{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:3HXJ2P3AV4NNDXQJWJALUEWC7Z","short_pith_number":"pith:3HXJ2P3A","canonical_record":{"source":{"id":"2305.17468","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2023-05-27T12:53:45Z","cross_cats_sorted":["math.DG","math.FA"],"title_canon_sha256":"1e0c2974a6c90e0a51d15ad0b0ebc5a557ea425c3f30b410d52ef23075a46afb","abstract_canon_sha256":"ab498db446ff2d9ad9910dfe374598ab32f6b2680c2c94ba0c6d34cce2050643"},"schema_version":"1.0"},"canonical_sha256":"d9ee9d3f60af1ad1de09b240ba12c2fe760bc02850bcd1650e4e0401a0478e64","source":{"kind":"arxiv","id":"2305.17468","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.17468","created_at":"2026-07-05T09:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"2305.17468v4","created_at":"2026-07-05T09:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.17468","created_at":"2026-07-05T09:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"3HXJ2P3AV4NN","created_at":"2026-07-05T09:30:03Z"},{"alias_kind":"pith_short_16","alias_value":"3HXJ2P3AV4NNDXQJ","created_at":"2026-07-05T09:30:03Z"},{"alias_kind":"pith_short_8","alias_value":"3HXJ2P3A","created_at":"2026-07-05T09:30:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:3HXJ2P3AV4NNDXQJWJALUEWC7Z","target":"record","payload":{"canonical_record":{"source":{"id":"2305.17468","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2023-05-27T12:53:45Z","cross_cats_sorted":["math.DG","math.FA"],"title_canon_sha256":"1e0c2974a6c90e0a51d15ad0b0ebc5a557ea425c3f30b410d52ef23075a46afb","abstract_canon_sha256":"ab498db446ff2d9ad9910dfe374598ab32f6b2680c2c94ba0c6d34cce2050643"},"schema_version":"1.0"},"canonical_sha256":"d9ee9d3f60af1ad1de09b240ba12c2fe760bc02850bcd1650e4e0401a0478e64","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:30:03.032166Z","signature_b64":"yZ8s/DAitrE/4b+zGkxc8IvmAGD48vXPYhy1W/ysJxfwBgrd+zNrxVxoW6bPscpwMR41eu6Cg12FARRn1uW7Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9ee9d3f60af1ad1de09b240ba12c2fe760bc02850bcd1650e4e0401a0478e64","last_reissued_at":"2026-07-05T09:30:03.031794Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:30:03.031794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2305.17468","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:30:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PWnsiz7qp2OS/7NMoIpnyrqE7C9L+KkR8DhCqqGfibfZqQLn2jyKfpFxgLYO2YX1lhiN5BX3WUzUYIdIZ6DxDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T23:45:13.158486Z"},"content_sha256":"dc36be1f5ce98413b197d94c463ea3774110082f68a08d0d5b91b6fd0f97cd83","schema_version":"1.0","event_id":"sha256:dc36be1f5ce98413b197d94c463ea3774110082f68a08d0d5b91b6fd0f97cd83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:3HXJ2P3AV4NNDXQJWJALUEWC7Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher-Order Lp Isoperimetric and Sobolev Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.MG","authors_text":"Deping Ye, Dylan Langharst, Eli Putterman, Juli\\'an Haddad, Michael Roysdon","submitted_at":"2023-05-27T12:53:45Z","abstract_excerpt":"Schneider introduced an inter-dimensional difference body operator on convex bodies and proved an associated inequality. In the prequel to this work, we showed that this concept can be extended to a rich class of operators from convex geometry and proved the associated isoperimetric inequalities. The role of cosine-like operators, which generate convex bodies in $\\mathbb R^n$ from those in $\\mathbb R^n$, were replaced by inter-dimensional simplicial operators, which generate convex bodies in $\\mathbb R^{nm}$ from those in $\\mathbb R^{n}$ (or vice versa). In this work, we treat the $L^p$ extens"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.17468","kind":"arxiv","version":4},"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/2305.17468/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":"2026-07-05T09:30:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ODXP6De9wrbYV2sInakotIdZC0JymNRA42kHboVQRX23C0yxeU+OVxrdi6HQp/ojC9vsYwP+AS5vnlJOE05zDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T23:45:13.159206Z"},"content_sha256":"1b8801874ee4193b12ec11b4e90e1a121399bd9a7c0b967d3d053694c274bbc4","schema_version":"1.0","event_id":"sha256:1b8801874ee4193b12ec11b4e90e1a121399bd9a7c0b967d3d053694c274bbc4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3HXJ2P3AV4NNDXQJWJALUEWC7Z/bundle.json","state_url":"https://pith.science/pith/3HXJ2P3AV4NNDXQJWJALUEWC7Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3HXJ2P3AV4NNDXQJWJALUEWC7Z/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":"2026-08-21T23:45:13Z","links":{"resolver":"https://pith.science/pith/3HXJ2P3AV4NNDXQJWJALUEWC7Z","bundle":"https://pith.science/pith/3HXJ2P3AV4NNDXQJWJALUEWC7Z/bundle.json","state":"https://pith.science/pith/3HXJ2P3AV4NNDXQJWJALUEWC7Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3HXJ2P3AV4NNDXQJWJALUEWC7Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:3HXJ2P3AV4NNDXQJWJALUEWC7Z","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":"ab498db446ff2d9ad9910dfe374598ab32f6b2680c2c94ba0c6d34cce2050643","cross_cats_sorted":["math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2023-05-27T12:53:45Z","title_canon_sha256":"1e0c2974a6c90e0a51d15ad0b0ebc5a557ea425c3f30b410d52ef23075a46afb"},"schema_version":"1.0","source":{"id":"2305.17468","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2305.17468","created_at":"2026-07-05T09:30:03Z"},{"alias_kind":"arxiv_version","alias_value":"2305.17468v4","created_at":"2026-07-05T09:30:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2305.17468","created_at":"2026-07-05T09:30:03Z"},{"alias_kind":"pith_short_12","alias_value":"3HXJ2P3AV4NN","created_at":"2026-07-05T09:30:03Z"},{"alias_kind":"pith_short_16","alias_value":"3HXJ2P3AV4NNDXQJ","created_at":"2026-07-05T09:30:03Z"},{"alias_kind":"pith_short_8","alias_value":"3HXJ2P3A","created_at":"2026-07-05T09:30:03Z"}],"graph_snapshots":[{"event_id":"sha256:1b8801874ee4193b12ec11b4e90e1a121399bd9a7c0b967d3d053694c274bbc4","target":"graph","created_at":"2026-07-05T09:30:03Z","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/2305.17468/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Schneider introduced an inter-dimensional difference body operator on convex bodies and proved an associated inequality. In the prequel to this work, we showed that this concept can be extended to a rich class of operators from convex geometry and proved the associated isoperimetric inequalities. The role of cosine-like operators, which generate convex bodies in $\\mathbb R^n$ from those in $\\mathbb R^n$, were replaced by inter-dimensional simplicial operators, which generate convex bodies in $\\mathbb R^{nm}$ from those in $\\mathbb R^{n}$ (or vice versa). In this work, we treat the $L^p$ extens","authors_text":"Deping Ye, Dylan Langharst, Eli Putterman, Juli\\'an Haddad, Michael Roysdon","cross_cats":["math.DG","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2023-05-27T12:53:45Z","title":"Higher-Order Lp Isoperimetric and Sobolev Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.17468","kind":"arxiv","version":4},"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:dc36be1f5ce98413b197d94c463ea3774110082f68a08d0d5b91b6fd0f97cd83","target":"record","created_at":"2026-07-05T09:30:03Z","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":"ab498db446ff2d9ad9910dfe374598ab32f6b2680c2c94ba0c6d34cce2050643","cross_cats_sorted":["math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2023-05-27T12:53:45Z","title_canon_sha256":"1e0c2974a6c90e0a51d15ad0b0ebc5a557ea425c3f30b410d52ef23075a46afb"},"schema_version":"1.0","source":{"id":"2305.17468","kind":"arxiv","version":4}},"canonical_sha256":"d9ee9d3f60af1ad1de09b240ba12c2fe760bc02850bcd1650e4e0401a0478e64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9ee9d3f60af1ad1de09b240ba12c2fe760bc02850bcd1650e4e0401a0478e64","first_computed_at":"2026-07-05T09:30:03.031794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:30:03.031794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yZ8s/DAitrE/4b+zGkxc8IvmAGD48vXPYhy1W/ysJxfwBgrd+zNrxVxoW6bPscpwMR41eu6Cg12FARRn1uW7Dg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:30:03.032166Z","signed_message":"canonical_sha256_bytes"},"source_id":"2305.17468","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc36be1f5ce98413b197d94c463ea3774110082f68a08d0d5b91b6fd0f97cd83","sha256:1b8801874ee4193b12ec11b4e90e1a121399bd9a7c0b967d3d053694c274bbc4"],"state_sha256":"6ada584d30667455dd2358e85872120e55c79a59ad52cf78ab714d583ad5f4c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d0jnx89hxsPQuKbiWkPIY1nmzw6J7P2IsbUVN17NyVvEXi9IzP/oCAgsiMED19Goc5kCy5tcnoFAColodsT/CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T23:45:13.165448Z","bundle_sha256":"b586aea693f4431b117706bd47b8d95ddf550fa87a97fb2c00bbb58ddec2b52a"}}