{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:AJDJGGN7TU6HQ4DKURDDGRWUR7","short_pith_number":"pith:AJDJGGN7","canonical_record":{"source":{"id":"1912.00880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-12-02T15:58:03Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"45d45aa43ee675a63157454910fd25e7c2e117f5cd9def327b3644b71e26850a","abstract_canon_sha256":"e8bc33fca2a8e27f0fe709edfe782e198fff3a4abee89ed06d75f51dbfb66ed8"},"schema_version":"1.0"},"canonical_sha256":"02469319bf9d3c78706aa4463346d48fc0a4f083c4b898e77063c5531303c74c","source":{"kind":"arxiv","id":"1912.00880","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.00880","created_at":"2026-07-05T00:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"1912.00880v1","created_at":"2026-07-05T00:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.00880","created_at":"2026-07-05T00:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"AJDJGGN7TU6H","created_at":"2026-07-05T00:23:17Z"},{"alias_kind":"pith_short_16","alias_value":"AJDJGGN7TU6HQ4DK","created_at":"2026-07-05T00:23:17Z"},{"alias_kind":"pith_short_8","alias_value":"AJDJGGN7","created_at":"2026-07-05T00:23:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:AJDJGGN7TU6HQ4DKURDDGRWUR7","target":"record","payload":{"canonical_record":{"source":{"id":"1912.00880","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-12-02T15:58:03Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"45d45aa43ee675a63157454910fd25e7c2e117f5cd9def327b3644b71e26850a","abstract_canon_sha256":"e8bc33fca2a8e27f0fe709edfe782e198fff3a4abee89ed06d75f51dbfb66ed8"},"schema_version":"1.0"},"canonical_sha256":"02469319bf9d3c78706aa4463346d48fc0a4f083c4b898e77063c5531303c74c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:23:17.779339Z","signature_b64":"UK/SWjlL7ev8Juu9wXgvAGHsTAEdTNofN+frjJsVENfHoZobYNXbaSYnGyjxwSQIbkiQhx9wNf/jbKcmQyk1BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02469319bf9d3c78706aa4463346d48fc0a4f083c4b898e77063c5531303c74c","last_reissued_at":"2026-07-05T00:23:17.778926Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:23:17.778926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1912.00880","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":"2026-07-05T00:23:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zdb0YlH1ArkcbFwcOwuzTIqim2SdR7qGl1nSgrKB2/fGZg+IpqSMi2xPDF07r2vmlGgG76hTr9qYVRULY3gxCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T05:44:33.541441Z"},"content_sha256":"fa85d4a2b0d419b5efd967afb457dced8f6ae3fa47e0e88daa3560f173b00a69","schema_version":"1.0","event_id":"sha256:fa85d4a2b0d419b5efd967afb457dced8f6ae3fa47e0e88daa3560f173b00a69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:AJDJGGN7TU6HQ4DKURDDGRWUR7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Measure comparison and distance inequalities for convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Alexander Koldobsky, Artem Zvavitch, Grigoris Paouris","submitted_at":"2019-12-02T15:58:03Z","abstract_excerpt":"We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We also prove a sharp upper estimate for the outer volume ratio distance from an arbitrary convex body to the unit balls of subspaces of $L_p$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.00880","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1912.00880/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":"2026-07-05T00:23:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N793+D6RFP1M277OuW3VSdG7ulno3gXpv5/i3UQmfpSgq5SeiXD8+P0y3Kny7sqn5+aZ4n0xwpH6V303ibkBBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T05:44:33.542084Z"},"content_sha256":"bd13698d02e45a205c2e3e1f0c291dcffb09a315b77747322ca0cba592fea6fc","schema_version":"1.0","event_id":"sha256:bd13698d02e45a205c2e3e1f0c291dcffb09a315b77747322ca0cba592fea6fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AJDJGGN7TU6HQ4DKURDDGRWUR7/bundle.json","state_url":"https://pith.science/pith/AJDJGGN7TU6HQ4DKURDDGRWUR7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AJDJGGN7TU6HQ4DKURDDGRWUR7/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":"2026-08-22T05:44:33Z","links":{"resolver":"https://pith.science/pith/AJDJGGN7TU6HQ4DKURDDGRWUR7","bundle":"https://pith.science/pith/AJDJGGN7TU6HQ4DKURDDGRWUR7/bundle.json","state":"https://pith.science/pith/AJDJGGN7TU6HQ4DKURDDGRWUR7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AJDJGGN7TU6HQ4DKURDDGRWUR7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:AJDJGGN7TU6HQ4DKURDDGRWUR7","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":"e8bc33fca2a8e27f0fe709edfe782e198fff3a4abee89ed06d75f51dbfb66ed8","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-12-02T15:58:03Z","title_canon_sha256":"45d45aa43ee675a63157454910fd25e7c2e117f5cd9def327b3644b71e26850a"},"schema_version":"1.0","source":{"id":"1912.00880","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1912.00880","created_at":"2026-07-05T00:23:17Z"},{"alias_kind":"arxiv_version","alias_value":"1912.00880v1","created_at":"2026-07-05T00:23:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1912.00880","created_at":"2026-07-05T00:23:17Z"},{"alias_kind":"pith_short_12","alias_value":"AJDJGGN7TU6H","created_at":"2026-07-05T00:23:17Z"},{"alias_kind":"pith_short_16","alias_value":"AJDJGGN7TU6HQ4DK","created_at":"2026-07-05T00:23:17Z"},{"alias_kind":"pith_short_8","alias_value":"AJDJGGN7","created_at":"2026-07-05T00:23:17Z"}],"graph_snapshots":[{"event_id":"sha256:bd13698d02e45a205c2e3e1f0c291dcffb09a315b77747322ca0cba592fea6fc","target":"graph","created_at":"2026-07-05T00:23:17Z","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/1912.00880/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove new versions of the isomorphic Busemann-Petty problem for two different measures and show how these results can be used to recover slicing and distance inequalities. We also prove a sharp upper estimate for the outer volume ratio distance from an arbitrary convex body to the unit balls of subspaces of $L_p$.","authors_text":"Alexander Koldobsky, Artem Zvavitch, Grigoris Paouris","cross_cats":["math.CA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-12-02T15:58:03Z","title":"Measure comparison and distance inequalities for convex bodies"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1912.00880","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:fa85d4a2b0d419b5efd967afb457dced8f6ae3fa47e0e88daa3560f173b00a69","target":"record","created_at":"2026-07-05T00:23:17Z","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":"e8bc33fca2a8e27f0fe709edfe782e198fff3a4abee89ed06d75f51dbfb66ed8","cross_cats_sorted":["math.CA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-12-02T15:58:03Z","title_canon_sha256":"45d45aa43ee675a63157454910fd25e7c2e117f5cd9def327b3644b71e26850a"},"schema_version":"1.0","source":{"id":"1912.00880","kind":"arxiv","version":1}},"canonical_sha256":"02469319bf9d3c78706aa4463346d48fc0a4f083c4b898e77063c5531303c74c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02469319bf9d3c78706aa4463346d48fc0a4f083c4b898e77063c5531303c74c","first_computed_at":"2026-07-05T00:23:17.778926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:23:17.778926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UK/SWjlL7ev8Juu9wXgvAGHsTAEdTNofN+frjJsVENfHoZobYNXbaSYnGyjxwSQIbkiQhx9wNf/jbKcmQyk1BA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:23:17.779339Z","signed_message":"canonical_sha256_bytes"},"source_id":"1912.00880","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fa85d4a2b0d419b5efd967afb457dced8f6ae3fa47e0e88daa3560f173b00a69","sha256:bd13698d02e45a205c2e3e1f0c291dcffb09a315b77747322ca0cba592fea6fc"],"state_sha256":"941369ba138a90554f356e06b2b3ead949df6128cd0110b340ef7d8fcea2c248"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nyISVguUoErP6LTI+qoSeqYl6/CCWh08Jc+dpw4eX9W7qm96B1ZfvyCg87UK79tql7Y8iIPIIfCTRaOBMwwrBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T05:44:33.547121Z","bundle_sha256":"d6e34ae4bcb3ca2b01257c88d98f214c582b3bd5033ed5d4c91b7eb2e7023b04"}}