{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:5T2N5IOUSUMX4CLLSRMJFNRHSF","short_pith_number":"pith:5T2N5IOU","canonical_record":{"source":{"id":"2301.04958","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2023-01-12T12:06:40Z","cross_cats_sorted":[],"title_canon_sha256":"c6acb7abcaf1a8e24b530415b56659fdc2d72e8fb6fe68cef8bc2e9e4e2db90c","abstract_canon_sha256":"223fd35fa3e565965b0886bfd682f98ffc4437a824cb5d4fdf874bfed0ca606b"},"schema_version":"1.0"},"canonical_sha256":"ecf4dea1d495197e096b945892b627917fbbfcdc7ade8b4803670f67cab205a0","source":{"kind":"arxiv","id":"2301.04958","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.04958","created_at":"2026-07-05T10:06:36Z"},{"alias_kind":"arxiv_version","alias_value":"2301.04958v2","created_at":"2026-07-05T10:06:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.04958","created_at":"2026-07-05T10:06:36Z"},{"alias_kind":"pith_short_12","alias_value":"5T2N5IOUSUMX","created_at":"2026-07-05T10:06:36Z"},{"alias_kind":"pith_short_16","alias_value":"5T2N5IOUSUMX4CLL","created_at":"2026-07-05T10:06:36Z"},{"alias_kind":"pith_short_8","alias_value":"5T2N5IOU","created_at":"2026-07-05T10:06:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:5T2N5IOUSUMX4CLLSRMJFNRHSF","target":"record","payload":{"canonical_record":{"source":{"id":"2301.04958","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2023-01-12T12:06:40Z","cross_cats_sorted":[],"title_canon_sha256":"c6acb7abcaf1a8e24b530415b56659fdc2d72e8fb6fe68cef8bc2e9e4e2db90c","abstract_canon_sha256":"223fd35fa3e565965b0886bfd682f98ffc4437a824cb5d4fdf874bfed0ca606b"},"schema_version":"1.0"},"canonical_sha256":"ecf4dea1d495197e096b945892b627917fbbfcdc7ade8b4803670f67cab205a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:06:36.855410Z","signature_b64":"zTSKa8VQdLeC/r3RwBom5wZpTULmBMeQGjLFEIXQGCTmN4gHBXNxqcIzwgr6U525G58X6cLYgeyk3TPvoaz4CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecf4dea1d495197e096b945892b627917fbbfcdc7ade8b4803670f67cab205a0","last_reissued_at":"2026-07-05T10:06:36.855050Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:06:36.855050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2301.04958","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:06:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5RfGxzIevA+jf6MqU1P30V2zatFUlYYdhabY3ZSpxgehQrd2yl6D2A4zIUMh8i7dk3Y8YoCdV9+5boMxd3bkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T20:22:48.137405Z"},"content_sha256":"676ae6537ff61b389f10c8ad1ed364fba310fcbf0dfdd56b62525b513dd16a4b","schema_version":"1.0","event_id":"sha256:676ae6537ff61b389f10c8ad1ed364fba310fcbf0dfdd56b62525b513dd16a4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:5T2N5IOUSUMX4CLLSRMJFNRHSF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multifractal analysis of measures arising from random substitutions","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Alex Rutar, Andrew Mitchell","submitted_at":"2023-01-12T12:06:40Z","abstract_excerpt":"We study regularity properties of frequency measures arising from random substitutions, which are a generalisation of (deterministic) substitutions where the substituted image of each letter is chosen independently from a fixed finite set. In particular, for a natural class of such measures, we derive a closed-form analytic formula for the $L^q$-spectrum and prove that the multifractal formalism holds. This provides an interesting new class of measures satisfying the multifractal formalism. More generally, we establish results concerning the $L^q$-spectrum of a broad class of frequency measure"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.04958","kind":"arxiv","version":2},"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/2301.04958/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":"2026-07-05T10:06:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wjw2x8xiIOSPu94lORPdf0KH4Tm2h/J6qp94Sd0waMPTerc0qkqOzDH5IjemQW1e7jRLSXAg46HW1kKmfBgsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T20:22:48.138010Z"},"content_sha256":"2541ae1f6481f488269e28fc663f6b0bed7a2f58533538f099770daf92d816c8","schema_version":"1.0","event_id":"sha256:2541ae1f6481f488269e28fc663f6b0bed7a2f58533538f099770daf92d816c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5T2N5IOUSUMX4CLLSRMJFNRHSF/bundle.json","state_url":"https://pith.science/pith/5T2N5IOUSUMX4CLLSRMJFNRHSF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5T2N5IOUSUMX4CLLSRMJFNRHSF/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":"2026-08-18T20:22:48Z","links":{"resolver":"https://pith.science/pith/5T2N5IOUSUMX4CLLSRMJFNRHSF","bundle":"https://pith.science/pith/5T2N5IOUSUMX4CLLSRMJFNRHSF/bundle.json","state":"https://pith.science/pith/5T2N5IOUSUMX4CLLSRMJFNRHSF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5T2N5IOUSUMX4CLLSRMJFNRHSF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:5T2N5IOUSUMX4CLLSRMJFNRHSF","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":"223fd35fa3e565965b0886bfd682f98ffc4437a824cb5d4fdf874bfed0ca606b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2023-01-12T12:06:40Z","title_canon_sha256":"c6acb7abcaf1a8e24b530415b56659fdc2d72e8fb6fe68cef8bc2e9e4e2db90c"},"schema_version":"1.0","source":{"id":"2301.04958","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2301.04958","created_at":"2026-07-05T10:06:36Z"},{"alias_kind":"arxiv_version","alias_value":"2301.04958v2","created_at":"2026-07-05T10:06:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2301.04958","created_at":"2026-07-05T10:06:36Z"},{"alias_kind":"pith_short_12","alias_value":"5T2N5IOUSUMX","created_at":"2026-07-05T10:06:36Z"},{"alias_kind":"pith_short_16","alias_value":"5T2N5IOUSUMX4CLL","created_at":"2026-07-05T10:06:36Z"},{"alias_kind":"pith_short_8","alias_value":"5T2N5IOU","created_at":"2026-07-05T10:06:36Z"}],"graph_snapshots":[{"event_id":"sha256:2541ae1f6481f488269e28fc663f6b0bed7a2f58533538f099770daf92d816c8","target":"graph","created_at":"2026-07-05T10:06:36Z","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/2301.04958/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study regularity properties of frequency measures arising from random substitutions, which are a generalisation of (deterministic) substitutions where the substituted image of each letter is chosen independently from a fixed finite set. In particular, for a natural class of such measures, we derive a closed-form analytic formula for the $L^q$-spectrum and prove that the multifractal formalism holds. This provides an interesting new class of measures satisfying the multifractal formalism. More generally, we establish results concerning the $L^q$-spectrum of a broad class of frequency measure","authors_text":"Alex Rutar, Andrew Mitchell","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2023-01-12T12:06:40Z","title":"Multifractal analysis of measures arising from random substitutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2301.04958","kind":"arxiv","version":2},"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":"sha256:676ae6537ff61b389f10c8ad1ed364fba310fcbf0dfdd56b62525b513dd16a4b","target":"record","created_at":"2026-07-05T10:06:36Z","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":"223fd35fa3e565965b0886bfd682f98ffc4437a824cb5d4fdf874bfed0ca606b","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DS","submitted_at":"2023-01-12T12:06:40Z","title_canon_sha256":"c6acb7abcaf1a8e24b530415b56659fdc2d72e8fb6fe68cef8bc2e9e4e2db90c"},"schema_version":"1.0","source":{"id":"2301.04958","kind":"arxiv","version":2}},"canonical_sha256":"ecf4dea1d495197e096b945892b627917fbbfcdc7ade8b4803670f67cab205a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ecf4dea1d495197e096b945892b627917fbbfcdc7ade8b4803670f67cab205a0","first_computed_at":"2026-07-05T10:06:36.855050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:06:36.855050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zTSKa8VQdLeC/r3RwBom5wZpTULmBMeQGjLFEIXQGCTmN4gHBXNxqcIzwgr6U525G58X6cLYgeyk3TPvoaz4CA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:06:36.855410Z","signed_message":"canonical_sha256_bytes"},"source_id":"2301.04958","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:676ae6537ff61b389f10c8ad1ed364fba310fcbf0dfdd56b62525b513dd16a4b","sha256:2541ae1f6481f488269e28fc663f6b0bed7a2f58533538f099770daf92d816c8"],"state_sha256":"30ff7cace33921f3a8ecbd512abeed5d04dafd78989667eea092ea723ad9d75a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mfcUqUYpw1TpEDbRmL4PSStn58k+dRxXQIBtrHUIcekpWmwsUqgyJISJ/PqkLjjWdyEqEFRJ2nU8qKZv6zj0Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T20:22:48.145070Z","bundle_sha256":"46e2f5299937ad4b1fd59489c80adad89c536215e727f3644a1a95c7dea481ee"}}