{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:77B47IJIIKLCM3XWCVEQUSTTA4","short_pith_number":"pith:77B47IJI","canonical_record":{"source":{"id":"1603.00651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-02T10:47:20Z","cross_cats_sorted":[],"title_canon_sha256":"f7b2b7df9d33f5812d1a2dae247869291bcbc84f7e1c9680184b509038d88583","abstract_canon_sha256":"96edaa9eb40f69fb588a7658d180e6e63a38f97b3b16fdc3e587a9b161a6a199"},"schema_version":"1.0"},"canonical_sha256":"ffc3cfa1284296266ef615490a4a7307245784f12b62af3c59c753fa7c777ac8","source":{"kind":"arxiv","id":"1603.00651","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00651","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00651v1","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00651","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"77B47IJIIKLC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"77B47IJIIKLCM3XW","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"77B47IJI","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:77B47IJIIKLCM3XWCVEQUSTTA4","target":"record","payload":{"canonical_record":{"source":{"id":"1603.00651","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-02T10:47:20Z","cross_cats_sorted":[],"title_canon_sha256":"f7b2b7df9d33f5812d1a2dae247869291bcbc84f7e1c9680184b509038d88583","abstract_canon_sha256":"96edaa9eb40f69fb588a7658d180e6e63a38f97b3b16fdc3e587a9b161a6a199"},"schema_version":"1.0"},"canonical_sha256":"ffc3cfa1284296266ef615490a4a7307245784f12b62af3c59c753fa7c777ac8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:24.631538Z","signature_b64":"yJqUMfScK5hgjG6sMNHkM2l3ls4BpzXVfGNCwKad8QF40OxroDSCQTZIRfJSmsx1ALRlXdX5tWYCxZmDThyiBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ffc3cfa1284296266ef615490a4a7307245784f12b62af3c59c753fa7c777ac8","last_reissued_at":"2026-05-18T01:10:24.631092Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:24.631092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.00651","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":"2026-05-18T01:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OHSF5GXCjT0kLLDk45MTrEe6OZjM7gmAuTbSSYaKehARigbeWwqBCqHEWGpCUdyuXxTFfpKHFZ5/1jWRkqa6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:15:16.407009Z"},"content_sha256":"346a63073f1bd432686fce0976dd47701e78658d9cd6472e55a793ecc215d6b1","schema_version":"1.0","event_id":"sha256:346a63073f1bd432686fce0976dd47701e78658d9cd6472e55a793ecc215d6b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:77B47IJIIKLCM3XWCVEQUSTTA4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perturbative Expansion for the Maximum of Fractional Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Kay J\\\"org Wiese, Mathieu Delorme","submitted_at":"2016-03-02T10:47:20Z","abstract_excerpt":"Brownian motion is the only random process which is Gaussian, stationary and Markovian. Dropping the Markovian property, i.e. allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst exponent $H$. For $H=1/2$, Brownian motion is recovered. We develop a perturbative approach to treat the non-locality in time in an expansion in $\\varepsilon = H-1/2$. This allows us to derive analytic results beyond scaling exponents for various observables related to extreme value statistics: The maximum $m$ of the process and the time $t_{\\text{max}}$ at whic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00651","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":"2026-05-18T01:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gwlfbFfDqYOZ0UM8GlT4TxDMBM7ad5vBkyn+asVQx5vKOULqPIemjf6f4S8gbDZS7Oxk36VuBquhNJYzhrcGDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:15:16.407703Z"},"content_sha256":"b72a57fabfdb061d3edd05dd748808d05c35dc06e75861dedc09ea6126ca6b1f","schema_version":"1.0","event_id":"sha256:b72a57fabfdb061d3edd05dd748808d05c35dc06e75861dedc09ea6126ca6b1f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/77B47IJIIKLCM3XWCVEQUSTTA4/bundle.json","state_url":"https://pith.science/pith/77B47IJIIKLCM3XWCVEQUSTTA4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/77B47IJIIKLCM3XWCVEQUSTTA4/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":"2026-05-30T06:15:16Z","links":{"resolver":"https://pith.science/pith/77B47IJIIKLCM3XWCVEQUSTTA4","bundle":"https://pith.science/pith/77B47IJIIKLCM3XWCVEQUSTTA4/bundle.json","state":"https://pith.science/pith/77B47IJIIKLCM3XWCVEQUSTTA4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/77B47IJIIKLCM3XWCVEQUSTTA4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:77B47IJIIKLCM3XWCVEQUSTTA4","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":"96edaa9eb40f69fb588a7658d180e6e63a38f97b3b16fdc3e587a9b161a6a199","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-02T10:47:20Z","title_canon_sha256":"f7b2b7df9d33f5812d1a2dae247869291bcbc84f7e1c9680184b509038d88583"},"schema_version":"1.0","source":{"id":"1603.00651","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00651","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00651v1","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00651","created_at":"2026-05-18T01:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"77B47IJIIKLC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"77B47IJIIKLCM3XW","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"77B47IJI","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:b72a57fabfdb061d3edd05dd748808d05c35dc06e75861dedc09ea6126ca6b1f","target":"graph","created_at":"2026-05-18T01:10:24Z","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":"Brownian motion is the only random process which is Gaussian, stationary and Markovian. Dropping the Markovian property, i.e. allowing for memory, one obtains a class of processes called fractional Brownian motion, indexed by the Hurst exponent $H$. For $H=1/2$, Brownian motion is recovered. We develop a perturbative approach to treat the non-locality in time in an expansion in $\\varepsilon = H-1/2$. This allows us to derive analytic results beyond scaling exponents for various observables related to extreme value statistics: The maximum $m$ of the process and the time $t_{\\text{max}}$ at whic","authors_text":"Kay J\\\"org Wiese, Mathieu Delorme","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-02T10:47:20Z","title":"Perturbative Expansion for the Maximum of Fractional Brownian Motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00651","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":"sha256:346a63073f1bd432686fce0976dd47701e78658d9cd6472e55a793ecc215d6b1","target":"record","created_at":"2026-05-18T01:10:24Z","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":"96edaa9eb40f69fb588a7658d180e6e63a38f97b3b16fdc3e587a9b161a6a199","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2016-03-02T10:47:20Z","title_canon_sha256":"f7b2b7df9d33f5812d1a2dae247869291bcbc84f7e1c9680184b509038d88583"},"schema_version":"1.0","source":{"id":"1603.00651","kind":"arxiv","version":1}},"canonical_sha256":"ffc3cfa1284296266ef615490a4a7307245784f12b62af3c59c753fa7c777ac8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ffc3cfa1284296266ef615490a4a7307245784f12b62af3c59c753fa7c777ac8","first_computed_at":"2026-05-18T01:10:24.631092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:24.631092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yJqUMfScK5hgjG6sMNHkM2l3ls4BpzXVfGNCwKad8QF40OxroDSCQTZIRfJSmsx1ALRlXdX5tWYCxZmDThyiBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:24.631538Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00651","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:346a63073f1bd432686fce0976dd47701e78658d9cd6472e55a793ecc215d6b1","sha256:b72a57fabfdb061d3edd05dd748808d05c35dc06e75861dedc09ea6126ca6b1f"],"state_sha256":"c408885868b6ceb1833b23a8caa35baa29c2b000bdc0d465f2b70e7b98927fb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e/3NGwfEnall4EZzd1HWxhWL3KLHpISnrxMQVzThWIsNit8GrUB29p46akP+Ey7CQ4ABWG2+cMZopjJRkxTxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:15:16.411182Z","bundle_sha256":"cdd78b04b9ecd8ce0629db2916a90dca1bf6cd32eff53006818481f8edabb1d6"}}