{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ST5YH6SWTZ63RTRPESLXK7ISU3","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":"a7be0dc52c7b98e210d8101dd8ba2e1923151b31fe5771b1963eea2b0eca0cc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-01-25T08:07:32Z","title_canon_sha256":"a954871402d67657907b060947edb636ad1758df63c5440663c7f866eec8ea1c"},"schema_version":"1.0","source":{"id":"1001.4337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.4337","created_at":"2026-05-18T02:09:30Z"},{"alias_kind":"arxiv_version","alias_value":"1001.4337v1","created_at":"2026-05-18T02:09:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.4337","created_at":"2026-05-18T02:09:30Z"},{"alias_kind":"pith_short_12","alias_value":"ST5YH6SWTZ63","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"ST5YH6SWTZ63RTRP","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"ST5YH6SW","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:b0afa228df6fca5d3ba944ae7ab0d34d3276a1a5c631e432975226c729df2016","target":"graph","created_at":"2026-05-18T02:09:30Z","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 consider multifractal random wavelet series built from Gibbs measures, and study the singularity spectra associated with the graph and range of these functions restricted to their iso-H\\\"older sets. To obtain these singularity spectra, we use a family of Gibbs measures defined on a sequence of topologically transitive subshift of finite type whose Hausdorff distance to the set of zeros of the mother wavelet tends to 0.","authors_text":"Xiong Jin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-01-25T08:07:32Z","title":"The Graph and Range Singularity Spectra of Random Wavelet Series built from Gibbs measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.4337","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:f40e959c7803473a18bc07b407d6639cb60ef2361cd263e77f79355ed8fa23a9","target":"record","created_at":"2026-05-18T02:09:30Z","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":"a7be0dc52c7b98e210d8101dd8ba2e1923151b31fe5771b1963eea2b0eca0cc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-01-25T08:07:32Z","title_canon_sha256":"a954871402d67657907b060947edb636ad1758df63c5440663c7f866eec8ea1c"},"schema_version":"1.0","source":{"id":"1001.4337","kind":"arxiv","version":1}},"canonical_sha256":"94fb83fa569e7db8ce2f2497757d12a6c57b191469827923b99bf483bb09f2ba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94fb83fa569e7db8ce2f2497757d12a6c57b191469827923b99bf483bb09f2ba","first_computed_at":"2026-05-18T02:09:30.492303Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:09:30.492303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1u/gnrY/JvMfqwiSlVjRSbNnjGkg8xG1L1H2ABtuc/+ZaCfsc4cTYD7KC3wxKjvkoE4123yiCvNpczHahU7bDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:09:30.492899Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.4337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f40e959c7803473a18bc07b407d6639cb60ef2361cd263e77f79355ed8fa23a9","sha256:b0afa228df6fca5d3ba944ae7ab0d34d3276a1a5c631e432975226c729df2016"],"state_sha256":"398365ee8256c6dcfc77a48b59b0de8825093c325b60e0f58750ed8c8077f03f"}