{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:OCWQXPLKLF6EWCGGELT47XOMXJ","short_pith_number":"pith:OCWQXPLK","canonical_record":{"source":{"id":"2211.16410","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2022-11-29T17:30:49Z","cross_cats_sorted":["math.MG","math.PR"],"title_canon_sha256":"4e0b4c79c428100f604836da89f52d0d18d8c348e09fe9f75e90f7565409896d","abstract_canon_sha256":"aa0c929196caa30bf5c0d197128311902626335e4fbf0663e707680c39d6374a"},"schema_version":"1.0"},"canonical_sha256":"70ad0bbd6a597c4b08c622e7cfddccba4ddd867c98a95f1053420d0d4af0b0a1","source":{"kind":"arxiv","id":"2211.16410","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.16410","created_at":"2026-07-05T07:13:39Z"},{"alias_kind":"arxiv_version","alias_value":"2211.16410v3","created_at":"2026-07-05T07:13:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.16410","created_at":"2026-07-05T07:13:39Z"},{"alias_kind":"pith_short_12","alias_value":"OCWQXPLKLF6E","created_at":"2026-07-05T07:13:39Z"},{"alias_kind":"pith_short_16","alias_value":"OCWQXPLKLF6EWCGG","created_at":"2026-07-05T07:13:39Z"},{"alias_kind":"pith_short_8","alias_value":"OCWQXPLK","created_at":"2026-07-05T07:13:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:OCWQXPLKLF6EWCGGELT47XOMXJ","target":"record","payload":{"canonical_record":{"source":{"id":"2211.16410","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2022-11-29T17:30:49Z","cross_cats_sorted":["math.MG","math.PR"],"title_canon_sha256":"4e0b4c79c428100f604836da89f52d0d18d8c348e09fe9f75e90f7565409896d","abstract_canon_sha256":"aa0c929196caa30bf5c0d197128311902626335e4fbf0663e707680c39d6374a"},"schema_version":"1.0"},"canonical_sha256":"70ad0bbd6a597c4b08c622e7cfddccba4ddd867c98a95f1053420d0d4af0b0a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:13:39.554998Z","signature_b64":"wlkL46bYUwxDO99KhRwgkaCsTVsTLsS6k9Gc9YRMabUVxQlLHwDfopKhMf145r8ksO4LvJEi6+o7aB3UpKjwAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70ad0bbd6a597c4b08c622e7cfddccba4ddd867c98a95f1053420d0d4af0b0a1","last_reissued_at":"2026-07-05T07:13:39.554518Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:13:39.554518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2211.16410","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:13:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mpf6TnW5OH/seFNb6eFuDz0cIrGN9uMRUiB4cFRyXT3h353hk/uknkhts4mIIrbFwwre4U2UO5wiNkVLzqUFAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:34:03.968709Z"},"content_sha256":"750fe164b4141a6bd9b3f2b9de63be28f6ab66c59ca4d4efd552da4ef02a3bf2","schema_version":"1.0","event_id":"sha256:750fe164b4141a6bd9b3f2b9de63be28f6ab66c59ca4d4efd552da4ef02a3bf2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:OCWQXPLKLF6EWCGGELT47XOMXJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Furstenberg sumset conjecture and Mandelbrot percolations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.MG","math.PR"],"primary_cat":"math.DS","authors_text":"Catherine Bruce, Xiong Jin","submitted_at":"2022-11-29T17:30:49Z","abstract_excerpt":"In this paper we extend Hochman and Shmerkin's projection theorem to product measures of Mandelbrot cascades acting on ergodic measures imaged through canonical mappings of one-dimensional iterated function systems without any separation conditions. Consequently we extend Furstenberg sumset theorem to images of subshifts on symbolic spaces, and to Mandelbrot percolations on invariant sets. We also obtain dimension results for convolutions of Bernoulli convolutions and that of Mandelbrot cascade measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.16410","kind":"arxiv","version":3},"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/2211.16410/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":"2026-07-05T07:13:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cJeRbFmNysoqXZSvRjDb9KEhiJbseeOgecKYNPCiP3p5qgwpUoARDDKiDmSkAPx6EXonQ36ElRPzgSwRANcNCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T23:34:03.969667Z"},"content_sha256":"b52e386f8e995c224dd44fb36afa523524fdcaf94d43d2c77292621ff1d5ad71","schema_version":"1.0","event_id":"sha256:b52e386f8e995c224dd44fb36afa523524fdcaf94d43d2c77292621ff1d5ad71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OCWQXPLKLF6EWCGGELT47XOMXJ/bundle.json","state_url":"https://pith.science/pith/OCWQXPLKLF6EWCGGELT47XOMXJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OCWQXPLKLF6EWCGGELT47XOMXJ/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":"2026-08-08T23:34:03Z","links":{"resolver":"https://pith.science/pith/OCWQXPLKLF6EWCGGELT47XOMXJ","bundle":"https://pith.science/pith/OCWQXPLKLF6EWCGGELT47XOMXJ/bundle.json","state":"https://pith.science/pith/OCWQXPLKLF6EWCGGELT47XOMXJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OCWQXPLKLF6EWCGGELT47XOMXJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:OCWQXPLKLF6EWCGGELT47XOMXJ","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":"aa0c929196caa30bf5c0d197128311902626335e4fbf0663e707680c39d6374a","cross_cats_sorted":["math.MG","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2022-11-29T17:30:49Z","title_canon_sha256":"4e0b4c79c428100f604836da89f52d0d18d8c348e09fe9f75e90f7565409896d"},"schema_version":"1.0","source":{"id":"2211.16410","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.16410","created_at":"2026-07-05T07:13:39Z"},{"alias_kind":"arxiv_version","alias_value":"2211.16410v3","created_at":"2026-07-05T07:13:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.16410","created_at":"2026-07-05T07:13:39Z"},{"alias_kind":"pith_short_12","alias_value":"OCWQXPLKLF6E","created_at":"2026-07-05T07:13:39Z"},{"alias_kind":"pith_short_16","alias_value":"OCWQXPLKLF6EWCGG","created_at":"2026-07-05T07:13:39Z"},{"alias_kind":"pith_short_8","alias_value":"OCWQXPLK","created_at":"2026-07-05T07:13:39Z"}],"graph_snapshots":[{"event_id":"sha256:b52e386f8e995c224dd44fb36afa523524fdcaf94d43d2c77292621ff1d5ad71","target":"graph","created_at":"2026-07-05T07:13:39Z","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/2211.16410/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we extend Hochman and Shmerkin's projection theorem to product measures of Mandelbrot cascades acting on ergodic measures imaged through canonical mappings of one-dimensional iterated function systems without any separation conditions. Consequently we extend Furstenberg sumset theorem to images of subshifts on symbolic spaces, and to Mandelbrot percolations on invariant sets. We also obtain dimension results for convolutions of Bernoulli convolutions and that of Mandelbrot cascade measures.","authors_text":"Catherine Bruce, Xiong Jin","cross_cats":["math.MG","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2022-11-29T17:30:49Z","title":"Furstenberg sumset conjecture and Mandelbrot percolations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.16410","kind":"arxiv","version":3},"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":"sha256:750fe164b4141a6bd9b3f2b9de63be28f6ab66c59ca4d4efd552da4ef02a3bf2","target":"record","created_at":"2026-07-05T07:13:39Z","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":"aa0c929196caa30bf5c0d197128311902626335e4fbf0663e707680c39d6374a","cross_cats_sorted":["math.MG","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2022-11-29T17:30:49Z","title_canon_sha256":"4e0b4c79c428100f604836da89f52d0d18d8c348e09fe9f75e90f7565409896d"},"schema_version":"1.0","source":{"id":"2211.16410","kind":"arxiv","version":3}},"canonical_sha256":"70ad0bbd6a597c4b08c622e7cfddccba4ddd867c98a95f1053420d0d4af0b0a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70ad0bbd6a597c4b08c622e7cfddccba4ddd867c98a95f1053420d0d4af0b0a1","first_computed_at":"2026-07-05T07:13:39.554518Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:13:39.554518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wlkL46bYUwxDO99KhRwgkaCsTVsTLsS6k9Gc9YRMabUVxQlLHwDfopKhMf145r8ksO4LvJEi6+o7aB3UpKjwAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:13:39.554998Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.16410","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:750fe164b4141a6bd9b3f2b9de63be28f6ab66c59ca4d4efd552da4ef02a3bf2","sha256:b52e386f8e995c224dd44fb36afa523524fdcaf94d43d2c77292621ff1d5ad71"],"state_sha256":"4b27d82c3ce950f77d8879e30c509caa7bb981f413ec7cc77d592bc23fe77dcf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kLEyPJmIYU6ogZhPpQnMnRmwTKyV0cgHshPbiVNhEr4OUYx534I4BOJ4Re6XrL7SXUdU6UqZyqM5JUJUOcA7BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T23:34:03.974784Z","bundle_sha256":"15b32aa0e32c1640db62628c0ea7335326be8812014fe7e9dd48abaf7d0cef70"}}