{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:PPVJVGTYHMBPQENXURUUGOIWD2","short_pith_number":"pith:PPVJVGTY","canonical_record":{"source":{"id":"1711.11088","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-29T20:10:53Z","cross_cats_sorted":[],"title_canon_sha256":"3273801493d4b9698d8458bf352953dd193cd26c8db9826f5f603edcbe79d24b","abstract_canon_sha256":"8acccd83ff9c8466317945a509ceec5a4b7892933d5095bc16d3abf4a5f3a33d"},"schema_version":"1.0"},"canonical_sha256":"7bea9a9a783b02f811b7a4694339161ebc8ac047eed809af601d532625b16c76","source":{"kind":"arxiv","id":"1711.11088","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11088","created_at":"2026-05-18T00:08:54Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11088v2","created_at":"2026-05-18T00:08:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11088","created_at":"2026-05-18T00:08:54Z"},{"alias_kind":"pith_short_12","alias_value":"PPVJVGTYHMBP","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PPVJVGTYHMBPQENX","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PPVJVGTY","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:PPVJVGTYHMBPQENXURUUGOIWD2","target":"record","payload":{"canonical_record":{"source":{"id":"1711.11088","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-29T20:10:53Z","cross_cats_sorted":[],"title_canon_sha256":"3273801493d4b9698d8458bf352953dd193cd26c8db9826f5f603edcbe79d24b","abstract_canon_sha256":"8acccd83ff9c8466317945a509ceec5a4b7892933d5095bc16d3abf4a5f3a33d"},"schema_version":"1.0"},"canonical_sha256":"7bea9a9a783b02f811b7a4694339161ebc8ac047eed809af601d532625b16c76","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:54.917788Z","signature_b64":"W3s6o1R/wMWEPpmsE2NB+8YJk0+dcx2qE9DcXsf+tUuzbNf/vKwFHA1XGVfdRa8P4WR9ZoJVolm+bX1GKlYhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bea9a9a783b02f811b7a4694339161ebc8ac047eed809af601d532625b16c76","last_reissued_at":"2026-05-18T00:08:54.917253Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:54.917253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.11088","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":"2026-05-18T00:08:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bALqmed49KrFMHDP+TfANsJSFiT/xAkLBx/BEbSB58GU7Rew5aH8X4vzyVo8k3h5jbrOe6vNVQHfNAnw/5+3CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:50:43.655570Z"},"content_sha256":"f2f710e7a74c32010829bc7396e94426d46ad3f469934b265a03b58f8697bddb","schema_version":"1.0","event_id":"sha256:f2f710e7a74c32010829bc7396e94426d46ad3f469934b265a03b58f8697bddb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:PPVJVGTYHMBPQENXURUUGOIWD2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Floating functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ben Li, Carsten Schuett, Elisabeth M. Werner","submitted_at":"2017-11-29T20:10:53Z","abstract_excerpt":"We introduce floating bodies for convex, not necessarily bounded subsets of $\\mathbb{R}^n$. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of the integral difference of a log concave function and its floating function. This gives rise to a new affine invariant which bears striking similarities to the Euclidean affine surface area."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11088","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":"2026-05-18T00:08:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nt1hu28WKslBM6MxDqiL5GB5+h2Fhj4nc92rf4vWPmvvOLMXBCUItQvjW6EFk8vJjtPXrvNz5d14UdIa4dEzCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:50:43.656140Z"},"content_sha256":"815e0815f327c5804e0855e424c667d08be407054b3a17955bfd264975b44d53","schema_version":"1.0","event_id":"sha256:815e0815f327c5804e0855e424c667d08be407054b3a17955bfd264975b44d53"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PPVJVGTYHMBPQENXURUUGOIWD2/bundle.json","state_url":"https://pith.science/pith/PPVJVGTYHMBPQENXURUUGOIWD2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PPVJVGTYHMBPQENXURUUGOIWD2/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":"2026-05-31T02:50:43Z","links":{"resolver":"https://pith.science/pith/PPVJVGTYHMBPQENXURUUGOIWD2","bundle":"https://pith.science/pith/PPVJVGTYHMBPQENXURUUGOIWD2/bundle.json","state":"https://pith.science/pith/PPVJVGTYHMBPQENXURUUGOIWD2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PPVJVGTYHMBPQENXURUUGOIWD2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PPVJVGTYHMBPQENXURUUGOIWD2","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":"8acccd83ff9c8466317945a509ceec5a4b7892933d5095bc16d3abf4a5f3a33d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-29T20:10:53Z","title_canon_sha256":"3273801493d4b9698d8458bf352953dd193cd26c8db9826f5f603edcbe79d24b"},"schema_version":"1.0","source":{"id":"1711.11088","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11088","created_at":"2026-05-18T00:08:54Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11088v2","created_at":"2026-05-18T00:08:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11088","created_at":"2026-05-18T00:08:54Z"},{"alias_kind":"pith_short_12","alias_value":"PPVJVGTYHMBP","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PPVJVGTYHMBPQENX","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PPVJVGTY","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:815e0815f327c5804e0855e424c667d08be407054b3a17955bfd264975b44d53","target":"graph","created_at":"2026-05-18T00:08:54Z","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 introduce floating bodies for convex, not necessarily bounded subsets of $\\mathbb{R}^n$. This allows us to define floating functions for convex and log concave functions and log concave measures. We establish the asymptotic behavior of the integral difference of a log concave function and its floating function. This gives rise to a new affine invariant which bears striking similarities to the Euclidean affine surface area.","authors_text":"Ben Li, Carsten Schuett, Elisabeth M. Werner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-29T20:10:53Z","title":"Floating functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11088","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:f2f710e7a74c32010829bc7396e94426d46ad3f469934b265a03b58f8697bddb","target":"record","created_at":"2026-05-18T00:08:54Z","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":"8acccd83ff9c8466317945a509ceec5a4b7892933d5095bc16d3abf4a5f3a33d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-29T20:10:53Z","title_canon_sha256":"3273801493d4b9698d8458bf352953dd193cd26c8db9826f5f603edcbe79d24b"},"schema_version":"1.0","source":{"id":"1711.11088","kind":"arxiv","version":2}},"canonical_sha256":"7bea9a9a783b02f811b7a4694339161ebc8ac047eed809af601d532625b16c76","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bea9a9a783b02f811b7a4694339161ebc8ac047eed809af601d532625b16c76","first_computed_at":"2026-05-18T00:08:54.917253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:54.917253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W3s6o1R/wMWEPpmsE2NB+8YJk0+dcx2qE9DcXsf+tUuzbNf/vKwFHA1XGVfdRa8P4WR9ZoJVolm+bX1GKlYhBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:54.917788Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11088","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2f710e7a74c32010829bc7396e94426d46ad3f469934b265a03b58f8697bddb","sha256:815e0815f327c5804e0855e424c667d08be407054b3a17955bfd264975b44d53"],"state_sha256":"c4db8a3581502c0d16eaec6bdfffa3a3aa3e2de5da33c37304db8ef12a9a81b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v69R4hc71BfTPsrC9n5vX9qAh/o35SvdSWCJrsQVsd0DkaNpOXaqTHMwSvG/i+/j7JL2PSXfuYeV7F+FG4qpCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:50:43.658337Z","bundle_sha256":"e25bad89a282473458f8139307c9185adef8c3af76ff0e334ea0849cb48fed9f"}}