{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:7EJHNUSKE7D2I4M7UVXPEG2JPH","short_pith_number":"pith:7EJHNUSK","canonical_record":{"source":{"id":"2309.12092","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2023-09-21T14:06:09Z","cross_cats_sorted":[],"title_canon_sha256":"58e2a3e4fe24dcdf047ee4f92d9acc4041bda8194d6ed407174ccf9e6505f3c1","abstract_canon_sha256":"2f58d68ed0c3030069ff51bd10307ee69f6fe3975144b7d86f14f48d3d2a4bd5"},"schema_version":"1.0"},"canonical_sha256":"f91276d24a27c7a4719fa56ef21b4979e9e983580c5a78d2fe51d4679798aa6d","source":{"kind":"arxiv","id":"2309.12092","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.12092","created_at":"2026-06-10T01:09:10Z"},{"alias_kind":"arxiv_version","alias_value":"2309.12092v2","created_at":"2026-06-10T01:09:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.12092","created_at":"2026-06-10T01:09:10Z"},{"alias_kind":"pith_short_12","alias_value":"7EJHNUSKE7D2","created_at":"2026-06-10T01:09:10Z"},{"alias_kind":"pith_short_16","alias_value":"7EJHNUSKE7D2I4M7","created_at":"2026-06-10T01:09:10Z"},{"alias_kind":"pith_short_8","alias_value":"7EJHNUSK","created_at":"2026-06-10T01:09:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:7EJHNUSKE7D2I4M7UVXPEG2JPH","target":"record","payload":{"canonical_record":{"source":{"id":"2309.12092","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2023-09-21T14:06:09Z","cross_cats_sorted":[],"title_canon_sha256":"58e2a3e4fe24dcdf047ee4f92d9acc4041bda8194d6ed407174ccf9e6505f3c1","abstract_canon_sha256":"2f58d68ed0c3030069ff51bd10307ee69f6fe3975144b7d86f14f48d3d2a4bd5"},"schema_version":"1.0"},"canonical_sha256":"f91276d24a27c7a4719fa56ef21b4979e9e983580c5a78d2fe51d4679798aa6d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-10T01:09:10.764289Z","signature_b64":"Ba68IEpz7OAsB37m5DD6/wYabglJk3bZOn3lJm7mb2hY7lCRYyEySDeaeRq7TEQ8yt+fM/7TIoipVbckDpPyCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f91276d24a27c7a4719fa56ef21b4979e9e983580c5a78d2fe51d4679798aa6d","last_reissued_at":"2026-06-10T01:09:10.763705Z","signature_status":"signed_v1","first_computed_at":"2026-06-10T01:09:10.763705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.12092","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":"2026-06-10T01:09:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/ER+mjIAoa1DZjblIGQyx2tK4xEo62xCs6OYRzeRGpGS1VP+y+2s8JGphGU31Tovj3FF97Pk32Uuu+cMShF6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:34:05.143127Z"},"content_sha256":"4d2ebdab5dff634801b7f85f281bf1a161de7ff8765ba40bda79fe8d7d53349f","schema_version":"1.0","event_id":"sha256:4d2ebdab5dff634801b7f85f281bf1a161de7ff8765ba40bda79fe8d7d53349f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:7EJHNUSKE7D2I4M7UVXPEG2JPH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jung-type Inequalities and Blaschke-Santal\\'o Diagrams for Different Diameter Variants","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Mia Runge, Ren\\'e Brandenberg","submitted_at":"2023-09-21T14:06:09Z","abstract_excerpt":"We study geometric inequalities for the circumradius and diameter with respect to general gauges, partly also involving the inradius and the Minkowski asymmetry. There are a number of options for defining the diameter of a convex body that fall apart when we consider non-symmetric gauges. These definitions correspond to different symmetrizations of the gauge, i.e. means of the gauge $C$ and its origin reflection $-C$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.12092","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.12092/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":"2026-06-10T01:09:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VNb06QX91GybqdC0khrHfA5HgDpqYtreYaDp6P1SM//jIa78X7aG6n+sROlAiKAC/CbpTLdSwVzDXam1OH5zBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T11:34:05.143516Z"},"content_sha256":"e36e75533e1715b5454dc466113c1e5d88fcbc70a265635e4ee71b281fa65f98","schema_version":"1.0","event_id":"sha256:e36e75533e1715b5454dc466113c1e5d88fcbc70a265635e4ee71b281fa65f98"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7EJHNUSKE7D2I4M7UVXPEG2JPH/bundle.json","state_url":"https://pith.science/pith/7EJHNUSKE7D2I4M7UVXPEG2JPH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7EJHNUSKE7D2I4M7UVXPEG2JPH/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":"2026-06-21T11:34:05Z","links":{"resolver":"https://pith.science/pith/7EJHNUSKE7D2I4M7UVXPEG2JPH","bundle":"https://pith.science/pith/7EJHNUSKE7D2I4M7UVXPEG2JPH/bundle.json","state":"https://pith.science/pith/7EJHNUSKE7D2I4M7UVXPEG2JPH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7EJHNUSKE7D2I4M7UVXPEG2JPH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:7EJHNUSKE7D2I4M7UVXPEG2JPH","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":"2f58d68ed0c3030069ff51bd10307ee69f6fe3975144b7d86f14f48d3d2a4bd5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2023-09-21T14:06:09Z","title_canon_sha256":"58e2a3e4fe24dcdf047ee4f92d9acc4041bda8194d6ed407174ccf9e6505f3c1"},"schema_version":"1.0","source":{"id":"2309.12092","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.12092","created_at":"2026-06-10T01:09:10Z"},{"alias_kind":"arxiv_version","alias_value":"2309.12092v2","created_at":"2026-06-10T01:09:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.12092","created_at":"2026-06-10T01:09:10Z"},{"alias_kind":"pith_short_12","alias_value":"7EJHNUSKE7D2","created_at":"2026-06-10T01:09:10Z"},{"alias_kind":"pith_short_16","alias_value":"7EJHNUSKE7D2I4M7","created_at":"2026-06-10T01:09:10Z"},{"alias_kind":"pith_short_8","alias_value":"7EJHNUSK","created_at":"2026-06-10T01:09:10Z"}],"graph_snapshots":[{"event_id":"sha256:e36e75533e1715b5454dc466113c1e5d88fcbc70a265635e4ee71b281fa65f98","target":"graph","created_at":"2026-06-10T01:09:10Z","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/2309.12092/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study geometric inequalities for the circumradius and diameter with respect to general gauges, partly also involving the inradius and the Minkowski asymmetry. There are a number of options for defining the diameter of a convex body that fall apart when we consider non-symmetric gauges. These definitions correspond to different symmetrizations of the gauge, i.e. means of the gauge $C$ and its origin reflection $-C$.","authors_text":"Mia Runge, Ren\\'e Brandenberg","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2023-09-21T14:06:09Z","title":"Jung-type Inequalities and Blaschke-Santal\\'o Diagrams for Different Diameter Variants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.12092","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":"sha256:4d2ebdab5dff634801b7f85f281bf1a161de7ff8765ba40bda79fe8d7d53349f","target":"record","created_at":"2026-06-10T01:09:10Z","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":"2f58d68ed0c3030069ff51bd10307ee69f6fe3975144b7d86f14f48d3d2a4bd5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2023-09-21T14:06:09Z","title_canon_sha256":"58e2a3e4fe24dcdf047ee4f92d9acc4041bda8194d6ed407174ccf9e6505f3c1"},"schema_version":"1.0","source":{"id":"2309.12092","kind":"arxiv","version":2}},"canonical_sha256":"f91276d24a27c7a4719fa56ef21b4979e9e983580c5a78d2fe51d4679798aa6d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f91276d24a27c7a4719fa56ef21b4979e9e983580c5a78d2fe51d4679798aa6d","first_computed_at":"2026-06-10T01:09:10.763705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-10T01:09:10.763705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ba68IEpz7OAsB37m5DD6/wYabglJk3bZOn3lJm7mb2hY7lCRYyEySDeaeRq7TEQ8yt+fM/7TIoipVbckDpPyCA==","signature_status":"signed_v1","signed_at":"2026-06-10T01:09:10.764289Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.12092","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d2ebdab5dff634801b7f85f281bf1a161de7ff8765ba40bda79fe8d7d53349f","sha256:e36e75533e1715b5454dc466113c1e5d88fcbc70a265635e4ee71b281fa65f98"],"state_sha256":"c0b0b614483169c80b4bad5ddcc5a57f3c2c955f49630652fa45b493f016a204"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9IvoeHEfjxZXeHIBSjnXW1t/Z2ZqeGH4XSHUOw5UauZyC3d+yShSxz9+9FQQqauAwLFodf9eX7m+GwgjyReYAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T11:34:05.145541Z","bundle_sha256":"c3d5be8edaaf5d2b65d58641a722e288fbba7da84d73bbcaeec1d6cad53adc4a"}}