{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:W2YHHQ534T6VTBQ53AIQEIVKVF","short_pith_number":"pith:W2YHHQ53","canonical_record":{"source":{"id":"1305.5112","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-22T12:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"ef2df1329347a245570b3abf5754fed1a86baa4521b4eb860cdc0db43184aee6","abstract_canon_sha256":"53b969802a0cccd3ac81426791d640ff95d39de8ad54865354ca53be42b091a4"},"schema_version":"1.0"},"canonical_sha256":"b6b073c3bbe4fd59861dd8110222aaa97cc791ba687d439da84806cb969dd213","source":{"kind":"arxiv","id":"1305.5112","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5112","created_at":"2026-05-18T01:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5112v2","created_at":"2026-05-18T01:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5112","created_at":"2026-05-18T01:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"W2YHHQ534T6V","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W2YHHQ534T6VTBQ5","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W2YHHQ53","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:W2YHHQ534T6VTBQ53AIQEIVKVF","target":"record","payload":{"canonical_record":{"source":{"id":"1305.5112","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-22T12:54:44Z","cross_cats_sorted":[],"title_canon_sha256":"ef2df1329347a245570b3abf5754fed1a86baa4521b4eb860cdc0db43184aee6","abstract_canon_sha256":"53b969802a0cccd3ac81426791d640ff95d39de8ad54865354ca53be42b091a4"},"schema_version":"1.0"},"canonical_sha256":"b6b073c3bbe4fd59861dd8110222aaa97cc791ba687d439da84806cb969dd213","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:47.836347Z","signature_b64":"29wWxasZEA06OgQmGi6b7TEiX8ME3587RuPJtaynhhjBj05u2NKRmr1My1G23vHF3Gij5Zz9lJegbHxfQnwGAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b6b073c3bbe4fd59861dd8110222aaa97cc791ba687d439da84806cb969dd213","last_reissued_at":"2026-05-18T01:49:47.835703Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:47.835703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.5112","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":"2026-05-18T01:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8b49jT8ZCn/clw9EE1SdmPpITPP69b/fIUsPGViYbCr4kS3CWD6pnjrJxHGHGp7dda7T7BnUlaF1eBp6tOKYBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:34:09.218481Z"},"content_sha256":"1dd3e75caedc0d5a269226787dd7eae0f41c80798015cf3a0fba875ec5049673","schema_version":"1.0","event_id":"sha256:1dd3e75caedc0d5a269226787dd7eae0f41c80798015cf3a0fba875ec5049673"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:W2YHHQ534T6VTBQ53AIQEIVKVF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A family of random walks with generalized Dirichlet steps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alessandro De Gregorio","submitted_at":"2013-05-22T12:54:44Z","abstract_excerpt":"We analyze a class of continuous time random walks in $\\mathbb R^d,d\\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes of orientation, we provide the analytic form of the probability density function of the position $\\{\\underline{\\bf X}_d(t),t>0\\}$ reached, at time $t>0$, by the random motion. In particular, we analyze the case of random walks with two steps.\n  In general, it is an hard task to obtain the explicit probability distributions for the process $\\{\\underline{\\bf "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5112","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":"2026-05-18T01:49:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5596sxAlA0mM8QWy2dl4PGw06vRGrhG5XO9V7IPGRag3UPFeY5FR6ZL41RMef/EVteMwz9rJ13k9aonrFJ1HDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:34:09.218841Z"},"content_sha256":"9e65d3d8e6ed057b1e559dd953ceda7a5f33d2e7635dff696eaed7d9b0221adc","schema_version":"1.0","event_id":"sha256:9e65d3d8e6ed057b1e559dd953ceda7a5f33d2e7635dff696eaed7d9b0221adc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/W2YHHQ534T6VTBQ53AIQEIVKVF/bundle.json","state_url":"https://pith.science/pith/W2YHHQ534T6VTBQ53AIQEIVKVF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/W2YHHQ534T6VTBQ53AIQEIVKVF/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":"2026-05-28T03:34:09Z","links":{"resolver":"https://pith.science/pith/W2YHHQ534T6VTBQ53AIQEIVKVF","bundle":"https://pith.science/pith/W2YHHQ534T6VTBQ53AIQEIVKVF/bundle.json","state":"https://pith.science/pith/W2YHHQ534T6VTBQ53AIQEIVKVF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/W2YHHQ534T6VTBQ53AIQEIVKVF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W2YHHQ534T6VTBQ53AIQEIVKVF","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":"53b969802a0cccd3ac81426791d640ff95d39de8ad54865354ca53be42b091a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-22T12:54:44Z","title_canon_sha256":"ef2df1329347a245570b3abf5754fed1a86baa4521b4eb860cdc0db43184aee6"},"schema_version":"1.0","source":{"id":"1305.5112","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5112","created_at":"2026-05-18T01:49:47Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5112v2","created_at":"2026-05-18T01:49:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5112","created_at":"2026-05-18T01:49:47Z"},{"alias_kind":"pith_short_12","alias_value":"W2YHHQ534T6V","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W2YHHQ534T6VTBQ5","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W2YHHQ53","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:9e65d3d8e6ed057b1e559dd953ceda7a5f33d2e7635dff696eaed7d9b0221adc","target":"graph","created_at":"2026-05-18T01:49:47Z","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 analyze a class of continuous time random walks in $\\mathbb R^d,d\\geq 2,$ with uniformly distributed directions. The steps performed by these processes are distributed according to a generalized Dirichlet law. Given the number of changes of orientation, we provide the analytic form of the probability density function of the position $\\{\\underline{\\bf X}_d(t),t>0\\}$ reached, at time $t>0$, by the random motion. In particular, we analyze the case of random walks with two steps.\n  In general, it is an hard task to obtain the explicit probability distributions for the process $\\{\\underline{\\bf ","authors_text":"Alessandro De Gregorio","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-22T12:54:44Z","title":"A family of random walks with generalized Dirichlet steps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5112","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":"sha256:1dd3e75caedc0d5a269226787dd7eae0f41c80798015cf3a0fba875ec5049673","target":"record","created_at":"2026-05-18T01:49:47Z","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":"53b969802a0cccd3ac81426791d640ff95d39de8ad54865354ca53be42b091a4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-05-22T12:54:44Z","title_canon_sha256":"ef2df1329347a245570b3abf5754fed1a86baa4521b4eb860cdc0db43184aee6"},"schema_version":"1.0","source":{"id":"1305.5112","kind":"arxiv","version":2}},"canonical_sha256":"b6b073c3bbe4fd59861dd8110222aaa97cc791ba687d439da84806cb969dd213","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b6b073c3bbe4fd59861dd8110222aaa97cc791ba687d439da84806cb969dd213","first_computed_at":"2026-05-18T01:49:47.835703Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:49:47.835703Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"29wWxasZEA06OgQmGi6b7TEiX8ME3587RuPJtaynhhjBj05u2NKRmr1My1G23vHF3Gij5Zz9lJegbHxfQnwGAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:49:47.836347Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5112","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dd3e75caedc0d5a269226787dd7eae0f41c80798015cf3a0fba875ec5049673","sha256:9e65d3d8e6ed057b1e559dd953ceda7a5f33d2e7635dff696eaed7d9b0221adc"],"state_sha256":"9ad05cb69d2b8f91b6437c3c0cc7a22d97955d93b4cfd41c7d296e6279f94fc6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MdpY47Pb2lbwz7bnnnKY7rHadtB0IxIFStbN07aEqSw7IYhIKMoD84QXGvm0kq1w4/UsXez1Cs8CfYj15QHxBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:34:09.220953Z","bundle_sha256":"83afb32ecf1cccb188f53bc131c17a44bc7d5283f90af27b8305b261df9fbd06"}}