{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:47O3TOKSX5CUKBECDNYDX4BQ3Y","short_pith_number":"pith:47O3TOKS","canonical_record":{"source":{"id":"1711.11549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T18:12:41Z","cross_cats_sorted":[],"title_canon_sha256":"aeaa6baccbbfcbcf5e292d114c3fc831cffd8d0e479028ccf08cc1673e6ef7af","abstract_canon_sha256":"f90d0e740ec2114941c8ef8c9f39c6ccc2c5d22f19303bcc3bd33d30569c20c6"},"schema_version":"1.0"},"canonical_sha256":"e7ddb9b952bf454504821b703bf030de0aa9e650f14a0aa17ec584f6e472f4bd","source":{"kind":"arxiv","id":"1711.11549","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11549","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11549v1","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11549","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"47O3TOKSX5CU","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"47O3TOKSX5CUKBEC","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"47O3TOKS","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:47O3TOKSX5CUKBECDNYDX4BQ3Y","target":"record","payload":{"canonical_record":{"source":{"id":"1711.11549","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T18:12:41Z","cross_cats_sorted":[],"title_canon_sha256":"aeaa6baccbbfcbcf5e292d114c3fc831cffd8d0e479028ccf08cc1673e6ef7af","abstract_canon_sha256":"f90d0e740ec2114941c8ef8c9f39c6ccc2c5d22f19303bcc3bd33d30569c20c6"},"schema_version":"1.0"},"canonical_sha256":"e7ddb9b952bf454504821b703bf030de0aa9e650f14a0aa17ec584f6e472f4bd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:11.310000Z","signature_b64":"IgBHil6EwGbT5eHpyg6T9vzZhuSFaomEj2n+Sv+Qxg5DIrizLPIiRhpXnBTcNZIJKg3ux6yZw/y43vDnQVWFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7ddb9b952bf454504821b703bf030de0aa9e650f14a0aa17ec584f6e472f4bd","last_reissued_at":"2026-05-18T00:29:11.309418Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:11.309418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.11549","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":"2026-05-18T00:29:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ruwnzuKwkfaGT7PIEkN7tKPyla3Jv9GD6x7v29JUEpeoMFLuhoJjkVUBwWO5Y3BxhfwkApJBGFQMOsoIt6wAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:39:28.437503Z"},"content_sha256":"9f9c342bc5310c7c4871155f208fd689121cbbb5487e21fed37819788343ed88","schema_version":"1.0","event_id":"sha256:9f9c342bc5310c7c4871155f208fd689121cbbb5487e21fed37819788343ed88"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:47O3TOKSX5CUKBECDNYDX4BQ3Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp Sobolev type embeddings on the entire Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Andrea Cianchi, Angela Alberico, Lenka Slavikova, Lubos Pick","submitted_at":"2017-11-30T18:12:41Z","abstract_excerpt":"A comprehensive approach to Sobolev-type embeddings, involving arbitrary rearrangement- invariant norms on the entire Euclidean space R^n, is offered. In particular, the optimal target space in any such embedding is exhibited. Crucial in our analysis is a new reduction principle for the relevant embeddings, showing their equivalence to a couple of considerably simpler one-dimensional inequalities. Applications to the classes of the Orlicz-Sobolev and the Lorentz-Sobolev spaces are also presented. These contributions fill in a gap in the existing literature, where sharp results in such a genera"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11549","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":""},"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":"2026-05-18T00:29:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s1bGh6wBFfEhNGonU3LFPwRx/2OS9PSWzy4O4JSFn6Zo8H32MzYeKmKC7yjkNGGB5JiW2HPjhaIwTeR5P47RAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T16:39:28.438206Z"},"content_sha256":"6fecfeeeab16fa4e2d74d93c3aaac22c1a149c91decb3a49477778f926ce7fb3","schema_version":"1.0","event_id":"sha256:6fecfeeeab16fa4e2d74d93c3aaac22c1a149c91decb3a49477778f926ce7fb3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/47O3TOKSX5CUKBECDNYDX4BQ3Y/bundle.json","state_url":"https://pith.science/pith/47O3TOKSX5CUKBECDNYDX4BQ3Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/47O3TOKSX5CUKBECDNYDX4BQ3Y/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":"2026-05-30T16:39:28Z","links":{"resolver":"https://pith.science/pith/47O3TOKSX5CUKBECDNYDX4BQ3Y","bundle":"https://pith.science/pith/47O3TOKSX5CUKBECDNYDX4BQ3Y/bundle.json","state":"https://pith.science/pith/47O3TOKSX5CUKBECDNYDX4BQ3Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/47O3TOKSX5CUKBECDNYDX4BQ3Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:47O3TOKSX5CUKBECDNYDX4BQ3Y","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":"f90d0e740ec2114941c8ef8c9f39c6ccc2c5d22f19303bcc3bd33d30569c20c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T18:12:41Z","title_canon_sha256":"aeaa6baccbbfcbcf5e292d114c3fc831cffd8d0e479028ccf08cc1673e6ef7af"},"schema_version":"1.0","source":{"id":"1711.11549","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11549","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11549v1","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11549","created_at":"2026-05-18T00:29:11Z"},{"alias_kind":"pith_short_12","alias_value":"47O3TOKSX5CU","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"47O3TOKSX5CUKBEC","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"47O3TOKS","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:6fecfeeeab16fa4e2d74d93c3aaac22c1a149c91decb3a49477778f926ce7fb3","target":"graph","created_at":"2026-05-18T00:29:11Z","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":"A comprehensive approach to Sobolev-type embeddings, involving arbitrary rearrangement- invariant norms on the entire Euclidean space R^n, is offered. In particular, the optimal target space in any such embedding is exhibited. Crucial in our analysis is a new reduction principle for the relevant embeddings, showing their equivalence to a couple of considerably simpler one-dimensional inequalities. Applications to the classes of the Orlicz-Sobolev and the Lorentz-Sobolev spaces are also presented. These contributions fill in a gap in the existing literature, where sharp results in such a genera","authors_text":"Andrea Cianchi, Angela Alberico, Lenka Slavikova, Lubos Pick","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T18:12:41Z","title":"Sharp Sobolev type embeddings on the entire Euclidean space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11549","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":"sha256:9f9c342bc5310c7c4871155f208fd689121cbbb5487e21fed37819788343ed88","target":"record","created_at":"2026-05-18T00:29:11Z","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":"f90d0e740ec2114941c8ef8c9f39c6ccc2c5d22f19303bcc3bd33d30569c20c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-11-30T18:12:41Z","title_canon_sha256":"aeaa6baccbbfcbcf5e292d114c3fc831cffd8d0e479028ccf08cc1673e6ef7af"},"schema_version":"1.0","source":{"id":"1711.11549","kind":"arxiv","version":1}},"canonical_sha256":"e7ddb9b952bf454504821b703bf030de0aa9e650f14a0aa17ec584f6e472f4bd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7ddb9b952bf454504821b703bf030de0aa9e650f14a0aa17ec584f6e472f4bd","first_computed_at":"2026-05-18T00:29:11.309418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:11.309418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IgBHil6EwGbT5eHpyg6T9vzZhuSFaomEj2n+Sv+Qxg5DIrizLPIiRhpXnBTcNZIJKg3ux6yZw/y43vDnQVWFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:11.310000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11549","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f9c342bc5310c7c4871155f208fd689121cbbb5487e21fed37819788343ed88","sha256:6fecfeeeab16fa4e2d74d93c3aaac22c1a149c91decb3a49477778f926ce7fb3"],"state_sha256":"80cc2f82256e4a527f986838325280660cd330824a5d0bf00782941d05b2eeb4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/FhgmdhjjIeQ7ZbYc87WdkNP+afmCB0Fsek+IRDXRE3/QQ8EgKRYI7rw02DlV/VcY8cwIVKUCS30KdXviBDPDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T16:39:28.442209Z","bundle_sha256":"10183d7c328c878e6d54882b0b9b647c33b478d90b6a8622937e825033d21bb8"}}