{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YANJMV7LNPVHXNN5AABWIZFVTN","short_pith_number":"pith:YANJMV7L","canonical_record":{"source":{"id":"1110.6011","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-27T08:46:32Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"5b534003b4b91482656ae9b25e64f38d87ac927980762cc75b646fcbd4a1aff2","abstract_canon_sha256":"596bd2dbc0be302adb9245508e78ad6976d9189e1cf66dc450918f7fa7a1c6d6"},"schema_version":"1.0"},"canonical_sha256":"c01a9657eb6bea7bb5bd00036464b59b738bfcdbe26772cda554d11a51625c7b","source":{"kind":"arxiv","id":"1110.6011","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6011","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6011v2","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6011","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"YANJMV7LNPVH","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YANJMV7LNPVHXNN5","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YANJMV7L","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YANJMV7LNPVHXNN5AABWIZFVTN","target":"record","payload":{"canonical_record":{"source":{"id":"1110.6011","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-27T08:46:32Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"5b534003b4b91482656ae9b25e64f38d87ac927980762cc75b646fcbd4a1aff2","abstract_canon_sha256":"596bd2dbc0be302adb9245508e78ad6976d9189e1cf66dc450918f7fa7a1c6d6"},"schema_version":"1.0"},"canonical_sha256":"c01a9657eb6bea7bb5bd00036464b59b738bfcdbe26772cda554d11a51625c7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:12.408819Z","signature_b64":"HNAK8QBMffubK14ZbiyrMjUqAfv6q1Eo9qwTnr71EpglOZQ2Ycbto5oSoQxbHr+ZLRHzjNowpugGVd3EewCrBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c01a9657eb6bea7bb5bd00036464b59b738bfcdbe26772cda554d11a51625c7b","last_reissued_at":"2026-05-18T02:28:12.408214Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:12.408214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.6011","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":"2026-05-18T02:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/k8cz2jcrh9BUdhq7O/LAqyYc1WL7APKo8UhbCHtIfn/1/OsDJIzdcEryL43FOgnY54Ecex8G8D+6hnf/WhXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:01:07.582294Z"},"content_sha256":"3a8e0f10c1d3247676ce6d9b6348d287a10a148f0b37af6b9be6712fe736d466","schema_version":"1.0","event_id":"sha256:3a8e0f10c1d3247676ce6d9b6348d287a10a148f0b37af6b9be6712fe736d466"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YANJMV7LNPVHXNN5AABWIZFVTN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimension, entropy, and the local distribution of measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Pablo Shmerkin, Tuomas Sahlsten, Ville Suomala","submitted_at":"2011-10-27T08:46:32Z","abstract_excerpt":"We present a general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local homogeneity, porosity and conical densities of measures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6011","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":""},"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":"2026-05-18T02:28:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o2WbHPJmJkBswhrn0EmXbT56KUu/VV5OxZrWYpFZeA9bLQG7+ysUV3esZ+CkokAnRF3wP6IXYo+kUXWm8Oc9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T10:01:07.582641Z"},"content_sha256":"f960b37bbd7fd2078837931ed8b3c5684400e8b62c2cc2ee5142e14a6c55caf7","schema_version":"1.0","event_id":"sha256:f960b37bbd7fd2078837931ed8b3c5684400e8b62c2cc2ee5142e14a6c55caf7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YANJMV7LNPVHXNN5AABWIZFVTN/bundle.json","state_url":"https://pith.science/pith/YANJMV7LNPVHXNN5AABWIZFVTN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YANJMV7LNPVHXNN5AABWIZFVTN/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":"2026-06-20T10:01:07Z","links":{"resolver":"https://pith.science/pith/YANJMV7LNPVHXNN5AABWIZFVTN","bundle":"https://pith.science/pith/YANJMV7LNPVHXNN5AABWIZFVTN/bundle.json","state":"https://pith.science/pith/YANJMV7LNPVHXNN5AABWIZFVTN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YANJMV7LNPVHXNN5AABWIZFVTN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YANJMV7LNPVHXNN5AABWIZFVTN","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":"596bd2dbc0be302adb9245508e78ad6976d9189e1cf66dc450918f7fa7a1c6d6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-27T08:46:32Z","title_canon_sha256":"5b534003b4b91482656ae9b25e64f38d87ac927980762cc75b646fcbd4a1aff2"},"schema_version":"1.0","source":{"id":"1110.6011","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.6011","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"arxiv_version","alias_value":"1110.6011v2","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.6011","created_at":"2026-05-18T02:28:12Z"},{"alias_kind":"pith_short_12","alias_value":"YANJMV7LNPVH","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YANJMV7LNPVHXNN5","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YANJMV7L","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:f960b37bbd7fd2078837931ed8b3c5684400e8b62c2cc2ee5142e14a6c55caf7","target":"graph","created_at":"2026-05-18T02:28:12Z","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 general approach to the study of the local distribution of measures on Euclidean spaces, based on local entropy averages. As concrete applications, we unify, generalize, and simplify a number of recent results on local homogeneity, porosity and conical densities of measures.","authors_text":"Pablo Shmerkin, Tuomas Sahlsten, Ville Suomala","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-27T08:46:32Z","title":"Dimension, entropy, and the local distribution of measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.6011","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":"sha256:3a8e0f10c1d3247676ce6d9b6348d287a10a148f0b37af6b9be6712fe736d466","target":"record","created_at":"2026-05-18T02:28:12Z","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":"596bd2dbc0be302adb9245508e78ad6976d9189e1cf66dc450918f7fa7a1c6d6","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-10-27T08:46:32Z","title_canon_sha256":"5b534003b4b91482656ae9b25e64f38d87ac927980762cc75b646fcbd4a1aff2"},"schema_version":"1.0","source":{"id":"1110.6011","kind":"arxiv","version":2}},"canonical_sha256":"c01a9657eb6bea7bb5bd00036464b59b738bfcdbe26772cda554d11a51625c7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c01a9657eb6bea7bb5bd00036464b59b738bfcdbe26772cda554d11a51625c7b","first_computed_at":"2026-05-18T02:28:12.408214Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:12.408214Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HNAK8QBMffubK14ZbiyrMjUqAfv6q1Eo9qwTnr71EpglOZQ2Ycbto5oSoQxbHr+ZLRHzjNowpugGVd3EewCrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:12.408819Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.6011","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a8e0f10c1d3247676ce6d9b6348d287a10a148f0b37af6b9be6712fe736d466","sha256:f960b37bbd7fd2078837931ed8b3c5684400e8b62c2cc2ee5142e14a6c55caf7"],"state_sha256":"e064beea95a1d93c3053af543e3e11385f168df4331405180d0c5ab41a3acf0a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6c7Rpw/av9lkPalQWG9iekASVJIw2CT8wyTibWD1g/9ZmgJhkZP69i9h1DkoPXBTrv8+sg9LwaCFzV81h9J2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T10:01:07.584404Z","bundle_sha256":"333be604c4ae87c2d6ba843ca6b146c7a0fe43672fe47a676cfe07267006394d"}}