{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:Z6GUJ642RXDOFKLGFABRP5UMID","short_pith_number":"pith:Z6GUJ642","canonical_record":{"source":{"id":"1607.03852","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-13T18:23:30Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"04f15c8676c68150660924b0254a264dab5dfe3fb755bccf14c98aafa7545748","abstract_canon_sha256":"ceb373bc1e1fcf98cb2d84437b60ff4c11ca610cf22d7ec04774f569f6fd61fe"},"schema_version":"1.0"},"canonical_sha256":"cf8d44fb9a8dc6e2a966280317f68c40d0022f70def43b3e6c5096bec9aa0062","source":{"kind":"arxiv","id":"1607.03852","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03852","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03852v3","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03852","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"Z6GUJ642RXDO","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z6GUJ642RXDOFKLG","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z6GUJ642","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:Z6GUJ642RXDOFKLGFABRP5UMID","target":"record","payload":{"canonical_record":{"source":{"id":"1607.03852","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-13T18:23:30Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"04f15c8676c68150660924b0254a264dab5dfe3fb755bccf14c98aafa7545748","abstract_canon_sha256":"ceb373bc1e1fcf98cb2d84437b60ff4c11ca610cf22d7ec04774f569f6fd61fe"},"schema_version":"1.0"},"canonical_sha256":"cf8d44fb9a8dc6e2a966280317f68c40d0022f70def43b3e6c5096bec9aa0062","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:40.359599Z","signature_b64":"Y7dW3jcaZSnLUJcVHHVvLTeNJk5UkryktVvrEhmsLzDxiPQYtFol2Jplv0ozhmzbjKSjFIBQpfSa9VgfqDx7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf8d44fb9a8dc6e2a966280317f68c40d0022f70def43b3e6c5096bec9aa0062","last_reissued_at":"2026-05-18T00:39:40.358985Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:40.358985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.03852","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:39:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iwhTRIkG3pfRgilp3khY12WpkX4ntDwn14kt9pmnAD+F+yuKPkLLRsGLpN8c/qPzUMTBqXnWS8L02AJB7dH4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:17:34.273457Z"},"content_sha256":"f8b6a10bc3ab0554acffcb22ab1ffeda673491fe7abbc1df661b9cc09660ac13","schema_version":"1.0","event_id":"sha256:f8b6a10bc3ab0554acffcb22ab1ffeda673491fe7abbc1df661b9cc09660ac13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:Z6GUJ642RXDOFKLGFABRP5UMID","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Elliptic Boundary Value Problems with Fractional Regularity Data: The First Order Approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Alex Amenta, Pascal Auscher","submitted_at":"2016-07-13T18:23:30Z","abstract_excerpt":"We study well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable, and with boundary data in fractional Besov-Hardy-Sobolev (BHS) spaces. Our approach uses minimal assumptions on the coefficients, and in particular does not require De Giorgi-Nash-Moser estimates. Our results are completely new for the Hardy-Sobolev case, and in the Besov case they extend results recently obtained by Barton and Mayboroda.\n  First we develop a theory of BHS spaces adapted to operators which are b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03852","kind":"arxiv","version":3},"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":"2026-05-18T00:39:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sAij5a1t1jwVzrnfnlT40I4JKuYJW0g4pz4Q5U2Ie6Sp4cGBRdTeFjws2pBYlPsdyG7ugdu41GOhl2WEnOk8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:17:34.274164Z"},"content_sha256":"a4df32196b9381eecad83fee47be00ad06202385142a9e2de406083d7809125c","schema_version":"1.0","event_id":"sha256:a4df32196b9381eecad83fee47be00ad06202385142a9e2de406083d7809125c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z6GUJ642RXDOFKLGFABRP5UMID/bundle.json","state_url":"https://pith.science/pith/Z6GUJ642RXDOFKLGFABRP5UMID/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z6GUJ642RXDOFKLGFABRP5UMID/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":"2026-06-01T02:17:34Z","links":{"resolver":"https://pith.science/pith/Z6GUJ642RXDOFKLGFABRP5UMID","bundle":"https://pith.science/pith/Z6GUJ642RXDOFKLGFABRP5UMID/bundle.json","state":"https://pith.science/pith/Z6GUJ642RXDOFKLGFABRP5UMID/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z6GUJ642RXDOFKLGFABRP5UMID/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:Z6GUJ642RXDOFKLGFABRP5UMID","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":"ceb373bc1e1fcf98cb2d84437b60ff4c11ca610cf22d7ec04774f569f6fd61fe","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-13T18:23:30Z","title_canon_sha256":"04f15c8676c68150660924b0254a264dab5dfe3fb755bccf14c98aafa7545748"},"schema_version":"1.0","source":{"id":"1607.03852","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.03852","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"arxiv_version","alias_value":"1607.03852v3","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.03852","created_at":"2026-05-18T00:39:40Z"},{"alias_kind":"pith_short_12","alias_value":"Z6GUJ642RXDO","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"Z6GUJ642RXDOFKLG","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"Z6GUJ642","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:a4df32196b9381eecad83fee47be00ad06202385142a9e2de406083d7809125c","target":"graph","created_at":"2026-05-18T00:39:40Z","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":"We study well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable, and with boundary data in fractional Besov-Hardy-Sobolev (BHS) spaces. Our approach uses minimal assumptions on the coefficients, and in particular does not require De Giorgi-Nash-Moser estimates. Our results are completely new for the Hardy-Sobolev case, and in the Besov case they extend results recently obtained by Barton and Mayboroda.\n  First we develop a theory of BHS spaces adapted to operators which are b","authors_text":"Alex Amenta, Pascal Auscher","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-13T18:23:30Z","title":"Elliptic Boundary Value Problems with Fractional Regularity Data: The First Order Approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.03852","kind":"arxiv","version":3},"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:f8b6a10bc3ab0554acffcb22ab1ffeda673491fe7abbc1df661b9cc09660ac13","target":"record","created_at":"2026-05-18T00:39:40Z","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":"ceb373bc1e1fcf98cb2d84437b60ff4c11ca610cf22d7ec04774f569f6fd61fe","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-13T18:23:30Z","title_canon_sha256":"04f15c8676c68150660924b0254a264dab5dfe3fb755bccf14c98aafa7545748"},"schema_version":"1.0","source":{"id":"1607.03852","kind":"arxiv","version":3}},"canonical_sha256":"cf8d44fb9a8dc6e2a966280317f68c40d0022f70def43b3e6c5096bec9aa0062","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf8d44fb9a8dc6e2a966280317f68c40d0022f70def43b3e6c5096bec9aa0062","first_computed_at":"2026-05-18T00:39:40.358985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:39:40.358985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y7dW3jcaZSnLUJcVHHVvLTeNJk5UkryktVvrEhmsLzDxiPQYtFol2Jplv0ozhmzbjKSjFIBQpfSa9VgfqDx7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:39:40.359599Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.03852","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f8b6a10bc3ab0554acffcb22ab1ffeda673491fe7abbc1df661b9cc09660ac13","sha256:a4df32196b9381eecad83fee47be00ad06202385142a9e2de406083d7809125c"],"state_sha256":"45fe8f13e74a9e02b74ec76c3a18a87978d4fb0a1547c1ae5b24e577c43def5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TwZPTjFYI1K2TAQJkpaU76Jp0zZE+if+gLSHzmM5otw3enH50/z4ebwFi+w1MuH4XtnGaH9FMJmAgFcZvZYwBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:17:34.277486Z","bundle_sha256":"f3a7a1acc118999311c3d11ea4932c765937e0511e4a004f2f52bb291e28ae1a"}}