{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:YEUZ6ADOXKX45KCOGPWDBNU5DH","short_pith_number":"pith:YEUZ6ADO","canonical_record":{"source":{"id":"0909.2929","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-09-16T06:26:07Z","cross_cats_sorted":[],"title_canon_sha256":"d8c991df01448c29f1cb609a5ba54ed262a410adc29ec29aff213965d1b47842","abstract_canon_sha256":"a2d92025d372c5d8d4767d363cff76d878a152f72ec8a16a887cf073d894a8cc"},"schema_version":"1.0"},"canonical_sha256":"c1299f006ebaafcea84e33ec30b69d19df688a47a725cdc8180bd54190edc719","source":{"kind":"arxiv","id":"0909.2929","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.2929","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"0909.2929v3","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2929","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"YEUZ6ADOXKX4","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YEUZ6ADOXKX45KCO","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YEUZ6ADO","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:YEUZ6ADOXKX45KCOGPWDBNU5DH","target":"record","payload":{"canonical_record":{"source":{"id":"0909.2929","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-09-16T06:26:07Z","cross_cats_sorted":[],"title_canon_sha256":"d8c991df01448c29f1cb609a5ba54ed262a410adc29ec29aff213965d1b47842","abstract_canon_sha256":"a2d92025d372c5d8d4767d363cff76d878a152f72ec8a16a887cf073d894a8cc"},"schema_version":"1.0"},"canonical_sha256":"c1299f006ebaafcea84e33ec30b69d19df688a47a725cdc8180bd54190edc719","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:42:35.337033Z","signature_b64":"fciZk3iCqijNRlGrHz4MOb6PECNMy1fghsSGsRSWpoblVdUQvBffcz+XTaOkGR02xKpqBNRRQa4BYZqRxBU+Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c1299f006ebaafcea84e33ec30b69d19df688a47a725cdc8180bd54190edc719","last_reissued_at":"2026-05-18T04:42:35.336388Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:42:35.336388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0909.2929","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":"2026-05-18T04:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x5QUbWndfIdVeSy37mh3eG4SmvWUqk/sxyIPWbAxnctpuo8Q8prfL4YTaL3eY1O+QzlZfLenyxA+n8DyDQ0jAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:56:34.691559Z"},"content_sha256":"c9068417bfeac641455f8793c984da22169e6b9e529b07a54f8733b6e7a4dfc1","schema_version":"1.0","event_id":"sha256:c9068417bfeac641455f8793c984da22169e6b9e529b07a54f8733b6e7a4dfc1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:YEUZ6ADOXKX45KCOGPWDBNU5DH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local time of a diffusion in a stable L\\'evy environment","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Guillaume Voisin (MAPMO), Roland Diel (MAPMO)","submitted_at":"2009-09-16T06:26:07Z","abstract_excerpt":"We consider a one-dimensional diffusion in a stable L\\'evy environment. We show that the normalized local time process refocused at the bottom of the standard valley with height $\\log t$, $(L_X(t,\\mathfrak m_{\\log t}+x)/t,x\\in \\R)$, converges in law to a functional of two independent L\\'evy processes conditioned to stay positive. To prove this result, we show that the law of the standard valley is close to a two-sided L\\'evy process conditioned to stay positive. We also obtain the limit law of the supremum of the normalized local time. This result has been obtained by Andreoletti and Diel in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2929","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":"2026-05-18T04:42:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/b6NwMaHM68PaudAFl7bcivIAEgx1cLfM4gpEtk4UlymZu2bLm005K9Ci7FbV02Dd0s4tR3gANJgOf4rkiHCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T09:56:34.691928Z"},"content_sha256":"f40df7ee7095e4b62e9c4a77bab7009bab443667a9202ec0fc4c5629d939b12e","schema_version":"1.0","event_id":"sha256:f40df7ee7095e4b62e9c4a77bab7009bab443667a9202ec0fc4c5629d939b12e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YEUZ6ADOXKX45KCOGPWDBNU5DH/bundle.json","state_url":"https://pith.science/pith/YEUZ6ADOXKX45KCOGPWDBNU5DH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YEUZ6ADOXKX45KCOGPWDBNU5DH/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":"2026-06-08T09:56:34Z","links":{"resolver":"https://pith.science/pith/YEUZ6ADOXKX45KCOGPWDBNU5DH","bundle":"https://pith.science/pith/YEUZ6ADOXKX45KCOGPWDBNU5DH/bundle.json","state":"https://pith.science/pith/YEUZ6ADOXKX45KCOGPWDBNU5DH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YEUZ6ADOXKX45KCOGPWDBNU5DH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:YEUZ6ADOXKX45KCOGPWDBNU5DH","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":"a2d92025d372c5d8d4767d363cff76d878a152f72ec8a16a887cf073d894a8cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-09-16T06:26:07Z","title_canon_sha256":"d8c991df01448c29f1cb609a5ba54ed262a410adc29ec29aff213965d1b47842"},"schema_version":"1.0","source":{"id":"0909.2929","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0909.2929","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"arxiv_version","alias_value":"0909.2929v3","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0909.2929","created_at":"2026-05-18T04:42:35Z"},{"alias_kind":"pith_short_12","alias_value":"YEUZ6ADOXKX4","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"YEUZ6ADOXKX45KCO","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"YEUZ6ADO","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:f40df7ee7095e4b62e9c4a77bab7009bab443667a9202ec0fc4c5629d939b12e","target":"graph","created_at":"2026-05-18T04:42:35Z","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 a one-dimensional diffusion in a stable L\\'evy environment. We show that the normalized local time process refocused at the bottom of the standard valley with height $\\log t$, $(L_X(t,\\mathfrak m_{\\log t}+x)/t,x\\in \\R)$, converges in law to a functional of two independent L\\'evy processes conditioned to stay positive. To prove this result, we show that the law of the standard valley is close to a two-sided L\\'evy process conditioned to stay positive. We also obtain the limit law of the supremum of the normalized local time. This result has been obtained by Andreoletti and Diel in t","authors_text":"Guillaume Voisin (MAPMO), Roland Diel (MAPMO)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-09-16T06:26:07Z","title":"Local time of a diffusion in a stable L\\'evy environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.2929","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:c9068417bfeac641455f8793c984da22169e6b9e529b07a54f8733b6e7a4dfc1","target":"record","created_at":"2026-05-18T04:42:35Z","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":"a2d92025d372c5d8d4767d363cff76d878a152f72ec8a16a887cf073d894a8cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-09-16T06:26:07Z","title_canon_sha256":"d8c991df01448c29f1cb609a5ba54ed262a410adc29ec29aff213965d1b47842"},"schema_version":"1.0","source":{"id":"0909.2929","kind":"arxiv","version":3}},"canonical_sha256":"c1299f006ebaafcea84e33ec30b69d19df688a47a725cdc8180bd54190edc719","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1299f006ebaafcea84e33ec30b69d19df688a47a725cdc8180bd54190edc719","first_computed_at":"2026-05-18T04:42:35.336388Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:42:35.336388Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fciZk3iCqijNRlGrHz4MOb6PECNMy1fghsSGsRSWpoblVdUQvBffcz+XTaOkGR02xKpqBNRRQa4BYZqRxBU+Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:42:35.337033Z","signed_message":"canonical_sha256_bytes"},"source_id":"0909.2929","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9068417bfeac641455f8793c984da22169e6b9e529b07a54f8733b6e7a4dfc1","sha256:f40df7ee7095e4b62e9c4a77bab7009bab443667a9202ec0fc4c5629d939b12e"],"state_sha256":"b86a648d4e68022dfe6179a20ace6c41f2bb1ad7fa5a0c49ee49c472264b067b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H4COaoPNyqBgULEE2gxBzEJdCbYOZ5oHnqKWmDTtI+DNoUhwcrrUbwSjs5wfEeao8OB5zl/B9uYK0HDgPN5UDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T09:56:34.694154Z","bundle_sha256":"0e3889bd75b49743f0ae3e14f8ddef9f3a0f50d2b2423531f5b0d06b1c9d71e7"}}