{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:D3QZJ6COG2CAVQDIKG6MQQJDFZ","short_pith_number":"pith:D3QZJ6CO","canonical_record":{"source":{"id":"0812.4269","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-22T19:09:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a62f9b8dc2b20eff0fbe23bdc1484568161eec66894fc112e9b480dee06e3a5d","abstract_canon_sha256":"5cc7af4e8985b6800333aeda29b35c43780f3f5242722928c6fd6697eb2e2d0d"},"schema_version":"1.0"},"canonical_sha256":"1ee194f84e36840ac06851bcc841232e47f3b348b796c20dd1007918a3b55b38","source":{"kind":"arxiv","id":"0812.4269","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4269","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4269v3","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4269","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"D3QZJ6COG2CA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"D3QZJ6COG2CAVQDI","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"D3QZJ6CO","created_at":"2026-05-18T12:25:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:D3QZJ6COG2CAVQDIKG6MQQJDFZ","target":"record","payload":{"canonical_record":{"source":{"id":"0812.4269","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-22T19:09:29Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a62f9b8dc2b20eff0fbe23bdc1484568161eec66894fc112e9b480dee06e3a5d","abstract_canon_sha256":"5cc7af4e8985b6800333aeda29b35c43780f3f5242722928c6fd6697eb2e2d0d"},"schema_version":"1.0"},"canonical_sha256":"1ee194f84e36840ac06851bcc841232e47f3b348b796c20dd1007918a3b55b38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:49.800706Z","signature_b64":"vgPjpOA4hAkfdoYKX6kp42CfYHEkjOzjQZrHWXEmlfV7rfQhBizl6ijVSgnxWtVCzCMZidzKSwIXYbQ/4P67AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ee194f84e36840ac06851bcc841232e47f3b348b796c20dd1007918a3b55b38","last_reissued_at":"2026-05-18T03:59:49.800276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:49.800276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0812.4269","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w3PSmSd5WHgNM92fPrQtWUy11xXdW4DkyVQNGYRzgctuSQvYvegx0b+ARu7ZVXVnrOjKn3wVAn2W3mrm4rgOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:14:34.528860Z"},"content_sha256":"07199abbdcad4d4eff9161b8fd67d35412adef3caede1b2e0a7229571f434566","schema_version":"1.0","event_id":"sha256:07199abbdcad4d4eff9161b8fd67d35412adef3caede1b2e0a7229571f434566"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:D3QZJ6COG2CAVQDIKG6MQQJDFZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Note on radial Dunkl processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Nizar Demni","submitted_at":"2008-12-22T19:09:29Z","abstract_excerpt":"We give shorter proofs of the following known results: the radial Dunkl process associated with a reduced system and a strictly positive multiplicity function is the unique strong solution for all times of a stochastic differential equation with a singular drift, the first hitting time of the Weyl chamber by a radial Dunkl process is finite almost surely for small values of the multiplicity function. Compared to the original proofs, ours give more information on the behavior of the process. More precisely, the first proof allows to give a positive answer to a conjecture announced by Gallardo a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4269","kind":"arxiv","version":3},"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":"2026-05-18T03:59:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5fE2hnXkm69gYL82MtsAityxqNdJJ1x2BekaW7bayxEZVJwgppWLSsqQUAKcsjce60l0zvZ3lRjQW1MGQJEdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:14:34.529542Z"},"content_sha256":"22db299f8b72fb4f83b5bced9505b63434c3bae22b22f4c820d7279f1cbbcd0e","schema_version":"1.0","event_id":"sha256:22db299f8b72fb4f83b5bced9505b63434c3bae22b22f4c820d7279f1cbbcd0e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D3QZJ6COG2CAVQDIKG6MQQJDFZ/bundle.json","state_url":"https://pith.science/pith/D3QZJ6COG2CAVQDIKG6MQQJDFZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D3QZJ6COG2CAVQDIKG6MQQJDFZ/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":"2026-06-06T21:14:34Z","links":{"resolver":"https://pith.science/pith/D3QZJ6COG2CAVQDIKG6MQQJDFZ","bundle":"https://pith.science/pith/D3QZJ6COG2CAVQDIKG6MQQJDFZ/bundle.json","state":"https://pith.science/pith/D3QZJ6COG2CAVQDIKG6MQQJDFZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D3QZJ6COG2CAVQDIKG6MQQJDFZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:D3QZJ6COG2CAVQDIKG6MQQJDFZ","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":"5cc7af4e8985b6800333aeda29b35c43780f3f5242722928c6fd6697eb2e2d0d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-22T19:09:29Z","title_canon_sha256":"a62f9b8dc2b20eff0fbe23bdc1484568161eec66894fc112e9b480dee06e3a5d"},"schema_version":"1.0","source":{"id":"0812.4269","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.4269","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"arxiv_version","alias_value":"0812.4269v3","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.4269","created_at":"2026-05-18T03:59:49Z"},{"alias_kind":"pith_short_12","alias_value":"D3QZJ6COG2CA","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"D3QZJ6COG2CAVQDI","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"D3QZJ6CO","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:22db299f8b72fb4f83b5bced9505b63434c3bae22b22f4c820d7279f1cbbcd0e","target":"graph","created_at":"2026-05-18T03:59:49Z","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 give shorter proofs of the following known results: the radial Dunkl process associated with a reduced system and a strictly positive multiplicity function is the unique strong solution for all times of a stochastic differential equation with a singular drift, the first hitting time of the Weyl chamber by a radial Dunkl process is finite almost surely for small values of the multiplicity function. Compared to the original proofs, ours give more information on the behavior of the process. More precisely, the first proof allows to give a positive answer to a conjecture announced by Gallardo a","authors_text":"Nizar Demni","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-22T19:09:29Z","title":"Note on radial Dunkl processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.4269","kind":"arxiv","version":3},"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":"sha256:07199abbdcad4d4eff9161b8fd67d35412adef3caede1b2e0a7229571f434566","target":"record","created_at":"2026-05-18T03:59:49Z","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":"5cc7af4e8985b6800333aeda29b35c43780f3f5242722928c6fd6697eb2e2d0d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-22T19:09:29Z","title_canon_sha256":"a62f9b8dc2b20eff0fbe23bdc1484568161eec66894fc112e9b480dee06e3a5d"},"schema_version":"1.0","source":{"id":"0812.4269","kind":"arxiv","version":3}},"canonical_sha256":"1ee194f84e36840ac06851bcc841232e47f3b348b796c20dd1007918a3b55b38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ee194f84e36840ac06851bcc841232e47f3b348b796c20dd1007918a3b55b38","first_computed_at":"2026-05-18T03:59:49.800276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:49.800276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vgPjpOA4hAkfdoYKX6kp42CfYHEkjOzjQZrHWXEmlfV7rfQhBizl6ijVSgnxWtVCzCMZidzKSwIXYbQ/4P67AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:49.800706Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.4269","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07199abbdcad4d4eff9161b8fd67d35412adef3caede1b2e0a7229571f434566","sha256:22db299f8b72fb4f83b5bced9505b63434c3bae22b22f4c820d7279f1cbbcd0e"],"state_sha256":"60035cfe91fa796e405c6855548d01caf8cf44192b69f82c9e30a3d8d7220b73"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1f3sLIGrScrJNii3Bcd6i1TmRbEtIaaHyiTxyahyDHA7VDFi+IFcnuDvv15Uywu1ZkccoVdad4Vus2OCMAY4CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:14:34.532092Z","bundle_sha256":"c85b99176d50e32f123b3e75a4fe6e2b2d4180544d5bd2564f5e2efca3e88b2c"}}