{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:754N5EPBIEI336B6KRGR3SH6MM","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":"b1e7147e0dc6dd4661480d61a5163d1431bde32c91ef427ebf9d77dfddfa259a","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2007-07-30T08:36:10Z","title_canon_sha256":"89ddf11fdf658d7caef9dfa5599c977e58c7fc78efc54f2295f1a804a53699d7"},"schema_version":"1.0","source":{"id":"0707.4355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0707.4355","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"arxiv_version","alias_value":"0707.4355v1","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0707.4355","created_at":"2026-05-18T04:09:15Z"},{"alias_kind":"pith_short_12","alias_value":"754N5EPBIEI3","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"754N5EPBIEI336B6","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"754N5EPB","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:ad2569c0d851f6c262d7d422b079b806513daf969b6cec2786a93195368ad5f4","target":"graph","created_at":"2026-05-18T04:09:15Z","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 study the upper tail behaviors of the local times of the additive L\\'{e}vy processes and additive random walks. The limit forms we establish are the moderate deviations and the laws of the iterated logarithm for the L_2-norms of the local times and for the local times at a fixed site.","authors_text":"Xia Chen","cross_cats":[],"headline":"","license":"","primary_cat":"math.PR","submitted_at":"2007-07-30T08:36:10Z","title":"Moderate deviations and laws of the iterated logarithm for the local times of additive L\\'{e}vy processes and additive random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.4355","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:ff1b9f0109577222d2beb4578cdea656f2fc799884f18bb239e1b70dfe3271a0","target":"record","created_at":"2026-05-18T04:09:15Z","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":"b1e7147e0dc6dd4661480d61a5163d1431bde32c91ef427ebf9d77dfddfa259a","cross_cats_sorted":[],"license":"","primary_cat":"math.PR","submitted_at":"2007-07-30T08:36:10Z","title_canon_sha256":"89ddf11fdf658d7caef9dfa5599c977e58c7fc78efc54f2295f1a804a53699d7"},"schema_version":"1.0","source":{"id":"0707.4355","kind":"arxiv","version":1}},"canonical_sha256":"ff78de91e14111bdf83e544d1dc8fe6323203cc62ecc2269167e168ec344061e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff78de91e14111bdf83e544d1dc8fe6323203cc62ecc2269167e168ec344061e","first_computed_at":"2026-05-18T04:09:15.341531Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:15.341531Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wOTQu3k4uZ/EFPamunlhGhY7T/PdTyL2ro738RZCCEXqNGnSL3ouf4FtXrGZyCRsDP/tVX45Nq3P1J+Mqoc0BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:15.341998Z","signed_message":"canonical_sha256_bytes"},"source_id":"0707.4355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff1b9f0109577222d2beb4578cdea656f2fc799884f18bb239e1b70dfe3271a0","sha256:ad2569c0d851f6c262d7d422b079b806513daf969b6cec2786a93195368ad5f4"],"state_sha256":"bdc0627c98f6b93232ec047678292af0b9bbe85d1fd0e078a778fb70b2a8ad8a"}