{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:BJMALOUL2Q5EWBKQXKZXHPLBND","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":"493a7f6a6eff6904a37aa844e8c663253c5b65f385b1a89c62ae859261896f1c","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2007-07-12T17:56:25Z","title_canon_sha256":"bc219e74f4f27db14bffe5148e69e130fe7fb2f9e8c3d56720d61094fdb6ae32"},"schema_version":"1.0","source":{"id":"0707.1845","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.1845","created_at":"2026-07-04T15:02:50Z"},{"alias_kind":"arxiv_version","alias_value":"0707.1845v1","created_at":"2026-07-04T15:02:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.1845","created_at":"2026-07-04T15:02:50Z"},{"alias_kind":"pith_short_12","alias_value":"BJMALOUL2Q5E","created_at":"2026-07-04T15:02:50Z"},{"alias_kind":"pith_short_16","alias_value":"BJMALOUL2Q5EWBKQ","created_at":"2026-07-04T15:02:50Z"},{"alias_kind":"pith_short_8","alias_value":"BJMALOUL","created_at":"2026-07-04T15:02:50Z"}],"graph_snapshots":[{"event_id":"sha256:e876f172dfec8476a84e4adef5d1e61112b93a6807af5e47948a6857adfdf76b","target":"graph","created_at":"2026-07-04T15:02:50Z","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/0707.1845/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove a theorem on additive Levy processes and give applications","authors_text":"Ming Yang","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2007-07-12T17:56:25Z","title":"On a theorem in multi-parameter potential theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.1845","kind":"arxiv","version":1},"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:fab3129bf548f6e657412ec583b22970187869a7a34fd12726e20a8063bb7300","target":"record","created_at":"2026-07-04T15:02:50Z","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":"493a7f6a6eff6904a37aa844e8c663253c5b65f385b1a89c62ae859261896f1c","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2007-07-12T17:56:25Z","title_canon_sha256":"bc219e74f4f27db14bffe5148e69e130fe7fb2f9e8c3d56720d61094fdb6ae32"},"schema_version":"1.0","source":{"id":"0707.1845","kind":"arxiv","version":1}},"canonical_sha256":"0a5805ba8bd43a4b0550bab373bd6168e624698bb8656f26b3079523b56f1426","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a5805ba8bd43a4b0550bab373bd6168e624698bb8656f26b3079523b56f1426","first_computed_at":"2026-07-04T15:02:50.704066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:02:50.704066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UJDwoFtwUMATIDxwgh2tFUw6rYE37mRUhyfdJ4JTmqbhhma4s4lMMB1kZTIGlWb77miNMylUTi++Wqe5q7h+AQ==","signature_status":"signed_v1","signed_at":"2026-07-04T15:02:50.704500Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.1845","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fab3129bf548f6e657412ec583b22970187869a7a34fd12726e20a8063bb7300","sha256:e876f172dfec8476a84e4adef5d1e61112b93a6807af5e47948a6857adfdf76b"],"state_sha256":"db651e00204258287ac1c3cb9d11563f224d8f1cff839d674d579f7465a288ea"}