{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:O5OC6CYVOQQNG7MYTSOJYYHG5H","short_pith_number":"pith:O5OC6CYV","canonical_record":{"source":{"id":"2408.10936","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-08-20T15:19:53Z","cross_cats_sorted":[],"title_canon_sha256":"71b90647d92b55217671e6283a9c1a1243cd739d2a3f64db4a0814f2d8feeded","abstract_canon_sha256":"49f825b8223fbc74d0f7a3a7789687a58ac85da8409b42e78794ebaea15201fc"},"schema_version":"1.0"},"canonical_sha256":"775c2f0b157420d37d989c9c9c60e6e9d081130302e63568a4a024bde11fae00","source":{"kind":"arxiv","id":"2408.10936","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.10936","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"2408.10936v2","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.10936","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"O5OC6CYVOQQN","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_16","alias_value":"O5OC6CYVOQQNG7MY","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_8","alias_value":"O5OC6CYV","created_at":"2026-05-28T01:04:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:O5OC6CYVOQQNG7MYTSOJYYHG5H","target":"record","payload":{"canonical_record":{"source":{"id":"2408.10936","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-08-20T15:19:53Z","cross_cats_sorted":[],"title_canon_sha256":"71b90647d92b55217671e6283a9c1a1243cd739d2a3f64db4a0814f2d8feeded","abstract_canon_sha256":"49f825b8223fbc74d0f7a3a7789687a58ac85da8409b42e78794ebaea15201fc"},"schema_version":"1.0"},"canonical_sha256":"775c2f0b157420d37d989c9c9c60e6e9d081130302e63568a4a024bde11fae00","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-28T01:04:25.051530Z","signature_b64":"uQkOQQSaOtunnO7GYZRVZDk0uxWnH6g2qtUpHbjOcR+N79jm3rZB9NiPLE0agbsXHw7Xw6mMy475ThAhV63yDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"775c2f0b157420d37d989c9c9c60e6e9d081130302e63568a4a024bde11fae00","last_reissued_at":"2026-05-28T01:04:25.050626Z","signature_status":"signed_v1","first_computed_at":"2026-05-28T01:04:25.050626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2408.10936","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":"2026-05-28T01:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YVcR1Dq75+7vIWEMuPWXG/Xwxk+NCH5FwgTdvuMcoEEt0VBo1HZmG6LIpwpaq3CYFww7pXcMyD6NHByVVemJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:28:59.236611Z"},"content_sha256":"b33414de43cf7b61d2118cbaad3b6e32c71fab919644ad6f0ee32375fac7de29","schema_version":"1.0","event_id":"sha256:b33414de43cf7b61d2118cbaad3b6e32c71fab919644ad6f0ee32375fac7de29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:O5OC6CYVOQQNG7MYTSOJYYHG5H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Currents of Fractional Brownian Motion: Existence and Regularity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Herry Pribawanto Suryawan, Jose Luis da Silva, Martin Grothaus, Thomas Ullrich","submitted_at":"2024-08-20T15:19:53Z","abstract_excerpt":"By using white noise analysis, we study the integral kernel $\\xi(x)$, $x\\in\\mathbb{R}^{d}$, of stochastic currents corresponding to fractional Brownian motion with Hurst parameter $H\\in(0,1)$. For $x\\in\\mathbb{R}^{d}\\backslash\\{0\\}$ and $d\\ge1$ we show that the kernel $\\xi(x)$ is well-defined as a Hida distribution for all $H\\in(0,1)$. For $x=0$ and $d=1$, $\\xi(0)$ is a Hida distribution for all $H\\in(0,1)$. For $d\\ge2$, then $\\xi(0)$ is a Hida distribution only for $H\\in(0,1/d)$. For $d=1$, $x \\neq 0$, and $H \\in (0,1)$, we show that $\\xi(x) \\in \\mathcal{G}'$, the space of regular generalized"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.10936","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2408.10936/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-28T01:04:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"S6GMELtu5Z/lMS9112B+Jc8yYzq2UEuIELVwEmbM9Q97eTowk42DGb+abWCvtjN61GIxKDlJyzTh5f3ZOTzWBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:28:59.237387Z"},"content_sha256":"b78c5bef81e0a1b57fdd2a0a31f0f5a244e7f4710ddf0d626fa0786ee5769f49","schema_version":"1.0","event_id":"sha256:b78c5bef81e0a1b57fdd2a0a31f0f5a244e7f4710ddf0d626fa0786ee5769f49"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O5OC6CYVOQQNG7MYTSOJYYHG5H/bundle.json","state_url":"https://pith.science/pith/O5OC6CYVOQQNG7MYTSOJYYHG5H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O5OC6CYVOQQNG7MYTSOJYYHG5H/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":"2026-06-10T08:28:59Z","links":{"resolver":"https://pith.science/pith/O5OC6CYVOQQNG7MYTSOJYYHG5H","bundle":"https://pith.science/pith/O5OC6CYVOQQNG7MYTSOJYYHG5H/bundle.json","state":"https://pith.science/pith/O5OC6CYVOQQNG7MYTSOJYYHG5H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O5OC6CYVOQQNG7MYTSOJYYHG5H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:O5OC6CYVOQQNG7MYTSOJYYHG5H","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":"49f825b8223fbc74d0f7a3a7789687a58ac85da8409b42e78794ebaea15201fc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-08-20T15:19:53Z","title_canon_sha256":"71b90647d92b55217671e6283a9c1a1243cd739d2a3f64db4a0814f2d8feeded"},"schema_version":"1.0","source":{"id":"2408.10936","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2408.10936","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"arxiv_version","alias_value":"2408.10936v2","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2408.10936","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_12","alias_value":"O5OC6CYVOQQN","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_16","alias_value":"O5OC6CYVOQQNG7MY","created_at":"2026-05-28T01:04:25Z"},{"alias_kind":"pith_short_8","alias_value":"O5OC6CYV","created_at":"2026-05-28T01:04:25Z"}],"graph_snapshots":[{"event_id":"sha256:b78c5bef81e0a1b57fdd2a0a31f0f5a244e7f4710ddf0d626fa0786ee5769f49","target":"graph","created_at":"2026-05-28T01:04:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2408.10936/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By using white noise analysis, we study the integral kernel $\\xi(x)$, $x\\in\\mathbb{R}^{d}$, of stochastic currents corresponding to fractional Brownian motion with Hurst parameter $H\\in(0,1)$. For $x\\in\\mathbb{R}^{d}\\backslash\\{0\\}$ and $d\\ge1$ we show that the kernel $\\xi(x)$ is well-defined as a Hida distribution for all $H\\in(0,1)$. For $x=0$ and $d=1$, $\\xi(0)$ is a Hida distribution for all $H\\in(0,1)$. For $d\\ge2$, then $\\xi(0)$ is a Hida distribution only for $H\\in(0,1/d)$. For $d=1$, $x \\neq 0$, and $H \\in (0,1)$, we show that $\\xi(x) \\in \\mathcal{G}'$, the space of regular generalized","authors_text":"Herry Pribawanto Suryawan, Jose Luis da Silva, Martin Grothaus, Thomas Ullrich","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-08-20T15:19:53Z","title":"Stochastic Currents of Fractional Brownian Motion: Existence and Regularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.10936","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:b33414de43cf7b61d2118cbaad3b6e32c71fab919644ad6f0ee32375fac7de29","target":"record","created_at":"2026-05-28T01:04:25Z","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":"49f825b8223fbc74d0f7a3a7789687a58ac85da8409b42e78794ebaea15201fc","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2024-08-20T15:19:53Z","title_canon_sha256":"71b90647d92b55217671e6283a9c1a1243cd739d2a3f64db4a0814f2d8feeded"},"schema_version":"1.0","source":{"id":"2408.10936","kind":"arxiv","version":2}},"canonical_sha256":"775c2f0b157420d37d989c9c9c60e6e9d081130302e63568a4a024bde11fae00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"775c2f0b157420d37d989c9c9c60e6e9d081130302e63568a4a024bde11fae00","first_computed_at":"2026-05-28T01:04:25.050626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-28T01:04:25.050626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uQkOQQSaOtunnO7GYZRVZDk0uxWnH6g2qtUpHbjOcR+N79jm3rZB9NiPLE0agbsXHw7Xw6mMy475ThAhV63yDA==","signature_status":"signed_v1","signed_at":"2026-05-28T01:04:25.051530Z","signed_message":"canonical_sha256_bytes"},"source_id":"2408.10936","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b33414de43cf7b61d2118cbaad3b6e32c71fab919644ad6f0ee32375fac7de29","sha256:b78c5bef81e0a1b57fdd2a0a31f0f5a244e7f4710ddf0d626fa0786ee5769f49"],"state_sha256":"3347f82715365919b2c3080f547dbd1a74af849fca9e554c4639b9cb603234ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WaQV1I8ZPxAcMsAHXYKRP9uLn6RE0/23dH7veavwA99w8R6z6AhI3oXSTPwtIfKyNUFRPcK7YCIwq8W5MvAoDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T08:28:59.241812Z","bundle_sha256":"f96072e00a2b046b4725fbf1094d286f3efc3ccb8de7846b012fe2d5849a4a97"}}