{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:CT3I2NADV4XWFTDN2JDE276GTP","short_pith_number":"pith:CT3I2NAD","canonical_record":{"source":{"id":"1101.4969","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-25T22:45:39Z","cross_cats_sorted":[],"title_canon_sha256":"c7947dc9c8eec9aa8b9837307b275223b2ed99946f35f3f37f0b692d2802fcde","abstract_canon_sha256":"0e9de4e501ac23e1fefd8b722a0a3994717e45432d08193d56a39d001f8081d3"},"schema_version":"1.0"},"canonical_sha256":"14f68d3403af2f62cc6dd2464d7fc69bdb7ccaa0f669f3d7ee272a6dfd6e8d15","source":{"kind":"arxiv","id":"1101.4969","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4969","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4969v2","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4969","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"CT3I2NADV4XW","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CT3I2NADV4XWFTDN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CT3I2NAD","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:CT3I2NADV4XWFTDN2JDE276GTP","target":"record","payload":{"canonical_record":{"source":{"id":"1101.4969","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-25T22:45:39Z","cross_cats_sorted":[],"title_canon_sha256":"c7947dc9c8eec9aa8b9837307b275223b2ed99946f35f3f37f0b692d2802fcde","abstract_canon_sha256":"0e9de4e501ac23e1fefd8b722a0a3994717e45432d08193d56a39d001f8081d3"},"schema_version":"1.0"},"canonical_sha256":"14f68d3403af2f62cc6dd2464d7fc69bdb7ccaa0f669f3d7ee272a6dfd6e8d15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:49.695731Z","signature_b64":"hHuyv1V9faKsUFfIUT3vaZEwSg9FJnvITrTfuU7X+l4mbAh19vdLRpNZY6vKs1rrvUerJYDeZbPGy7KukiumCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14f68d3403af2f62cc6dd2464d7fc69bdb7ccaa0f669f3d7ee272a6dfd6e8d15","last_reissued_at":"2026-05-18T02:22:49.694905Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:49.694905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.4969","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":"2026-05-18T02:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BrwsTO1IgVERTN9qFnplW6y8/aXuZDRbs8DZGBEUkPIcuqoMftA+cN0AtIkmncd5tP6nwcU6qPUnxi/EBKoaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:31:13.689343Z"},"content_sha256":"e805c554adbf8accd34357718c370c3019906c1ce4a362cea9373ca22345f533","schema_version":"1.0","event_id":"sha256:e805c554adbf8accd34357718c370c3019906c1ce4a362cea9373ca22345f533"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:CT3I2NADV4XWFTDN2JDE276GTP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sample Path Properties of Volterra Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Eyal Neuman, Leonid Mytnik","submitted_at":"2011-01-25T22:45:39Z","abstract_excerpt":"We consider the regularity of sample paths of Volterra processes. These processes are defined as stochastic integrals $$ M(t)=\\int_{0}^{t}F(t,r)dX(r), \\ \\ t \\in \\mathds{R}_{+}, $$ where $X$ is a semimartingale and $F$ is a deterministic real-valued function. We derive the information on the modulus of continuity for these processes under regularity assumptions on the function $F$ and show that $M(t)$ has \"worst\" regularity properties at times of jumps of $X(t)$. We apply our results to obtain the optimal H\\\"older exponent for fractional L\\'{e}vy processes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4969","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":"2026-05-18T02:22:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Wxs41/kGEUBMr4mBkP+vg4ggZVjdiLuD44liRnvuC/Bp4Eaf2VidaMiCFKs6sLpBtSPX8154Stnm76dN0JGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T01:31:13.689691Z"},"content_sha256":"b6b54ff1a2f369c55994124588737d449adb997ef8bdbd311e3fce0cb5d40528","schema_version":"1.0","event_id":"sha256:b6b54ff1a2f369c55994124588737d449adb997ef8bdbd311e3fce0cb5d40528"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CT3I2NADV4XWFTDN2JDE276GTP/bundle.json","state_url":"https://pith.science/pith/CT3I2NADV4XWFTDN2JDE276GTP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CT3I2NADV4XWFTDN2JDE276GTP/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":"2026-06-03T01:31:13Z","links":{"resolver":"https://pith.science/pith/CT3I2NADV4XWFTDN2JDE276GTP","bundle":"https://pith.science/pith/CT3I2NADV4XWFTDN2JDE276GTP/bundle.json","state":"https://pith.science/pith/CT3I2NADV4XWFTDN2JDE276GTP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CT3I2NADV4XWFTDN2JDE276GTP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:CT3I2NADV4XWFTDN2JDE276GTP","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":"0e9de4e501ac23e1fefd8b722a0a3994717e45432d08193d56a39d001f8081d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-25T22:45:39Z","title_canon_sha256":"c7947dc9c8eec9aa8b9837307b275223b2ed99946f35f3f37f0b692d2802fcde"},"schema_version":"1.0","source":{"id":"1101.4969","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4969","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4969v2","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4969","created_at":"2026-05-18T02:22:49Z"},{"alias_kind":"pith_short_12","alias_value":"CT3I2NADV4XW","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"CT3I2NADV4XWFTDN","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"CT3I2NAD","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:b6b54ff1a2f369c55994124588737d449adb997ef8bdbd311e3fce0cb5d40528","target":"graph","created_at":"2026-05-18T02:22:49Z","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":"We consider the regularity of sample paths of Volterra processes. These processes are defined as stochastic integrals $$ M(t)=\\int_{0}^{t}F(t,r)dX(r), \\ \\ t \\in \\mathds{R}_{+}, $$ where $X$ is a semimartingale and $F$ is a deterministic real-valued function. We derive the information on the modulus of continuity for these processes under regularity assumptions on the function $F$ and show that $M(t)$ has \"worst\" regularity properties at times of jumps of $X(t)$. We apply our results to obtain the optimal H\\\"older exponent for fractional L\\'{e}vy processes.","authors_text":"Eyal Neuman, Leonid Mytnik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-25T22:45:39Z","title":"Sample Path Properties of Volterra Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4969","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:e805c554adbf8accd34357718c370c3019906c1ce4a362cea9373ca22345f533","target":"record","created_at":"2026-05-18T02:22:49Z","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":"0e9de4e501ac23e1fefd8b722a0a3994717e45432d08193d56a39d001f8081d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-01-25T22:45:39Z","title_canon_sha256":"c7947dc9c8eec9aa8b9837307b275223b2ed99946f35f3f37f0b692d2802fcde"},"schema_version":"1.0","source":{"id":"1101.4969","kind":"arxiv","version":2}},"canonical_sha256":"14f68d3403af2f62cc6dd2464d7fc69bdb7ccaa0f669f3d7ee272a6dfd6e8d15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"14f68d3403af2f62cc6dd2464d7fc69bdb7ccaa0f669f3d7ee272a6dfd6e8d15","first_computed_at":"2026-05-18T02:22:49.694905Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:49.694905Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hHuyv1V9faKsUFfIUT3vaZEwSg9FJnvITrTfuU7X+l4mbAh19vdLRpNZY6vKs1rrvUerJYDeZbPGy7KukiumCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:49.695731Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4969","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e805c554adbf8accd34357718c370c3019906c1ce4a362cea9373ca22345f533","sha256:b6b54ff1a2f369c55994124588737d449adb997ef8bdbd311e3fce0cb5d40528"],"state_sha256":"79db7583ca734d4822073ec2e4aa46b7a24f5114c9d04cc5f5087ce0dc0661b3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dly2dFUtMQ4/qpHD+gBN0AHcXjaaDLu86aEmAvJihApq0qkiCya0+vsFVWlilU6wdox3ssvUnbwKoavrPnzCAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T01:31:13.691660Z","bundle_sha256":"1b35b979adb67a286c8253d985a622b0c1c0afeb158e6b2d2cbed35db5cd29bf"}}