077e89e7130b8fe6dd80daa303536ecb63a1f05c9","target":"graph","created_at":"2026-05-18T02:00:58Z","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":"Since the middle of the 90's, multifractional processes have been introduced for overcoming some limitations of the classical Fractional Brownian Motion model. In their context, the Hurst parameter becomes a Holder continuous function H(?) of the time variable t. Linear Multifractional Stable Motion (LMSM) is the most known one of them with heavy-tailed distributions. Generally speaking, global and local sample path roughness of a multifractional process are determined by values of its parameter $H(\\cdot)$; therefore, since about two decades, several authors have been interested in their stat","authors_text":"Antoine Ayache, Julien Hamonier","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-07-12T14:58:35Z","title":"Uniformly and strongly consistent estimation for the Hurst function of a Linear Multifractional Stable Motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3395","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":"sha256:3949f746a2474514b089a4eb6c4de6c1f32d4d43c3c45c3c0170756f6e71bd68","target":"record","created_at":"2026-05-18T02:00:58Z","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":"f92d27d9145fe672bc51bae457c8397ad6d97dbc0f803cf0e952ba24231c6935","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2014-07-12T14:58:35Z","title_canon_sha256":"c244e044b986a790d3fc3b894c483424dc6e9b14f46d7b5184a8575221a083f8"},"schema_version":"1.0","source":{"id":"1407.3395","kind":"arxiv","version":2}},"canonical_sha256":"cf716d85e65389d7e82e57ef401639d8a77f6cf63b329df5a9d190fe1f50b33d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf716d85e65389d7e82e57ef401639d8a77f6cf63b329df5a9d190fe1f50b33d","first_computed_at":"2026-05-18T02:00:58.970305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:58.970305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RrlN42UUZjpaZghzY/Fhr1G/xbYyWzVx6SGTZaU3A6tAPL1RNSyScREytNQnqXMnRnpAuhzqk0+cywL/dMtjBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:58.970946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.3395","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3949f746a2474514b089a4eb6c4de6c1f32d4d43c3c45c3c0170756f6e71bd68","sha256:e7b4716ecd8775fecd559c9077e89e7130b8fe6dd80daa303536ecb63a1f05c9"],"state_sha256":"07aa33e21becb899bdf34f8f02eaa2026d82042980299c332287d7a0ff2e4ae0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"enqZrzHsbq/z+F5DGhiDbN3A+qlTlQ5cprXwSZu74KzATDTx3LmQoEnZP8Lm+5+ipmjXAwrJUXGdzF0Ol73aDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T11:42:23.880806Z","bundle_sha256":"8befc2c693b7c1378416d342b65072a3bdf0ecf052589414c194b6676f6b3577"}}