{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HDPDTNTTEOT7BJYZI55HUWG37O","short_pith_number":"pith:HDPDTNTT","canonical_record":{"source":{"id":"2606.08683","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-07T15:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"5502923ff7a149b927de0a819ec51b40e93bda3a99628b894201d95843c0cd89","abstract_canon_sha256":"c3175c234df58c843b5e627d954d8fc82349b58650ca24c1559278c2a601beae"},"schema_version":"1.0"},"canonical_sha256":"38de39b67323a7f0a719477a7a58dbfb859f8ccb71dee0f5012b27b0a706ff5e","source":{"kind":"arxiv","id":"2606.08683","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08683","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08683v1","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08683","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"HDPDTNTTEOT7","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"pith_short_16","alias_value":"HDPDTNTTEOT7BJYZ","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"pith_short_8","alias_value":"HDPDTNTT","created_at":"2026-06-09T01:05:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HDPDTNTTEOT7BJYZI55HUWG37O","target":"record","payload":{"canonical_record":{"source":{"id":"2606.08683","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-07T15:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"5502923ff7a149b927de0a819ec51b40e93bda3a99628b894201d95843c0cd89","abstract_canon_sha256":"c3175c234df58c843b5e627d954d8fc82349b58650ca24c1559278c2a601beae"},"schema_version":"1.0"},"canonical_sha256":"38de39b67323a7f0a719477a7a58dbfb859f8ccb71dee0f5012b27b0a706ff5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:47.362407Z","signature_b64":"nS+XHrwm/vh3r1hL+P68vSewTOriA0/xzMqtvnjUXEm4bzcVDVu94mZyuWzRot0ZY8p1e/byzxN5OJIVCfM8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"38de39b67323a7f0a719477a7a58dbfb859f8ccb71dee0f5012b27b0a706ff5e","last_reissued_at":"2026-06-09T01:05:47.361937Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:47.361937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.08683","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-09T01:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DneOn/Mpud1jBSlHPduR46re4frAH1jhmYqOUgdk5FbUw4HXhWAMjvH+dJKF5HBLWZausB2kGBeLtLqkyQMADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:30:12.162659Z"},"content_sha256":"e678c97c1c4943255bfcc724db3ed1ce9e3c2cf4a5b1d30ce65fc6f57d3ab1b1","schema_version":"1.0","event_id":"sha256:e678c97c1c4943255bfcc724db3ed1ce9e3c2cf4a5b1d30ce65fc6f57d3ab1b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HDPDTNTTEOT7BJYZI55HUWG37O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chengbo Xiao, Guozheng Cheng, Hongdou Qu, Menghan Li, Xiang Fang, Yin Cai","submitted_at":"2026-06-07T15:35:06Z","abstract_excerpt":"We determine the Fourier dimension of the canonical dyadic Mandelbrot cascade on the unit interval under the minimal Kahane--Peyriere condition $W \\ge 0$, $\\mathbb{E}W=1$, $\\mathbb{E}[W\\log_2^+ W]<\\infty$, and $\\mathbb{E}[W\\log_2 W]<1$. Almost surely on non-extinction, $\\dim_F(\\mu)=\\dim_E(\\mu)=\\dim_2(\\mu)=\\sup_{1<q<2}\\max\\{0,2-(2/q)(1+\\log_2\\mathbb{E}[W^q])\\}$, with the convention that the corresponding term is zero when $\\mathbb{E}[W^q]=\\infty$. The proof is carried out in a vector-valued cascade model allowing arbitrary dependence between sibling weights; the classical independent cascade is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08683","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.08683/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-09T01:05:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lTDkBK5S8EAy8nF/IjweEc1bJkv7Ke6NFKD3evC+Dzott8YodQcQfVC4GKuDYsOsJJff4GHWZ5T0l1rF0atTAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T13:30:12.163029Z"},"content_sha256":"6aefc0ccdfe096721c844adfdb730afce788e2acf41ba345b289378148c764e8","schema_version":"1.0","event_id":"sha256:6aefc0ccdfe096721c844adfdb730afce788e2acf41ba345b289378148c764e8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HDPDTNTTEOT7BJYZI55HUWG37O/bundle.json","state_url":"https://pith.science/pith/HDPDTNTTEOT7BJYZI55HUWG37O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HDPDTNTTEOT7BJYZI55HUWG37O/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":"2026-06-27T13:30:12Z","links":{"resolver":"https://pith.science/pith/HDPDTNTTEOT7BJYZI55HUWG37O","bundle":"https://pith.science/pith/HDPDTNTTEOT7BJYZI55HUWG37O/bundle.json","state":"https://pith.science/pith/HDPDTNTTEOT7BJYZI55HUWG37O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HDPDTNTTEOT7BJYZI55HUWG37O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HDPDTNTTEOT7BJYZI55HUWG37O","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":"c3175c234df58c843b5e627d954d8fc82349b58650ca24c1559278c2a601beae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-07T15:35:06Z","title_canon_sha256":"5502923ff7a149b927de0a819ec51b40e93bda3a99628b894201d95843c0cd89"},"schema_version":"1.0","source":{"id":"2606.08683","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.08683","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.08683v1","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.08683","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"pith_short_12","alias_value":"HDPDTNTTEOT7","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"pith_short_16","alias_value":"HDPDTNTTEOT7BJYZ","created_at":"2026-06-09T01:05:47Z"},{"alias_kind":"pith_short_8","alias_value":"HDPDTNTT","created_at":"2026-06-09T01:05:47Z"}],"graph_snapshots":[{"event_id":"sha256:6aefc0ccdfe096721c844adfdb730afce788e2acf41ba345b289378148c764e8","target":"graph","created_at":"2026-06-09T01:05:47Z","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/2606.08683/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We determine the Fourier dimension of the canonical dyadic Mandelbrot cascade on the unit interval under the minimal Kahane--Peyriere condition $W \\ge 0$, $\\mathbb{E}W=1$, $\\mathbb{E}[W\\log_2^+ W]<\\infty$, and $\\mathbb{E}[W\\log_2 W]<1$. Almost surely on non-extinction, $\\dim_F(\\mu)=\\dim_E(\\mu)=\\dim_2(\\mu)=\\sup_{1<q<2}\\max\\{0,2-(2/q)(1+\\log_2\\mathbb{E}[W^q])\\}$, with the convention that the corresponding term is zero when $\\mathbb{E}[W^q]=\\infty$. The proof is carried out in a vector-valued cascade model allowing arbitrary dependence between sibling weights; the classical independent cascade is","authors_text":"Chengbo Xiao, Guozheng Cheng, Hongdou Qu, Menghan Li, Xiang Fang, Yin Cai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-07T15:35:06Z","title":"Exact Fourier dimensions of dyadic Mandelbrot cascades under minimal integrability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.08683","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:e678c97c1c4943255bfcc724db3ed1ce9e3c2cf4a5b1d30ce65fc6f57d3ab1b1","target":"record","created_at":"2026-06-09T01:05:47Z","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":"c3175c234df58c843b5e627d954d8fc82349b58650ca24c1559278c2a601beae","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-07T15:35:06Z","title_canon_sha256":"5502923ff7a149b927de0a819ec51b40e93bda3a99628b894201d95843c0cd89"},"schema_version":"1.0","source":{"id":"2606.08683","kind":"arxiv","version":1}},"canonical_sha256":"38de39b67323a7f0a719477a7a58dbfb859f8ccb71dee0f5012b27b0a706ff5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"38de39b67323a7f0a719477a7a58dbfb859f8ccb71dee0f5012b27b0a706ff5e","first_computed_at":"2026-06-09T01:05:47.361937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-09T01:05:47.361937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nS+XHrwm/vh3r1hL+P68vSewTOriA0/xzMqtvnjUXEm4bzcVDVu94mZyuWzRot0ZY8p1e/byzxN5OJIVCfM8Aw==","signature_status":"signed_v1","signed_at":"2026-06-09T01:05:47.362407Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.08683","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e678c97c1c4943255bfcc724db3ed1ce9e3c2cf4a5b1d30ce65fc6f57d3ab1b1","sha256:6aefc0ccdfe096721c844adfdb730afce788e2acf41ba345b289378148c764e8"],"state_sha256":"5bf3c5a3ae114ff2164d5fc170f0b444c1194ea658a320f985891aefa22e6c9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6sgGt9naq4eHGuTaGFEpjKYtEom6/7os5dsUbfTcurAZ1/leBhdNKWqVw71xWjHtv6IuRogBzVbCE5nwIoN+CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T13:30:12.165025Z","bundle_sha256":"a7c8a0d2a3e5671d87de1ed8f8a4c924de11ddeea7521fa38756218b10416dce"}}