{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:S4GEKJ2GMKBUHFN4IZJK6KIVB4","short_pith_number":"pith:S4GEKJ2G","canonical_record":{"source":{"id":"1706.00591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-02T08:45:59Z","cross_cats_sorted":["math.DG","math.FA"],"title_canon_sha256":"7f518dc0aa2453da51290877f7e1dd8aab481c3da814b14429697bc8132a891a","abstract_canon_sha256":"91b9afccf58ca7c15654e16587b7dea52630e8d4429d6ab2258617ab30ae6de4"},"schema_version":"1.0"},"canonical_sha256":"970c45274662834395bc4652af29150f02ad65a17ae5556ab866d1df17e7c8b3","source":{"kind":"arxiv","id":"1706.00591","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00591","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00591v2","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00591","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"S4GEKJ2GMKBU","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S4GEKJ2GMKBUHFN4","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S4GEKJ2G","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:S4GEKJ2GMKBUHFN4IZJK6KIVB4","target":"record","payload":{"canonical_record":{"source":{"id":"1706.00591","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-02T08:45:59Z","cross_cats_sorted":["math.DG","math.FA"],"title_canon_sha256":"7f518dc0aa2453da51290877f7e1dd8aab481c3da814b14429697bc8132a891a","abstract_canon_sha256":"91b9afccf58ca7c15654e16587b7dea52630e8d4429d6ab2258617ab30ae6de4"},"schema_version":"1.0"},"canonical_sha256":"970c45274662834395bc4652af29150f02ad65a17ae5556ab866d1df17e7c8b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:13.454986Z","signature_b64":"E04W+d0ClO5pfDabOUpvLig/IwhqD3U8BRnLjS/R7b5Mz6VOnVPNpjY8uOKLXMF1uIP1RtoAy8HcKDrMCNaUCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"970c45274662834395bc4652af29150f02ad65a17ae5556ab866d1df17e7c8b3","last_reissued_at":"2026-05-18T00:17:13.454380Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:13.454380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.00591","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":"2026-05-18T00:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E0WaonfI/iW7X5gp2yYzTWqrtsgo5OwGcAhwC4uSQ0MIQnT2Pv01UIrO/r/jbAjvzgk8kESh1ePAYpDO/n0aCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:57:06.682240Z"},"content_sha256":"4f61c9308b5ffd041434e91dc6323f05fb90ddc709599bb5bda4b8da7fa6898d","schema_version":"1.0","event_id":"sha256:4f61c9308b5ffd041434e91dc6323f05fb90ddc709599bb5bda4b8da7fa6898d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:S4GEKJ2GMKBUHFN4IZJK6KIVB4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L^{p}$-interpolation inequalities and global Sobolev regularity results (with an appendix by Ognjen Milatovic)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.FA"],"primary_cat":"math.AP","authors_text":"Batu G\\\"uneysu, Stefano Pigola","submitted_at":"2017-06-02T08:45:59Z","abstract_excerpt":"On any complete Riemannian manifold $M$ and for all $p\\in [2,\\infty)$, we prove a family of second order $L^{p}$-interpolation inequalities that arise from the following simple $L^{p}$-estimate valid for every $u \\in C^{\\infty}(M)$: $$\n  \\|\\nabla u\\|_{p}^p \\leq \\|u \\Delta_{p} u\\|_1\\in [0,\\infty], $$ where $\\Delta_p$ denotes the $p$-Laplace operator. We show that these inequalities, in combination with abstract functional analytic arguments, allow to establish new global Sobolev regularity results for $L^p$-solutions of the Poisson equation for all $p\\in (1,\\infty)$, and new global Sobolev regu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00591","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":"2026-05-18T00:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YbObSVWrIhR1nt5IXJyG9QkBRRnX7BMP+vsAEV0NfGR8xx8jowAKGLf1+Yck7X+gqhLHSvaLVS2XAZyyEp64DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T07:57:06.682606Z"},"content_sha256":"3c798b551a3b56aec11edd1c05da7aab755baf41c1f53da7f1a7ef06d2bd0568","schema_version":"1.0","event_id":"sha256:3c798b551a3b56aec11edd1c05da7aab755baf41c1f53da7f1a7ef06d2bd0568"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S4GEKJ2GMKBUHFN4IZJK6KIVB4/bundle.json","state_url":"https://pith.science/pith/S4GEKJ2GMKBUHFN4IZJK6KIVB4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S4GEKJ2GMKBUHFN4IZJK6KIVB4/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":"2026-06-01T07:57:06Z","links":{"resolver":"https://pith.science/pith/S4GEKJ2GMKBUHFN4IZJK6KIVB4","bundle":"https://pith.science/pith/S4GEKJ2GMKBUHFN4IZJK6KIVB4/bundle.json","state":"https://pith.science/pith/S4GEKJ2GMKBUHFN4IZJK6KIVB4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S4GEKJ2GMKBUHFN4IZJK6KIVB4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:S4GEKJ2GMKBUHFN4IZJK6KIVB4","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":"91b9afccf58ca7c15654e16587b7dea52630e8d4429d6ab2258617ab30ae6de4","cross_cats_sorted":["math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-02T08:45:59Z","title_canon_sha256":"7f518dc0aa2453da51290877f7e1dd8aab481c3da814b14429697bc8132a891a"},"schema_version":"1.0","source":{"id":"1706.00591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.00591","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"1706.00591v2","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.00591","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"S4GEKJ2GMKBU","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"S4GEKJ2GMKBUHFN4","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"S4GEKJ2G","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:3c798b551a3b56aec11edd1c05da7aab755baf41c1f53da7f1a7ef06d2bd0568","target":"graph","created_at":"2026-05-18T00:17:13Z","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":"On any complete Riemannian manifold $M$ and for all $p\\in [2,\\infty)$, we prove a family of second order $L^{p}$-interpolation inequalities that arise from the following simple $L^{p}$-estimate valid for every $u \\in C^{\\infty}(M)$: $$\n  \\|\\nabla u\\|_{p}^p \\leq \\|u \\Delta_{p} u\\|_1\\in [0,\\infty], $$ where $\\Delta_p$ denotes the $p$-Laplace operator. We show that these inequalities, in combination with abstract functional analytic arguments, allow to establish new global Sobolev regularity results for $L^p$-solutions of the Poisson equation for all $p\\in (1,\\infty)$, and new global Sobolev regu","authors_text":"Batu G\\\"uneysu, Stefano Pigola","cross_cats":["math.DG","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-02T08:45:59Z","title":"$L^{p}$-interpolation inequalities and global Sobolev regularity results (with an appendix by Ognjen Milatovic)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00591","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":"sha256:4f61c9308b5ffd041434e91dc6323f05fb90ddc709599bb5bda4b8da7fa6898d","target":"record","created_at":"2026-05-18T00:17:13Z","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":"91b9afccf58ca7c15654e16587b7dea52630e8d4429d6ab2258617ab30ae6de4","cross_cats_sorted":["math.DG","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-06-02T08:45:59Z","title_canon_sha256":"7f518dc0aa2453da51290877f7e1dd8aab481c3da814b14429697bc8132a891a"},"schema_version":"1.0","source":{"id":"1706.00591","kind":"arxiv","version":2}},"canonical_sha256":"970c45274662834395bc4652af29150f02ad65a17ae5556ab866d1df17e7c8b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"970c45274662834395bc4652af29150f02ad65a17ae5556ab866d1df17e7c8b3","first_computed_at":"2026-05-18T00:17:13.454380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:13.454380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E04W+d0ClO5pfDabOUpvLig/IwhqD3U8BRnLjS/R7b5Mz6VOnVPNpjY8uOKLXMF1uIP1RtoAy8HcKDrMCNaUCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:13.454986Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.00591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f61c9308b5ffd041434e91dc6323f05fb90ddc709599bb5bda4b8da7fa6898d","sha256:3c798b551a3b56aec11edd1c05da7aab755baf41c1f53da7f1a7ef06d2bd0568"],"state_sha256":"a663351f61a7c386d2b0a4587dfbfeda68e0a04b2bd801c4cbc08451cd315687"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ftRgetCx3o1FTHbcuot3/m0RO4MlbPX1NZ8Smju2ITT+IqauD2pP6qqC6lIjb4VPz3lMeyy9POuowwqhOG49Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T07:57:06.684632Z","bundle_sha256":"9f16edfb2637cd39a29963d93ab73f434e9ed1879cc363e0ec4b1ee42f0d0f98"}}