{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:KEU32M6KVXRAUQHR4ATABWR4M3","short_pith_number":"pith:KEU32M6K","canonical_record":{"source":{"id":"1302.2433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-11T10:14:32Z","cross_cats_sorted":[],"title_canon_sha256":"4613bed7986d319ad75aebf0fa95dbefa4c15462e9a040b124cc90cfc493f183","abstract_canon_sha256":"5c496aa98b46cad395687495d5db7b58641a3ec11cdf49f94371ede738c21695"},"schema_version":"1.0"},"canonical_sha256":"5129bd33caade20a40f1e02600da3c66d2cdd88f58d3a612d84003bb089593eb","source":{"kind":"arxiv","id":"1302.2433","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2433","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2433v1","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2433","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"KEU32M6KVXRA","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KEU32M6KVXRAUQHR","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KEU32M6K","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:KEU32M6KVXRAUQHR4ATABWR4M3","target":"record","payload":{"canonical_record":{"source":{"id":"1302.2433","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-11T10:14:32Z","cross_cats_sorted":[],"title_canon_sha256":"4613bed7986d319ad75aebf0fa95dbefa4c15462e9a040b124cc90cfc493f183","abstract_canon_sha256":"5c496aa98b46cad395687495d5db7b58641a3ec11cdf49f94371ede738c21695"},"schema_version":"1.0"},"canonical_sha256":"5129bd33caade20a40f1e02600da3c66d2cdd88f58d3a612d84003bb089593eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:01.157413Z","signature_b64":"G6lDwJ+s384GXRsbdfp4siQ3yd3hTfkPoYJyFTdZBRM4/leIBoQdjh9st5JUSXiSInMg0FBouHjcByavrCvkBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5129bd33caade20a40f1e02600da3c66d2cdd88f58d3a612d84003bb089593eb","last_reissued_at":"2026-05-18T03:34:01.156671Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:01.156671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.2433","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":"2026-05-18T03:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hQvshPJx2T76lRFFy6S3dvgr1R5jIUi9NBTYItvhHrxTHa1pq7OEjA36rp9jWb1mb8pMlfe4vbcC2vdWpCW4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:57:25.981580Z"},"content_sha256":"77f347b023ba86c2272f91a18f788160e9de08936b2e3881b8cb1e6fefa0a505","schema_version":"1.0","event_id":"sha256:77f347b023ba86c2272f91a18f788160e9de08936b2e3881b8cb1e6fefa0a505"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:KEU32M6KVXRAUQHR4ATABWR4M3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On measures resisting multifractal analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"J\\\"org Schmeling, St\\'ephane Seuret","submitted_at":"2013-02-11T10:14:32Z","abstract_excerpt":"Any ergodic measure of a smooth map on a compact manifold has a multifractal spectrum with one point - the dimension of the measure itself - at the diagonal. We will construct examples where this fails in the most drastic way for invariant measures invariant under linear maps of the circle."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2433","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":"2026-05-18T03:34:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/PzkszwN07iGfW3MkJ3lZKAEX14kRTqJvlCUxwUaXbXTE6U/wcL3Tpe6j6klSxi7qfGS5gR4Tv73nLXfF/kFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T06:57:25.982214Z"},"content_sha256":"da05e12de9870f76b98319d9d6246e80e47723f93bb3909255fa804bf5d1dfb5","schema_version":"1.0","event_id":"sha256:da05e12de9870f76b98319d9d6246e80e47723f93bb3909255fa804bf5d1dfb5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KEU32M6KVXRAUQHR4ATABWR4M3/bundle.json","state_url":"https://pith.science/pith/KEU32M6KVXRAUQHR4ATABWR4M3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KEU32M6KVXRAUQHR4ATABWR4M3/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":"2026-06-01T06:57:25Z","links":{"resolver":"https://pith.science/pith/KEU32M6KVXRAUQHR4ATABWR4M3","bundle":"https://pith.science/pith/KEU32M6KVXRAUQHR4ATABWR4M3/bundle.json","state":"https://pith.science/pith/KEU32M6KVXRAUQHR4ATABWR4M3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KEU32M6KVXRAUQHR4ATABWR4M3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:KEU32M6KVXRAUQHR4ATABWR4M3","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":"5c496aa98b46cad395687495d5db7b58641a3ec11cdf49f94371ede738c21695","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-11T10:14:32Z","title_canon_sha256":"4613bed7986d319ad75aebf0fa95dbefa4c15462e9a040b124cc90cfc493f183"},"schema_version":"1.0","source":{"id":"1302.2433","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.2433","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"arxiv_version","alias_value":"1302.2433v1","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.2433","created_at":"2026-05-18T03:34:01Z"},{"alias_kind":"pith_short_12","alias_value":"KEU32M6KVXRA","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"KEU32M6KVXRAUQHR","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"KEU32M6K","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:da05e12de9870f76b98319d9d6246e80e47723f93bb3909255fa804bf5d1dfb5","target":"graph","created_at":"2026-05-18T03:34:01Z","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":"Any ergodic measure of a smooth map on a compact manifold has a multifractal spectrum with one point - the dimension of the measure itself - at the diagonal. We will construct examples where this fails in the most drastic way for invariant measures invariant under linear maps of the circle.","authors_text":"J\\\"org Schmeling, St\\'ephane Seuret","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-11T10:14:32Z","title":"On measures resisting multifractal analysis"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.2433","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":"sha256:77f347b023ba86c2272f91a18f788160e9de08936b2e3881b8cb1e6fefa0a505","target":"record","created_at":"2026-05-18T03:34:01Z","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":"5c496aa98b46cad395687495d5db7b58641a3ec11cdf49f94371ede738c21695","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-11T10:14:32Z","title_canon_sha256":"4613bed7986d319ad75aebf0fa95dbefa4c15462e9a040b124cc90cfc493f183"},"schema_version":"1.0","source":{"id":"1302.2433","kind":"arxiv","version":1}},"canonical_sha256":"5129bd33caade20a40f1e02600da3c66d2cdd88f58d3a612d84003bb089593eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5129bd33caade20a40f1e02600da3c66d2cdd88f58d3a612d84003bb089593eb","first_computed_at":"2026-05-18T03:34:01.156671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:01.156671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G6lDwJ+s384GXRsbdfp4siQ3yd3hTfkPoYJyFTdZBRM4/leIBoQdjh9st5JUSXiSInMg0FBouHjcByavrCvkBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:01.157413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.2433","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:77f347b023ba86c2272f91a18f788160e9de08936b2e3881b8cb1e6fefa0a505","sha256:da05e12de9870f76b98319d9d6246e80e47723f93bb3909255fa804bf5d1dfb5"],"state_sha256":"5cb2c7e731e21a127650b434a0797ad5d14e50283cf96ad323747da2dc279b6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5dC7kjJX4j+Z8iGODTzGGMj66W+PuOMwTABNn4/thDTGTRJSquz4NF2/ndHrgGmh8gpb02NlOL2MfbfJXTmOBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T06:57:25.985335Z","bundle_sha256":"b1698172a1d4c7313ecc245041218a0572c8c016f84e6d55a45fb2cc69ea2c1f"}}