{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:EA3AQSJQFRW5NSOKRTTD3LGYAZ","short_pith_number":"pith:EA3AQSJQ","canonical_record":{"source":{"id":"1907.07121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-13T17:50:36Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3e956fb369856380c991d87aeb897e797fa0e24be666855d11b80ed246b29873","abstract_canon_sha256":"4e8aa22fcf1201c7ceb411a90dd96c9852b9216f5ebba2a95f95ca6f79ca454f"},"schema_version":"1.0"},"canonical_sha256":"20360849302c6dd6c9ca8ce63dacd806435e1842e67c064000139bd1ecb17377","source":{"kind":"arxiv","id":"1907.07121","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.07121","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"arxiv_version","alias_value":"1907.07121v1","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07121","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"pith_short_12","alias_value":"EA3AQSJQFRW5","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EA3AQSJQFRW5NSOK","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EA3AQSJQ","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:EA3AQSJQFRW5NSOKRTTD3LGYAZ","target":"record","payload":{"canonical_record":{"source":{"id":"1907.07121","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-13T17:50:36Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3e956fb369856380c991d87aeb897e797fa0e24be666855d11b80ed246b29873","abstract_canon_sha256":"4e8aa22fcf1201c7ceb411a90dd96c9852b9216f5ebba2a95f95ca6f79ca454f"},"schema_version":"1.0"},"canonical_sha256":"20360849302c6dd6c9ca8ce63dacd806435e1842e67c064000139bd1ecb17377","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:27.987965Z","signature_b64":"Kzw0R3R5OYJTtfWIfw4KkNuH5SHHEEiPM+rP0ObVL9PXQ+Djzx8Ipjq6xlQ4eXlXnIpErnyLWASUHZ/MqoOSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20360849302c6dd6c9ca8ce63dacd806435e1842e67c064000139bd1ecb17377","last_reissued_at":"2026-05-17T23:40:27.987292Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:27.987292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.07121","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":"2026-05-17T23:40:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GejyQkNc3RLACkpLtslrCZKurP/33TJGuGJvdzCfMpBi2C1NmmbWv1TDuixuTal2ijYo9ycq1EQjetqTU2djDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:50:25.455664Z"},"content_sha256":"99aee68fbca584374245a62aa5dba56b6124365bbe99850188427ea6f66f489c","schema_version":"1.0","event_id":"sha256:99aee68fbca584374245a62aa5dba56b6124365bbe99850188427ea6f66f489c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:EA3AQSJQFRW5NSOKRTTD3LGYAZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L^q$ dimensions of self-similar measures, and applications: a survey","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.DS","authors_text":"Pablo Shmerkin","submitted_at":"2019-07-13T17:50:36Z","abstract_excerpt":"We present a self-contained proof of a formula for the $L^q$ dimensions of self-similar measures on the real line under exponential separation (up to the proof of an inverse theorem for the $L^q$ norm of convolutions). This is a special case of a more general result of the author from [Shmerkin, Pablo. On Furstenberg's intersection conjecture, self-similar measures, and the $L^q$ norms of convolutions. Ann. of Math., 2019], and one of the goals of this survey is to present the ideas in a simpler, but important, setting. We also review some applications of the main result to the study of Bernou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07121","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":""},"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":"2026-05-17T23:40:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gghg5wl/fn2ToU9FnMuzY/dvNVPiKttxjI1Nkw1Y5bRLyIZoPGxaEmWeT60bS4tBkJeCWpkjYcOu8A7W7p1EDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T08:50:25.456119Z"},"content_sha256":"4418ba435d01775d47daee90b674381a3ada3c7cb579606ca67583874e1f0677","schema_version":"1.0","event_id":"sha256:4418ba435d01775d47daee90b674381a3ada3c7cb579606ca67583874e1f0677"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EA3AQSJQFRW5NSOKRTTD3LGYAZ/bundle.json","state_url":"https://pith.science/pith/EA3AQSJQFRW5NSOKRTTD3LGYAZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EA3AQSJQFRW5NSOKRTTD3LGYAZ/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":"2026-06-05T08:50:25Z","links":{"resolver":"https://pith.science/pith/EA3AQSJQFRW5NSOKRTTD3LGYAZ","bundle":"https://pith.science/pith/EA3AQSJQFRW5NSOKRTTD3LGYAZ/bundle.json","state":"https://pith.science/pith/EA3AQSJQFRW5NSOKRTTD3LGYAZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EA3AQSJQFRW5NSOKRTTD3LGYAZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:EA3AQSJQFRW5NSOKRTTD3LGYAZ","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":"4e8aa22fcf1201c7ceb411a90dd96c9852b9216f5ebba2a95f95ca6f79ca454f","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-13T17:50:36Z","title_canon_sha256":"3e956fb369856380c991d87aeb897e797fa0e24be666855d11b80ed246b29873"},"schema_version":"1.0","source":{"id":"1907.07121","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.07121","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"arxiv_version","alias_value":"1907.07121v1","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.07121","created_at":"2026-05-17T23:40:27Z"},{"alias_kind":"pith_short_12","alias_value":"EA3AQSJQFRW5","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"EA3AQSJQFRW5NSOK","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"EA3AQSJQ","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:4418ba435d01775d47daee90b674381a3ada3c7cb579606ca67583874e1f0677","target":"graph","created_at":"2026-05-17T23:40:27Z","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 present a self-contained proof of a formula for the $L^q$ dimensions of self-similar measures on the real line under exponential separation (up to the proof of an inverse theorem for the $L^q$ norm of convolutions). This is a special case of a more general result of the author from [Shmerkin, Pablo. On Furstenberg's intersection conjecture, self-similar measures, and the $L^q$ norms of convolutions. Ann. of Math., 2019], and one of the goals of this survey is to present the ideas in a simpler, but important, setting. We also review some applications of the main result to the study of Bernou","authors_text":"Pablo Shmerkin","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-13T17:50:36Z","title":"$L^q$ dimensions of self-similar measures, and applications: a survey"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.07121","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":"sha256:99aee68fbca584374245a62aa5dba56b6124365bbe99850188427ea6f66f489c","target":"record","created_at":"2026-05-17T23:40:27Z","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":"4e8aa22fcf1201c7ceb411a90dd96c9852b9216f5ebba2a95f95ca6f79ca454f","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-07-13T17:50:36Z","title_canon_sha256":"3e956fb369856380c991d87aeb897e797fa0e24be666855d11b80ed246b29873"},"schema_version":"1.0","source":{"id":"1907.07121","kind":"arxiv","version":1}},"canonical_sha256":"20360849302c6dd6c9ca8ce63dacd806435e1842e67c064000139bd1ecb17377","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20360849302c6dd6c9ca8ce63dacd806435e1842e67c064000139bd1ecb17377","first_computed_at":"2026-05-17T23:40:27.987292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:27.987292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kzw0R3R5OYJTtfWIfw4KkNuH5SHHEEiPM+rP0ObVL9PXQ+Djzx8Ipjq6xlQ4eXlXnIpErnyLWASUHZ/MqoOSBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:27.987965Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.07121","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99aee68fbca584374245a62aa5dba56b6124365bbe99850188427ea6f66f489c","sha256:4418ba435d01775d47daee90b674381a3ada3c7cb579606ca67583874e1f0677"],"state_sha256":"7f328a7297fa09987fbfd6f7610b0c0ca16304eaf38c99477cb7bcaf81949d3f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XVQ/hegsRCDFZT0o9QtgdXIEHiLcKVdwPjhXbfqDca2r0QgiJKDqFQzn2jfFj58csfBvbQEGXGkd8Xm8BhQBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T08:50:25.458348Z","bundle_sha256":"0eb0006d341bd098bf33a73746dc19a5d7a80fcc005a0e9811c306e32032c1a0"}}