{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KMTKULCUBVRQ72RZRT5BB32ZP3","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":"23a00b59a08ba4bf8ec93dccdd655e93130a517be7e83a00dcd596c64ad1c20c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-02T06:39:41Z","title_canon_sha256":"ee3814961fabedc6f1527bb607fe3859571362672c7045f61e48b0c3178278df"},"schema_version":"1.0","source":{"id":"1807.00486","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00486","created_at":"2026-07-05T03:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00486v3","created_at":"2026-07-05T03:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00486","created_at":"2026-07-05T03:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"KMTKULCUBVRQ","created_at":"2026-07-05T03:18:23Z"},{"alias_kind":"pith_short_16","alias_value":"KMTKULCUBVRQ72RZ","created_at":"2026-07-05T03:18:23Z"},{"alias_kind":"pith_short_8","alias_value":"KMTKULCU","created_at":"2026-07-05T03:18:23Z"}],"graph_snapshots":[{"event_id":"sha256:b4de118a969bc4d5fab88d771b79410a41af7a587acbe60a60703b52b6df3e21","target":"graph","created_at":"2026-07-05T03:18:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1807.00486/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A systematic exposition of scale functions is given for positive self-similar Markov processes (pssMp) with one-sided jumps. The scale functions express as convolution series of the usual scale functions associated with spectrally one-sided L\\'evy processes that underly the pssMp through the Lamperti transform. This theory is then brought to bear on solving the spatio-temporal: (i) two-sided exit problem; (ii) joint first passage problem upwards for the the pssMp and its multiplicative drawdown (resp. drawup) in the spectrally negative (resp. positive) case.","authors_text":"Matija Vidmar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-02T06:39:41Z","title":"Exit problems for positive self-similar Markov processes with one-sided jumps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00486","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":"sha256:74eecbe968a930c950d689da4cbafcf18328992bbdf8bee41046ab29b8813bb0","target":"record","created_at":"2026-07-05T03:18:23Z","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":"23a00b59a08ba4bf8ec93dccdd655e93130a517be7e83a00dcd596c64ad1c20c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-02T06:39:41Z","title_canon_sha256":"ee3814961fabedc6f1527bb607fe3859571362672c7045f61e48b0c3178278df"},"schema_version":"1.0","source":{"id":"1807.00486","kind":"arxiv","version":3}},"canonical_sha256":"5326aa2c540d630fea398cfa10ef597ed5d46fa24be606d10b87768ea9303a78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5326aa2c540d630fea398cfa10ef597ed5d46fa24be606d10b87768ea9303a78","first_computed_at":"2026-07-05T03:18:23.027428Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:18:23.027428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c5aazpkixZnizv5NR04NzQ2Blo8ofPb/sOQnmmA3VDfKWjZoDFRICj1A6XRaPQm0zmCQyxYdHoBPE+Ddv2M8CA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:18:23.027773Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.00486","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:74eecbe968a930c950d689da4cbafcf18328992bbdf8bee41046ab29b8813bb0","sha256:b4de118a969bc4d5fab88d771b79410a41af7a587acbe60a60703b52b6df3e21"],"state_sha256":"8c469a288310e652998b16f554ef5c748f8df6e6039c9a63a997bca2d9709940"}