{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EVOZ7T6OGF7NNHWXVXPC3LZHDS","short_pith_number":"pith:EVOZ7T6O","canonical_record":{"source":{"id":"1811.09392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-23T09:09:56Z","cross_cats_sorted":[],"title_canon_sha256":"7ed515ed5790e1d672d9f1271010b23a5adcbb6e3d01c0fb400d9ea8c3bf0c0d","abstract_canon_sha256":"2142673e3ecc400e1849f3ee02b227c11a4389219d2732ef2212fccffaccd821"},"schema_version":"1.0"},"canonical_sha256":"255d9fcfce317ed69ed7adde2daf271c80494deed20c4d907113ffba6a51d970","source":{"kind":"arxiv","id":"1811.09392","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09392","created_at":"2026-05-18T00:00:03Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09392v1","created_at":"2026-05-18T00:00:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09392","created_at":"2026-05-18T00:00:03Z"},{"alias_kind":"pith_short_12","alias_value":"EVOZ7T6OGF7N","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EVOZ7T6OGF7NNHWX","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EVOZ7T6O","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EVOZ7T6OGF7NNHWXVXPC3LZHDS","target":"record","payload":{"canonical_record":{"source":{"id":"1811.09392","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-23T09:09:56Z","cross_cats_sorted":[],"title_canon_sha256":"7ed515ed5790e1d672d9f1271010b23a5adcbb6e3d01c0fb400d9ea8c3bf0c0d","abstract_canon_sha256":"2142673e3ecc400e1849f3ee02b227c11a4389219d2732ef2212fccffaccd821"},"schema_version":"1.0"},"canonical_sha256":"255d9fcfce317ed69ed7adde2daf271c80494deed20c4d907113ffba6a51d970","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:03.508179Z","signature_b64":"jpTBsjlM/KcWXXQdM/Ismw9L1nh/ViYxDeyU1nNWk90EK3yRjkW2FcD7QfSmfiufjrShXxV1jrLdMervwRc6Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"255d9fcfce317ed69ed7adde2daf271c80494deed20c4d907113ffba6a51d970","last_reissued_at":"2026-05-18T00:00:03.507715Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:03.507715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.09392","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":"2026-05-18T00:00:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OdCambbo7amNwznmQTylBSo4EMIlQwOa0bskA7F+4x/4mhB8YuBw4kXIcxPXdnIeTftiiNBe4iARZrz7BDPKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:16:05.692509Z"},"content_sha256":"2ffd2d34160b0b81edbb409b440508863e68b579bd89b1cc7321f4d856e92a5b","schema_version":"1.0","event_id":"sha256:2ffd2d34160b0b81edbb409b440508863e68b579bd89b1cc7321f4d856e92a5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EVOZ7T6OGF7NNHWXVXPC3LZHDS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L^\\infty$-estimates for the Neumann problem on general domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"A.F.M. ter Elst, Hannes Meinlschmidt, Joachim Rehberg","submitted_at":"2018-11-23T09:09:56Z","abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^d$ be bounded open and connected. Suppose that $W^{1,2}(\\Omega) \\subset L^r(\\Omega)$ for some $r > 2$. Let $A$ be a pure second-order elliptic differential operator with bounded real measurable coefficients on $\\Omega$. Let $q > d$ with $\\frac{1}{2}-\\frac{1}{q} > \\frac{1}{r}$. If $p$ is the dual exponent of $q$, then we show that the pre-image of the space $(W^{1,p}(\\Omega))^*$ under the map $A$ is contained in the space of bounded functions on $\\Omega$. The considerations are complemented by results on optimal Sobolev regularity for $A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09392","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":"2026-05-18T00:00:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xG5acvxxmLQIgSizjG9tFDvyElZY8RrZVP7NhHN2XXpmYWbkVrKwHBU6N8yN0DW0porrKn2uGo3g240VpxfvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:16:05.692868Z"},"content_sha256":"f2b0165377d64c27e0543619bd3f11d8bd788884d8c8130fa31a2aecbef26d69","schema_version":"1.0","event_id":"sha256:f2b0165377d64c27e0543619bd3f11d8bd788884d8c8130fa31a2aecbef26d69"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EVOZ7T6OGF7NNHWXVXPC3LZHDS/bundle.json","state_url":"https://pith.science/pith/EVOZ7T6OGF7NNHWXVXPC3LZHDS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EVOZ7T6OGF7NNHWXVXPC3LZHDS/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":"2026-05-27T14:16:05Z","links":{"resolver":"https://pith.science/pith/EVOZ7T6OGF7NNHWXVXPC3LZHDS","bundle":"https://pith.science/pith/EVOZ7T6OGF7NNHWXVXPC3LZHDS/bundle.json","state":"https://pith.science/pith/EVOZ7T6OGF7NNHWXVXPC3LZHDS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EVOZ7T6OGF7NNHWXVXPC3LZHDS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EVOZ7T6OGF7NNHWXVXPC3LZHDS","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":"2142673e3ecc400e1849f3ee02b227c11a4389219d2732ef2212fccffaccd821","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-23T09:09:56Z","title_canon_sha256":"7ed515ed5790e1d672d9f1271010b23a5adcbb6e3d01c0fb400d9ea8c3bf0c0d"},"schema_version":"1.0","source":{"id":"1811.09392","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09392","created_at":"2026-05-18T00:00:03Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09392v1","created_at":"2026-05-18T00:00:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09392","created_at":"2026-05-18T00:00:03Z"},{"alias_kind":"pith_short_12","alias_value":"EVOZ7T6OGF7N","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"EVOZ7T6OGF7NNHWX","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"EVOZ7T6O","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:f2b0165377d64c27e0543619bd3f11d8bd788884d8c8130fa31a2aecbef26d69","target":"graph","created_at":"2026-05-18T00:00:03Z","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"},"paper":{"abstract_excerpt":"Let $\\Omega \\subset \\mathbb{R}^d$ be bounded open and connected. Suppose that $W^{1,2}(\\Omega) \\subset L^r(\\Omega)$ for some $r > 2$. Let $A$ be a pure second-order elliptic differential operator with bounded real measurable coefficients on $\\Omega$. Let $q > d$ with $\\frac{1}{2}-\\frac{1}{q} > \\frac{1}{r}$. If $p$ is the dual exponent of $q$, then we show that the pre-image of the space $(W^{1,p}(\\Omega))^*$ under the map $A$ is contained in the space of bounded functions on $\\Omega$. The considerations are complemented by results on optimal Sobolev regularity for $A$.","authors_text":"A.F.M. ter Elst, Hannes Meinlschmidt, Joachim Rehberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-23T09:09:56Z","title":"$L^\\infty$-estimates for the Neumann problem on general domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09392","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":"sha256:2ffd2d34160b0b81edbb409b440508863e68b579bd89b1cc7321f4d856e92a5b","target":"record","created_at":"2026-05-18T00:00:03Z","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":"2142673e3ecc400e1849f3ee02b227c11a4389219d2732ef2212fccffaccd821","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-23T09:09:56Z","title_canon_sha256":"7ed515ed5790e1d672d9f1271010b23a5adcbb6e3d01c0fb400d9ea8c3bf0c0d"},"schema_version":"1.0","source":{"id":"1811.09392","kind":"arxiv","version":1}},"canonical_sha256":"255d9fcfce317ed69ed7adde2daf271c80494deed20c4d907113ffba6a51d970","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"255d9fcfce317ed69ed7adde2daf271c80494deed20c4d907113ffba6a51d970","first_computed_at":"2026-05-18T00:00:03.507715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:03.507715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jpTBsjlM/KcWXXQdM/Ismw9L1nh/ViYxDeyU1nNWk90EK3yRjkW2FcD7QfSmfiufjrShXxV1jrLdMervwRc6Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:03.508179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09392","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2ffd2d34160b0b81edbb409b440508863e68b579bd89b1cc7321f4d856e92a5b","sha256:f2b0165377d64c27e0543619bd3f11d8bd788884d8c8130fa31a2aecbef26d69"],"state_sha256":"667c36d4416d3ff367b868d2e4f93ed684ec93f8a65ca50434307d954d4d937a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SLV+tH9ycKEssdiPYPcv7Kk+4ZGfEy3tHCvl/zIyntXL9QPHmICbHehsOC971XmXAx703Rd/pH9AHsk6uyiJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:16:05.696066Z","bundle_sha256":"fe8cb5e17ccf5393e2a86a7e7b700a79532e1c9f4b6f05d65263fcb6865f01c4"}}