{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:UH44EUVD24W2DN2RDUEP7JCR2H","short_pith_number":"pith:UH44EUVD","canonical_record":{"source":{"id":"2002.02963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-06T22:03:25Z","cross_cats_sorted":[],"title_canon_sha256":"1a5d1e6f422366a872daf43e38128af0905740e0ecf99975f79b495f0d5e0b08","abstract_canon_sha256":"3d59fd72a3e2bed701b65020e962f76df640e62680ac74d28c8785bb6a9b9f12"},"schema_version":"1.0"},"canonical_sha256":"a1f9c252a3d72da1b7511d08ffa451d1d717cff782fadceb1a5b211d0738e795","source":{"kind":"arxiv","id":"2002.02963","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.02963","created_at":"2026-07-05T00:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"2002.02963v1","created_at":"2026-07-05T00:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.02963","created_at":"2026-07-05T00:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"UH44EUVD24W2","created_at":"2026-07-05T00:39:17Z"},{"alias_kind":"pith_short_16","alias_value":"UH44EUVD24W2DN2R","created_at":"2026-07-05T00:39:17Z"},{"alias_kind":"pith_short_8","alias_value":"UH44EUVD","created_at":"2026-07-05T00:39:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:UH44EUVD24W2DN2RDUEP7JCR2H","target":"record","payload":{"canonical_record":{"source":{"id":"2002.02963","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-06T22:03:25Z","cross_cats_sorted":[],"title_canon_sha256":"1a5d1e6f422366a872daf43e38128af0905740e0ecf99975f79b495f0d5e0b08","abstract_canon_sha256":"3d59fd72a3e2bed701b65020e962f76df640e62680ac74d28c8785bb6a9b9f12"},"schema_version":"1.0"},"canonical_sha256":"a1f9c252a3d72da1b7511d08ffa451d1d717cff782fadceb1a5b211d0738e795","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:39:17.700025Z","signature_b64":"wZFHBrzBZX27Mhpl6DZM9zJwkZD5incHrku1fY9CAMYm7fg+7VEOhPsDTNWpay1tKVoBBSKg0Cg0vtraDDwHDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1f9c252a3d72da1b7511d08ffa451d1d717cff782fadceb1a5b211d0738e795","last_reissued_at":"2026-07-05T00:39:17.699662Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:39:17.699662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.02963","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":"2026-07-05T00:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oionjG28obUJPiZm+wgznq8+lJB9ib8wIbJG6sIdJ6Q0oWcp93KRAYkRFRmakbO7ZctfyETQ5MLlUle0dC0mDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T18:24:02.143003Z"},"content_sha256":"5956752db4f90f85eff9d28a3f187748bfa849b3822e435eb54b517a605e4e4a","schema_version":"1.0","event_id":"sha256:5956752db4f90f85eff9d28a3f187748bfa849b3822e435eb54b517a605e4e4a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:UH44EUVD24W2DN2RDUEP7JCR2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The $L^p$ Neumann problem for higher order elliptic equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ariel Barton","submitted_at":"2020-02-06T22:03:25Z","abstract_excerpt":"We solve the Neumann problem in the half space $\\mathbb{R}^{n+1}_+$, for higher order elliptic differential equations with variable self-adjoint $t$-independent coefficients, and with boundary data in $L^p$, where $\\max\\bigl(1,\\frac{2n}{n+2}-\\varepsilon\\bigr) < p < 2$.\n  We also establish nontangential and area integral estimates on layer potentials with inputs in $L^p$ or $\\dot W^{\\pm1,p}$ for a similar range of~$p$, based on known bounds for $p\\geq2$; in this case we may relax the requirement of self-adjointess."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.02963","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2002.02963/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":"2026-07-05T00:39:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O3qYbyAZYZb1ormk7uO4nyGP7p30DHrJR4FMWKNO+cI7jfyIwUP801FRhOwsZBoUWbWJbjr76vSfkU5uC20WAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T18:24:02.143509Z"},"content_sha256":"8be5718b92727a00f4d13b9767f5d8c1ebb42cb0d19880325a37b865b668dac5","schema_version":"1.0","event_id":"sha256:8be5718b92727a00f4d13b9767f5d8c1ebb42cb0d19880325a37b865b668dac5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UH44EUVD24W2DN2RDUEP7JCR2H/bundle.json","state_url":"https://pith.science/pith/UH44EUVD24W2DN2RDUEP7JCR2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UH44EUVD24W2DN2RDUEP7JCR2H/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":"2026-08-22T18:24:02Z","links":{"resolver":"https://pith.science/pith/UH44EUVD24W2DN2RDUEP7JCR2H","bundle":"https://pith.science/pith/UH44EUVD24W2DN2RDUEP7JCR2H/bundle.json","state":"https://pith.science/pith/UH44EUVD24W2DN2RDUEP7JCR2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UH44EUVD24W2DN2RDUEP7JCR2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:UH44EUVD24W2DN2RDUEP7JCR2H","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":"3d59fd72a3e2bed701b65020e962f76df640e62680ac74d28c8785bb6a9b9f12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-06T22:03:25Z","title_canon_sha256":"1a5d1e6f422366a872daf43e38128af0905740e0ecf99975f79b495f0d5e0b08"},"schema_version":"1.0","source":{"id":"2002.02963","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.02963","created_at":"2026-07-05T00:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"2002.02963v1","created_at":"2026-07-05T00:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.02963","created_at":"2026-07-05T00:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"UH44EUVD24W2","created_at":"2026-07-05T00:39:17Z"},{"alias_kind":"pith_short_16","alias_value":"UH44EUVD24W2DN2R","created_at":"2026-07-05T00:39:17Z"},{"alias_kind":"pith_short_8","alias_value":"UH44EUVD","created_at":"2026-07-05T00:39:17Z"}],"graph_snapshots":[{"event_id":"sha256:8be5718b92727a00f4d13b9767f5d8c1ebb42cb0d19880325a37b865b668dac5","target":"graph","created_at":"2026-07-05T00:39:17Z","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/2002.02963/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We solve the Neumann problem in the half space $\\mathbb{R}^{n+1}_+$, for higher order elliptic differential equations with variable self-adjoint $t$-independent coefficients, and with boundary data in $L^p$, where $\\max\\bigl(1,\\frac{2n}{n+2}-\\varepsilon\\bigr) < p < 2$.\n  We also establish nontangential and area integral estimates on layer potentials with inputs in $L^p$ or $\\dot W^{\\pm1,p}$ for a similar range of~$p$, based on known bounds for $p\\geq2$; in this case we may relax the requirement of self-adjointess.","authors_text":"Ariel Barton","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-06T22:03:25Z","title":"The $L^p$ Neumann problem for higher order elliptic equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.02963","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":"sha256:5956752db4f90f85eff9d28a3f187748bfa849b3822e435eb54b517a605e4e4a","target":"record","created_at":"2026-07-05T00:39:17Z","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":"3d59fd72a3e2bed701b65020e962f76df640e62680ac74d28c8785bb6a9b9f12","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2020-02-06T22:03:25Z","title_canon_sha256":"1a5d1e6f422366a872daf43e38128af0905740e0ecf99975f79b495f0d5e0b08"},"schema_version":"1.0","source":{"id":"2002.02963","kind":"arxiv","version":1}},"canonical_sha256":"a1f9c252a3d72da1b7511d08ffa451d1d717cff782fadceb1a5b211d0738e795","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1f9c252a3d72da1b7511d08ffa451d1d717cff782fadceb1a5b211d0738e795","first_computed_at":"2026-07-05T00:39:17.699662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:39:17.699662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wZFHBrzBZX27Mhpl6DZM9zJwkZD5incHrku1fY9CAMYm7fg+7VEOhPsDTNWpay1tKVoBBSKg0Cg0vtraDDwHDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T00:39:17.700025Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.02963","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5956752db4f90f85eff9d28a3f187748bfa849b3822e435eb54b517a605e4e4a","sha256:8be5718b92727a00f4d13b9767f5d8c1ebb42cb0d19880325a37b865b668dac5"],"state_sha256":"c2ed610144c614f59a30127ebaee15c0b780f15344aa88241131a8e883e71ab9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yWTRjZp0U2fgtt9oBi3dg7s6iTnRJs2rUdv429TSwo/Hp9Jpu64278n2+IYNvJbCjA6H4rj03fW1S4zyaSqLAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T18:24:02.147342Z","bundle_sha256":"64c1d1b4b1479a5a0d20b08a25186e35d3d684adc68ab2946bebeccac8514656"}}