{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:UI6USKTPAYP7Q2KEJANUSLNE6K","short_pith_number":"pith:UI6USKTP","canonical_record":{"source":{"id":"1012.0936","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-04T17:56:14Z","cross_cats_sorted":[],"title_canon_sha256":"255ebedb75191a186220abc0e3892b61af5d20c0217be5eb774989524c82f288","abstract_canon_sha256":"ec251e94ff33ca428be5d580ebdf5c50e53eab38fa924dcc974c7dc9950787eb"},"schema_version":"1.0"},"canonical_sha256":"a23d492a6f061ff86944481b492da4f2a81edd02757af1ffd9cf700596dd7388","source":{"kind":"arxiv","id":"1012.0936","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0936","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0936v3","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0936","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"UI6USKTPAYP7","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UI6USKTPAYP7Q2KE","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UI6USKTP","created_at":"2026-05-18T12:26:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:UI6USKTPAYP7Q2KEJANUSLNE6K","target":"record","payload":{"canonical_record":{"source":{"id":"1012.0936","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-04T17:56:14Z","cross_cats_sorted":[],"title_canon_sha256":"255ebedb75191a186220abc0e3892b61af5d20c0217be5eb774989524c82f288","abstract_canon_sha256":"ec251e94ff33ca428be5d580ebdf5c50e53eab38fa924dcc974c7dc9950787eb"},"schema_version":"1.0"},"canonical_sha256":"a23d492a6f061ff86944481b492da4f2a81edd02757af1ffd9cf700596dd7388","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:04.086560Z","signature_b64":"oRtif1D7MLO/FT193TUmbB75hhfb8xC0ulFNvFG3kK/k0/L22p2ozwnw2rlBFlF/7eEVNRkR8fC6DwTA+6i0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a23d492a6f061ff86944481b492da4f2a81edd02757af1ffd9cf700596dd7388","last_reissued_at":"2026-05-18T04:05:04.085978Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:04.085978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1012.0936","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":"2026-05-18T04:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L0NJJukOV85qcs+2d1gBFOS/a5VwIaG8wIPhMpkxEnbsv8SppxtMbLMBGTxKG7/b8Ir9dSjUpTMutMGikvV7CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:29:31.835992Z"},"content_sha256":"00a2356ff318f1f05764b177ad94740889c0e91d800bdb809cdc8a10e16906bd","schema_version":"1.0","event_id":"sha256:00a2356ff318f1f05764b177ad94740889c0e91d800bdb809cdc8a10e16906bd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:UI6USKTPAYP7Q2KEJANUSLNE6K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the infimum attained by a reflected L\\'evy process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kamil Marcin Kosinski, Krzysztof Debicki, Michel Mandjes","submitted_at":"2010-12-04T17:56:14Z","abstract_excerpt":"This paper considers a L\\'evy-driven queue (i.e., a L\\'evy process reflected at 0), and focuses on the distribution of $M(t)$, that is, the minimal value attained in an interval of length $t$ (where it is assumed that the queue is in stationarity at the beginning of the interval). The first contribution is an explicit characterization of this distribution, in terms of Laplace transforms, for spectrally one-sided L\\'evy processes (i.e., either only positive jumps or only negative jumps). The second contribution concerns the asymptotics of $\\prob{M(T_u)> u}$ (for different classes of functions $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0936","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":"2026-05-18T04:05:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ngTy+1SIt+POjB3rXNShUg6jX7FCyzQahOOqf40y6Qg5FhOO8bdtD5KkqYO+KWBwWjlJQwKsPE1ALw9k6fgeDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:29:31.836743Z"},"content_sha256":"cd82183134f8b3dcaa8b679c28b11c2671cdf5e9519ec3887997b4546244ad37","schema_version":"1.0","event_id":"sha256:cd82183134f8b3dcaa8b679c28b11c2671cdf5e9519ec3887997b4546244ad37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UI6USKTPAYP7Q2KEJANUSLNE6K/bundle.json","state_url":"https://pith.science/pith/UI6USKTPAYP7Q2KEJANUSLNE6K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UI6USKTPAYP7Q2KEJANUSLNE6K/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":"2026-06-10T22:29:31Z","links":{"resolver":"https://pith.science/pith/UI6USKTPAYP7Q2KEJANUSLNE6K","bundle":"https://pith.science/pith/UI6USKTPAYP7Q2KEJANUSLNE6K/bundle.json","state":"https://pith.science/pith/UI6USKTPAYP7Q2KEJANUSLNE6K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UI6USKTPAYP7Q2KEJANUSLNE6K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UI6USKTPAYP7Q2KEJANUSLNE6K","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":"ec251e94ff33ca428be5d580ebdf5c50e53eab38fa924dcc974c7dc9950787eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-04T17:56:14Z","title_canon_sha256":"255ebedb75191a186220abc0e3892b61af5d20c0217be5eb774989524c82f288"},"schema_version":"1.0","source":{"id":"1012.0936","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.0936","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"arxiv_version","alias_value":"1012.0936v3","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.0936","created_at":"2026-05-18T04:05:04Z"},{"alias_kind":"pith_short_12","alias_value":"UI6USKTPAYP7","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UI6USKTPAYP7Q2KE","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UI6USKTP","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:cd82183134f8b3dcaa8b679c28b11c2671cdf5e9519ec3887997b4546244ad37","target":"graph","created_at":"2026-05-18T04:05:04Z","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":"This paper considers a L\\'evy-driven queue (i.e., a L\\'evy process reflected at 0), and focuses on the distribution of $M(t)$, that is, the minimal value attained in an interval of length $t$ (where it is assumed that the queue is in stationarity at the beginning of the interval). The first contribution is an explicit characterization of this distribution, in terms of Laplace transforms, for spectrally one-sided L\\'evy processes (i.e., either only positive jumps or only negative jumps). The second contribution concerns the asymptotics of $\\prob{M(T_u)> u}$ (for different classes of functions $","authors_text":"Kamil Marcin Kosinski, Krzysztof Debicki, Michel Mandjes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-04T17:56:14Z","title":"On the infimum attained by a reflected L\\'evy process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.0936","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":"sha256:00a2356ff318f1f05764b177ad94740889c0e91d800bdb809cdc8a10e16906bd","target":"record","created_at":"2026-05-18T04:05:04Z","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":"ec251e94ff33ca428be5d580ebdf5c50e53eab38fa924dcc974c7dc9950787eb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-12-04T17:56:14Z","title_canon_sha256":"255ebedb75191a186220abc0e3892b61af5d20c0217be5eb774989524c82f288"},"schema_version":"1.0","source":{"id":"1012.0936","kind":"arxiv","version":3}},"canonical_sha256":"a23d492a6f061ff86944481b492da4f2a81edd02757af1ffd9cf700596dd7388","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a23d492a6f061ff86944481b492da4f2a81edd02757af1ffd9cf700596dd7388","first_computed_at":"2026-05-18T04:05:04.085978Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:04.085978Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oRtif1D7MLO/FT193TUmbB75hhfb8xC0ulFNvFG3kK/k0/L22p2ozwnw2rlBFlF/7eEVNRkR8fC6DwTA+6i0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:04.086560Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.0936","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:00a2356ff318f1f05764b177ad94740889c0e91d800bdb809cdc8a10e16906bd","sha256:cd82183134f8b3dcaa8b679c28b11c2671cdf5e9519ec3887997b4546244ad37"],"state_sha256":"5339c3a2c34908e3fcd0e23ca1675c9cb1cb761b6c5111444c04cce51f359e90"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n1hKRevutPu0ZKBKLh52DCE4twwRM9ZhWxTSRW7HMbMQbYxg8cFAdITR8Ln341qqXx2uPumIYs0xWeV+zhqvDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:29:31.840485Z","bundle_sha256":"7d9364d62e91da8cc4563c5d90ca222dff795bceb791bc72bd5fb5363eb17ac9"}}