{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:EC3FW5ZD2M5WCTMHUXPEBROAAB","short_pith_number":"pith:EC3FW5ZD","canonical_record":{"source":{"id":"1405.3329","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-13T23:23:23Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"090d4e724cffa07176236a755682c29de755e59e9799492cb740138bd6382b7b","abstract_canon_sha256":"633d80ae65f23eacc1112c9bd310d5a4956a6066e687c37ba160e0c9014df4da"},"schema_version":"1.0"},"canonical_sha256":"20b65b7723d33b614d87a5de40c5c00060021f60e8726757b81ee7892ddd06ef","source":{"kind":"arxiv","id":"1405.3329","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3329","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3329v2","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3329","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"EC3FW5ZD2M5W","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EC3FW5ZD2M5WCTMH","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EC3FW5ZD","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:EC3FW5ZD2M5WCTMHUXPEBROAAB","target":"record","payload":{"canonical_record":{"source":{"id":"1405.3329","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-13T23:23:23Z","cross_cats_sorted":["math.CA","math.FA"],"title_canon_sha256":"090d4e724cffa07176236a755682c29de755e59e9799492cb740138bd6382b7b","abstract_canon_sha256":"633d80ae65f23eacc1112c9bd310d5a4956a6066e687c37ba160e0c9014df4da"},"schema_version":"1.0"},"canonical_sha256":"20b65b7723d33b614d87a5de40c5c00060021f60e8726757b81ee7892ddd06ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:50.710825Z","signature_b64":"3sKK0AWnAS+zSjivWdoaaLx5hOsBohC3UWdtjvaL3VUR1hEJvCvmZHftQl0CnsfZzj7DBrTtPNiDTl2VP47xCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20b65b7723d33b614d87a5de40c5c00060021f60e8726757b81ee7892ddd06ef","last_reissued_at":"2026-05-18T00:03:50.710299Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:50.710299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.3329","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":"2026-05-18T00:03:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XX5GE69dVQq3JNT1y8NNxJcdTzunBTSUmO4e2KiI4hEcsjv0+1kC+YsMLcfh5d5LwnooXW0h0uQaM9Fuvx9rAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:34:27.272707Z"},"content_sha256":"c5ae759ef64d24607ae61659d6255c19caf1934415155360d3c9dd1c4460bcb0","schema_version":"1.0","event_id":"sha256:c5ae759ef64d24607ae61659d6255c19caf1934415155360d3c9dd1c4460bcb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:EC3FW5ZD2M5WCTMHUXPEBROAAB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Dirichlet problem for elliptic systems with data in K\\\"othe function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.FA"],"primary_cat":"math.AP","authors_text":"Dorina Mitrea, Irina Mitrea, Jos\\'e Mar\\'ia Martell, Marius Mitrea","submitted_at":"2014-05-13T23:23:23Z","abstract_excerpt":"We show that the boundedness of the Hardy-Littlewood maximal operator on a K\\\"othe function space ${\\mathbb{X}}$ and on its K\\\"othe dual ${\\mathbb{X}}'$ is equivalent to the well-posedness of the $\\mathbb{X}$-Dirichlet and $\\mathbb{X}'$-Dirichlet problems in $\\mathbb{R}^{n}_{+}$ in the class of all second-order, homogeneous, elliptic systems, with constant complex coefficients. As a consequence, we obtain that the Dirichlet problem for such systems is well-posed for boundary data in Lebesgue spaces, variable exponent Lebesgue spaces, Lorentz spaces, Zygmund spaces, as well as their weighted ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3329","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":"2026-05-18T00:03:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Blo8haUuSb8BVRrIWxJRJI9wbi/7Lz5KwsnhNO3/2izhiqBjDmtvVG1UBDFUD2/l1ibcdBh2ZDBP0w14HcxiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:34:27.273479Z"},"content_sha256":"b776354fe466153e2aa9cb9acdf77b787f3e3c948fee22a77233d281ccfa36fd","schema_version":"1.0","event_id":"sha256:b776354fe466153e2aa9cb9acdf77b787f3e3c948fee22a77233d281ccfa36fd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EC3FW5ZD2M5WCTMHUXPEBROAAB/bundle.json","state_url":"https://pith.science/pith/EC3FW5ZD2M5WCTMHUXPEBROAAB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EC3FW5ZD2M5WCTMHUXPEBROAAB/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":"2026-05-27T16:34:27Z","links":{"resolver":"https://pith.science/pith/EC3FW5ZD2M5WCTMHUXPEBROAAB","bundle":"https://pith.science/pith/EC3FW5ZD2M5WCTMHUXPEBROAAB/bundle.json","state":"https://pith.science/pith/EC3FW5ZD2M5WCTMHUXPEBROAAB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EC3FW5ZD2M5WCTMHUXPEBROAAB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EC3FW5ZD2M5WCTMHUXPEBROAAB","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":"633d80ae65f23eacc1112c9bd310d5a4956a6066e687c37ba160e0c9014df4da","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-13T23:23:23Z","title_canon_sha256":"090d4e724cffa07176236a755682c29de755e59e9799492cb740138bd6382b7b"},"schema_version":"1.0","source":{"id":"1405.3329","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.3329","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"arxiv_version","alias_value":"1405.3329v2","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.3329","created_at":"2026-05-18T00:03:50Z"},{"alias_kind":"pith_short_12","alias_value":"EC3FW5ZD2M5W","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EC3FW5ZD2M5WCTMH","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EC3FW5ZD","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:b776354fe466153e2aa9cb9acdf77b787f3e3c948fee22a77233d281ccfa36fd","target":"graph","created_at":"2026-05-18T00:03:50Z","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 show that the boundedness of the Hardy-Littlewood maximal operator on a K\\\"othe function space ${\\mathbb{X}}$ and on its K\\\"othe dual ${\\mathbb{X}}'$ is equivalent to the well-posedness of the $\\mathbb{X}$-Dirichlet and $\\mathbb{X}'$-Dirichlet problems in $\\mathbb{R}^{n}_{+}$ in the class of all second-order, homogeneous, elliptic systems, with constant complex coefficients. As a consequence, we obtain that the Dirichlet problem for such systems is well-posed for boundary data in Lebesgue spaces, variable exponent Lebesgue spaces, Lorentz spaces, Zygmund spaces, as well as their weighted ve","authors_text":"Dorina Mitrea, Irina Mitrea, Jos\\'e Mar\\'ia Martell, Marius Mitrea","cross_cats":["math.CA","math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-13T23:23:23Z","title":"The Dirichlet problem for elliptic systems with data in K\\\"othe function spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3329","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:c5ae759ef64d24607ae61659d6255c19caf1934415155360d3c9dd1c4460bcb0","target":"record","created_at":"2026-05-18T00:03:50Z","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":"633d80ae65f23eacc1112c9bd310d5a4956a6066e687c37ba160e0c9014df4da","cross_cats_sorted":["math.CA","math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-05-13T23:23:23Z","title_canon_sha256":"090d4e724cffa07176236a755682c29de755e59e9799492cb740138bd6382b7b"},"schema_version":"1.0","source":{"id":"1405.3329","kind":"arxiv","version":2}},"canonical_sha256":"20b65b7723d33b614d87a5de40c5c00060021f60e8726757b81ee7892ddd06ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20b65b7723d33b614d87a5de40c5c00060021f60e8726757b81ee7892ddd06ef","first_computed_at":"2026-05-18T00:03:50.710299Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:50.710299Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3sKK0AWnAS+zSjivWdoaaLx5hOsBohC3UWdtjvaL3VUR1hEJvCvmZHftQl0CnsfZzj7DBrTtPNiDTl2VP47xCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:50.710825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.3329","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5ae759ef64d24607ae61659d6255c19caf1934415155360d3c9dd1c4460bcb0","sha256:b776354fe466153e2aa9cb9acdf77b787f3e3c948fee22a77233d281ccfa36fd"],"state_sha256":"5ea95e973b6d0b037ad6e78c6b6bfc5fc26c05b1936ce78ba096adfe8fe1cfa1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ODCge78cZuoz9bkntnM0LJcqSM55Nr1dXLXwdKhqPMoRldvv6QkLeMqvLqvTFufGAs+p3/hhZSyfw/iroqcFDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T16:34:27.276756Z","bundle_sha256":"aa53f108272db93d64a7fd5bd8996bb4998008542bc97901c5224c6bd3afa08f"}}