{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3EQ6UKD7UDJXJP2CLL6TX3VMYT","short_pith_number":"pith:3EQ6UKD7","canonical_record":{"source":{"id":"1401.0231","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-31T23:19:48Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a9039577c2d546a4e1948ee6f00d2eae07a509a64ec906756ba2ebb9143ad76e","abstract_canon_sha256":"489a019a2d478ce91533a09cb048de402d39fe3ba139e73c35feb301ebda0a3d"},"schema_version":"1.0"},"canonical_sha256":"d921ea287fa0d374bf425afd3beeacc4dc1d49a6c2eff305084a21584a8e4cb5","source":{"kind":"arxiv","id":"1401.0231","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0231","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0231v3","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0231","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"3EQ6UKD7UDJX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3EQ6UKD7UDJXJP2C","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3EQ6UKD7","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3EQ6UKD7UDJXJP2CLL6TX3VMYT","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0231","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-31T23:19:48Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"a9039577c2d546a4e1948ee6f00d2eae07a509a64ec906756ba2ebb9143ad76e","abstract_canon_sha256":"489a019a2d478ce91533a09cb048de402d39fe3ba139e73c35feb301ebda0a3d"},"schema_version":"1.0"},"canonical_sha256":"d921ea287fa0d374bf425afd3beeacc4dc1d49a6c2eff305084a21584a8e4cb5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:34.400281Z","signature_b64":"qtXdAnJvoqaCtLKeJowGRHJKXfexhJevFpeBAHNMtfjmFhA9W0ANwv1KgG/IJ1E1k8i3jnuX1i/JOwOmwA00Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d921ea287fa0d374bf425afd3beeacc4dc1d49a6c2eff305084a21584a8e4cb5","last_reissued_at":"2026-05-18T00:51:34.399895Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:34.399895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0231","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":"2026-05-18T00:51:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4z/Ndu9fse8+Gm6Ka0xrGSscNrsFolr3oO+EGWGXzISMvYkwVYRvXvUWyeG3OthJiTvKuyqPpHELfvitUkl9BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:06:49.139767Z"},"content_sha256":"c4b966fa2f371f2ba16195a5cb34464727728e901dad373fb88d7427f509afd0","schema_version":"1.0","event_id":"sha256:c4b966fa2f371f2ba16195a5cb34464727728e901dad373fb88d7427f509afd0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3EQ6UKD7UDJXJP2CLL6TX3VMYT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics of the scenery flow and geometry of measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Antti K\\\"aenm\\\"aki, Pablo Shmerkin, Tuomas Sahlsten","submitted_at":"2013-12-31T23:19:48Z","abstract_excerpt":"We employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its set-theoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-simil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0231","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":""},"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":"2026-05-18T00:51:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M7iA1sYcSNeSqxDqtIaKuROahVOOAKyatDYFwcaHfgNuY1tHEM4miQVOH7T8dJlp8SgzhbDUTdrQ/9F1t1MkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T04:06:49.140111Z"},"content_sha256":"6204976446d119130a388f957783a0fede931b4914c523833c7b6113eb7395e9","schema_version":"1.0","event_id":"sha256:6204976446d119130a388f957783a0fede931b4914c523833c7b6113eb7395e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3EQ6UKD7UDJXJP2CLL6TX3VMYT/bundle.json","state_url":"https://pith.science/pith/3EQ6UKD7UDJXJP2CLL6TX3VMYT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3EQ6UKD7UDJXJP2CLL6TX3VMYT/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":"2026-06-20T04:06:49Z","links":{"resolver":"https://pith.science/pith/3EQ6UKD7UDJXJP2CLL6TX3VMYT","bundle":"https://pith.science/pith/3EQ6UKD7UDJXJP2CLL6TX3VMYT/bundle.json","state":"https://pith.science/pith/3EQ6UKD7UDJXJP2CLL6TX3VMYT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3EQ6UKD7UDJXJP2CLL6TX3VMYT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3EQ6UKD7UDJXJP2CLL6TX3VMYT","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":"489a019a2d478ce91533a09cb048de402d39fe3ba139e73c35feb301ebda0a3d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-31T23:19:48Z","title_canon_sha256":"a9039577c2d546a4e1948ee6f00d2eae07a509a64ec906756ba2ebb9143ad76e"},"schema_version":"1.0","source":{"id":"1401.0231","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0231","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0231v3","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0231","created_at":"2026-05-18T00:51:34Z"},{"alias_kind":"pith_short_12","alias_value":"3EQ6UKD7UDJX","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3EQ6UKD7UDJXJP2C","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3EQ6UKD7","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:6204976446d119130a388f957783a0fede931b4914c523833c7b6113eb7395e9","target":"graph","created_at":"2026-05-18T00:51:34Z","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 employ the ergodic theoretic machinery of scenery flows to address classical geometric measure theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we show to be closely linked to rectifiability. Moreover, we show that the dimension theory of measure-theoretical porosity can be reduced back to its set-theoretic version, that Hausdorff and packing dimensions yield the same maximal dimension for porous and even mean porous measures, and that extremal measures exist and can be chosen to satisfy a generalized notion of self-simil","authors_text":"Antti K\\\"aenm\\\"aki, Pablo Shmerkin, Tuomas Sahlsten","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-31T23:19:48Z","title":"Dynamics of the scenery flow and geometry of measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0231","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:c4b966fa2f371f2ba16195a5cb34464727728e901dad373fb88d7427f509afd0","target":"record","created_at":"2026-05-18T00:51:34Z","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":"489a019a2d478ce91533a09cb048de402d39fe3ba139e73c35feb301ebda0a3d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-12-31T23:19:48Z","title_canon_sha256":"a9039577c2d546a4e1948ee6f00d2eae07a509a64ec906756ba2ebb9143ad76e"},"schema_version":"1.0","source":{"id":"1401.0231","kind":"arxiv","version":3}},"canonical_sha256":"d921ea287fa0d374bf425afd3beeacc4dc1d49a6c2eff305084a21584a8e4cb5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d921ea287fa0d374bf425afd3beeacc4dc1d49a6c2eff305084a21584a8e4cb5","first_computed_at":"2026-05-18T00:51:34.399895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:34.399895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qtXdAnJvoqaCtLKeJowGRHJKXfexhJevFpeBAHNMtfjmFhA9W0ANwv1KgG/IJ1E1k8i3jnuX1i/JOwOmwA00Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:34.400281Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0231","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4b966fa2f371f2ba16195a5cb34464727728e901dad373fb88d7427f509afd0","sha256:6204976446d119130a388f957783a0fede931b4914c523833c7b6113eb7395e9"],"state_sha256":"98270558f931c1840cf478e217e2c0758c21d076d457f107cb1252f7ddc73227"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jan3x/LzRZw1FG3bsvr9DPL5shHtTWaA9apBOxJgiX56uRhyCuASLiEqd3t6wzknCUZl0wGU+hloo9VP+uopBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T04:06:49.142087Z","bundle_sha256":"9e656637ae8aaee7d83a8256ecc1e7bbc6d0745e0d432b1c605bac2d367a09af"}}