{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:67G2OQTV2TYYBEBZT6DHOZKL7B","short_pith_number":"pith:67G2OQTV","canonical_record":{"source":{"id":"1105.3130","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-16T15:54:30Z","cross_cats_sorted":[],"title_canon_sha256":"2c909ef673beda03ec21c2e02f00aff1d0a1fd2e03c0a996688b5628a8170232","abstract_canon_sha256":"b25062c717ff52814856066010346cabf56e72f523737b82a9270b64c83fc57e"},"schema_version":"1.0"},"canonical_sha256":"f7cda74275d4f18090399f8677654bf86b79bb744ca6345488331e08447b8e4a","source":{"kind":"arxiv","id":"1105.3130","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3130","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3130v4","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3130","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"67G2OQTV2TYY","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"67G2OQTV2TYYBEBZ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"67G2OQTV","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:67G2OQTV2TYYBEBZT6DHOZKL7B","target":"record","payload":{"canonical_record":{"source":{"id":"1105.3130","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-16T15:54:30Z","cross_cats_sorted":[],"title_canon_sha256":"2c909ef673beda03ec21c2e02f00aff1d0a1fd2e03c0a996688b5628a8170232","abstract_canon_sha256":"b25062c717ff52814856066010346cabf56e72f523737b82a9270b64c83fc57e"},"schema_version":"1.0"},"canonical_sha256":"f7cda74275d4f18090399f8677654bf86b79bb744ca6345488331e08447b8e4a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:25.164093Z","signature_b64":"09J44OfmByX8tcCNiOYiBlKCUlQObblbczis0ClRaxqtiv9dB8N0a0Z+UYy4UcCJlqEk4uTXGIGcbYCuZxMvCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7cda74275d4f18090399f8677654bf86b79bb744ca6345488331e08447b8e4a","last_reissued_at":"2026-05-18T03:17:25.163447Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:25.163447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.3130","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qg7f8GGDOm7cCjpL9015RTnBL7vHUCVz0zMsEerKJnortGZgW5e1HdQvXEV1Z6o5UbaMddE3aGp4w8ALu2MDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:00:45.268134Z"},"content_sha256":"7cf9f3396ae67efcad02041a6514a12a30d4c452fcfd2725892deb8a577227b6","schema_version":"1.0","event_id":"sha256:7cf9f3396ae67efcad02041a6514a12a30d4c452fcfd2725892deb8a577227b6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:67G2OQTV2TYYBEBZT6DHOZKL7B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random walks at random times: Convergence to iterated L\\'{e}vy motion, fractional stable motions, and other self-similar processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Greg Markowsky, Paul Jung","submitted_at":"2011-05-16T15:54:30Z","abstract_excerpt":"For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the so-called iterated Brownian motion. Khoshnevisan and Lewis [Ann. Appl. Probab. 9 (1999) 629-667] suggested \"the existence of a form of measure-theoretic duality\" between iterated Brownian motion and a Brownian motion in random scenery. We show that a random walk at random time can be considered a random walk in \"alternating\" scenery, thus hinting at a mechanism"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3130","kind":"arxiv","version":4},"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":"2026-05-18T03:17:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iDVUcZL3UYabwrCdh6msaoMT8az2IIeEHUQBgjxIRAfGo2iXgyQK8KCQuIuk2hN64T7cnoC1CxWpPIsjaXDIDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:00:45.268506Z"},"content_sha256":"a8b39a76d0ace234566875094db49705d8a29208dc0a4915f52bc69c645a6f7c","schema_version":"1.0","event_id":"sha256:a8b39a76d0ace234566875094db49705d8a29208dc0a4915f52bc69c645a6f7c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/67G2OQTV2TYYBEBZT6DHOZKL7B/bundle.json","state_url":"https://pith.science/pith/67G2OQTV2TYYBEBZT6DHOZKL7B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/67G2OQTV2TYYBEBZT6DHOZKL7B/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":"2026-05-27T15:00:45Z","links":{"resolver":"https://pith.science/pith/67G2OQTV2TYYBEBZT6DHOZKL7B","bundle":"https://pith.science/pith/67G2OQTV2TYYBEBZT6DHOZKL7B/bundle.json","state":"https://pith.science/pith/67G2OQTV2TYYBEBZT6DHOZKL7B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/67G2OQTV2TYYBEBZT6DHOZKL7B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:67G2OQTV2TYYBEBZT6DHOZKL7B","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":"b25062c717ff52814856066010346cabf56e72f523737b82a9270b64c83fc57e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-16T15:54:30Z","title_canon_sha256":"2c909ef673beda03ec21c2e02f00aff1d0a1fd2e03c0a996688b5628a8170232"},"schema_version":"1.0","source":{"id":"1105.3130","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3130","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3130v4","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3130","created_at":"2026-05-18T03:17:25Z"},{"alias_kind":"pith_short_12","alias_value":"67G2OQTV2TYY","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"67G2OQTV2TYYBEBZ","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"67G2OQTV","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:a8b39a76d0ace234566875094db49705d8a29208dc0a4915f52bc69c645a6f7c","target":"graph","created_at":"2026-05-18T03:17:25Z","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"},"paper":{"abstract_excerpt":"For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the so-called iterated Brownian motion. Khoshnevisan and Lewis [Ann. Appl. Probab. 9 (1999) 629-667] suggested \"the existence of a form of measure-theoretic duality\" between iterated Brownian motion and a Brownian motion in random scenery. We show that a random walk at random time can be considered a random walk in \"alternating\" scenery, thus hinting at a mechanism","authors_text":"Greg Markowsky, Paul Jung","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-16T15:54:30Z","title":"Random walks at random times: Convergence to iterated L\\'{e}vy motion, fractional stable motions, and other self-similar processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3130","kind":"arxiv","version":4},"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":"sha256:7cf9f3396ae67efcad02041a6514a12a30d4c452fcfd2725892deb8a577227b6","target":"record","created_at":"2026-05-18T03:17:25Z","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":"b25062c717ff52814856066010346cabf56e72f523737b82a9270b64c83fc57e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-16T15:54:30Z","title_canon_sha256":"2c909ef673beda03ec21c2e02f00aff1d0a1fd2e03c0a996688b5628a8170232"},"schema_version":"1.0","source":{"id":"1105.3130","kind":"arxiv","version":4}},"canonical_sha256":"f7cda74275d4f18090399f8677654bf86b79bb744ca6345488331e08447b8e4a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7cda74275d4f18090399f8677654bf86b79bb744ca6345488331e08447b8e4a","first_computed_at":"2026-05-18T03:17:25.163447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:25.163447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"09J44OfmByX8tcCNiOYiBlKCUlQObblbczis0ClRaxqtiv9dB8N0a0Z+UYy4UcCJlqEk4uTXGIGcbYCuZxMvCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:25.164093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3130","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7cf9f3396ae67efcad02041a6514a12a30d4c452fcfd2725892deb8a577227b6","sha256:a8b39a76d0ace234566875094db49705d8a29208dc0a4915f52bc69c645a6f7c"],"state_sha256":"366452d4c51cf4a01a96cad6cc3a49376facc8f185478c5b4da04326b57070d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DnoAKs8xCjHP7X+XTLCOP2HkjhY1W29vaCu+v37mpZZ10mlyMB4AXShRdXxxnq0WK92QN1M0VKWpl96Mc3hpDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:00:45.271372Z","bundle_sha256":"62762f28ad8d553757c484adef5f07d4982f4c8d1f56d759c0f7cee2fcef1225"}}