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Diplomarbeit, FSU Jena","work_id":"aca6829a-4408-47c3-9a00-6af13985ec56","year":1999}],"snapshot_sha256":"768f7a7c472f788fe20f2d03c26a3553a4f54d84115cdb6c0f41ff8322db5b26"},"source":{"id":"2604.01701","kind":"arxiv","version":3},"verdict":{"created_at":"2026-05-13T21:21:42.053271Z","id":"8037f585-3f0e-4d05-8358-85c61fa165e9","model_set":{"reader":"grok-4.3"},"one_line_summary":"Chung-type laws of the iterated logarithm are established for m-fold weighted integrals of fractional Brownian motion, yielding explicit liminf expressions and resolving an exact constant from prior work.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"m-fold weighted integrals of fractional Brownian motion satisfy exact Chung-type laws of the iterated logarithm with explicit constants almost surely.","strongest_claim":"liminf_{T→∞} (log log T)^{H+m} / T^{H+m-α} sup_{0≤t≤T} |J_{m,α}(B_H)(t) / t^{α - α_1 - ⋯ - α_m}| = a_H (κ_{H+m} / (1 - α/(H+m)))^{H+m} a.s. for all α < H+m, with a similar explicit liminf for the (m-1)-fold case.","weakest_assumption":"The parameter restrictions α_1 + ⋯ + α_i < H + i for each i, together with the existence and precise form of small-ball probabilities for the m-fold integrated process; if these tail estimates fail or require additional regularity not stated, the conversion from small-ball probabilities to the liminf constant breaks."}},"verdict_id":"8037f585-3f0e-4d05-8358-85c61fa165e9"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1e49a2d3c0cf67a265853a0aa1aead6deced772b9034e6851f769a41637649d2","target":"record","created_at":"2026-05-20T00:00:37Z","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":"d62b1a1db66a6cc5b57f051547e00b8e3a06bbdbd3a4e9a035f95db21ca79bb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-04-02T06:59:07Z","title_canon_sha256":"d09d73834399056d9a1c41109fee806385cdff18487f1afd41165f7f9351b252"},"schema_version":"1.0","source":{"id":"2604.01701","kind":"arxiv","version":3}},"canonical_sha256":"bd6e9f582361bae9d25fb85dc7665ddd7edc44b440e8a081ea7767cd49aaed88","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd6e9f582361bae9d25fb85dc7665ddd7edc44b440e8a081ea7767cd49aaed88","first_computed_at":"2026-05-20T00:00:37.461026Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:37.461026Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bLXWSjOPqYAgpb8DDMMYT3I353REKVyW8bKaQzXFziDr2zT1c6pn5K+f51qWPp8bFotTbojVRVBvfjvAND7tAQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:37.461561Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.01701","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e49a2d3c0cf67a265853a0aa1aead6deced772b9034e6851f769a41637649d2","sha256:2610f6c2ff5df741a8f7242c986ed0b5a7191c048ed9caadb0b8c2f351841ae4"],"state_sha256":"7d4768b8123daa99dcd3e4a5e63bb8ee4ef2f6db5a1d1529042e9d149a09fb86"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G+zSL0GZ9g+XLuIVdmHkUlWq/Us6N8R0ll+lAVniQE1rnhYHN8G7y7XqsqP+oesNdDHbH+Ug06EZy68040yrBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T08:33:35.068908Z","bundle_sha256":"3e0867d5309f0a79b4212d65686ff1392e12105a581417884dfc192e8fd69b37"}}