{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:D76QGCRG4ZTRETTVABCDIUA4QF","short_pith_number":"pith:D76QGCRG","canonical_record":{"source":{"id":"1711.11198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T03:05:25Z","cross_cats_sorted":[],"title_canon_sha256":"665c46809690fff1115183ff63b5c9c668bacb48d7c1ac9ac10d028ef5bd73f2","abstract_canon_sha256":"14852d69e50f196eef36531c667a1fc66208289e3b31df31a6347340f4c4c3f9"},"schema_version":"1.0"},"canonical_sha256":"1ffd030a26e667124e75004434501c81426ec41d64af56b9363d8e09764b9f10","source":{"kind":"arxiv","id":"1711.11198","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11198","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11198v1","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11198","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"pith_short_12","alias_value":"D76QGCRG4ZTR","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D76QGCRG4ZTRETTV","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D76QGCRG","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:D76QGCRG4ZTRETTVABCDIUA4QF","target":"record","payload":{"canonical_record":{"source":{"id":"1711.11198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T03:05:25Z","cross_cats_sorted":[],"title_canon_sha256":"665c46809690fff1115183ff63b5c9c668bacb48d7c1ac9ac10d028ef5bd73f2","abstract_canon_sha256":"14852d69e50f196eef36531c667a1fc66208289e3b31df31a6347340f4c4c3f9"},"schema_version":"1.0"},"canonical_sha256":"1ffd030a26e667124e75004434501c81426ec41d64af56b9363d8e09764b9f10","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:12.234192Z","signature_b64":"x8TadTfQ64bmT8cRuYQwebil25BB4eCJHpHz7Jf/5Z3HenjzlVC6bq3oVzjYgs5vHYtCRTHxCeL+20ATtCL8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ffd030a26e667124e75004434501c81426ec41d64af56b9363d8e09764b9f10","last_reissued_at":"2026-05-18T00:29:12.233677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:12.233677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.11198","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":"2026-05-18T00:29:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FXHX/Em7XBAw7XuHTpUogAbWDVcV5o1i0Y0NSfAzQuvUckwLSGuKVAw43Rj59kYMvYlkrqrNlazXAsP5vXPyBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:36:57.105536Z"},"content_sha256":"147666111d21a96ceced04fa50b9a9f777b798b96a6515f43603e358255b9671","schema_version":"1.0","event_id":"sha256:147666111d21a96ceced04fa50b9a9f777b798b96a6515f43603e358255b9671"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:D76QGCRG4ZTRETTVABCDIUA4QF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subcritical approach to conformally invariant extension operators on the upper half space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mathew Gluck","submitted_at":"2017-11-30T03:05:25Z","abstract_excerpt":"In this work we obtain sharp embedding inequalities for a family of conformally invariant integral extension operators. This family includes among others the classical Poisson extension operator and the extension operator with Riesz kernel. We show that the sharp constants in these inequalities are attained and classify the corresponding extremal functions. We also compute the limiting behavior at the boundary of the extensions of the extremal functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11198","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":"2026-05-18T00:29:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VJkxFYwzvsC5EZORNQQ7BNOqBy4sHNP/R7gjlJASbIT7zUzRK0FdZz/5dhHk8t05bYaCQTxhVUSR2lk2P6NLDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T05:36:57.105877Z"},"content_sha256":"deddc69564d35bb8e8397d02b8093a1795ba1fa8fbae41bad0bff3fef5ba512f","schema_version":"1.0","event_id":"sha256:deddc69564d35bb8e8397d02b8093a1795ba1fa8fbae41bad0bff3fef5ba512f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D76QGCRG4ZTRETTVABCDIUA4QF/bundle.json","state_url":"https://pith.science/pith/D76QGCRG4ZTRETTVABCDIUA4QF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D76QGCRG4ZTRETTVABCDIUA4QF/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":"2026-06-12T05:36:57Z","links":{"resolver":"https://pith.science/pith/D76QGCRG4ZTRETTVABCDIUA4QF","bundle":"https://pith.science/pith/D76QGCRG4ZTRETTVABCDIUA4QF/bundle.json","state":"https://pith.science/pith/D76QGCRG4ZTRETTVABCDIUA4QF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D76QGCRG4ZTRETTVABCDIUA4QF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:D76QGCRG4ZTRETTVABCDIUA4QF","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":"14852d69e50f196eef36531c667a1fc66208289e3b31df31a6347340f4c4c3f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T03:05:25Z","title_canon_sha256":"665c46809690fff1115183ff63b5c9c668bacb48d7c1ac9ac10d028ef5bd73f2"},"schema_version":"1.0","source":{"id":"1711.11198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.11198","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"arxiv_version","alias_value":"1711.11198v1","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11198","created_at":"2026-05-18T00:29:12Z"},{"alias_kind":"pith_short_12","alias_value":"D76QGCRG4ZTR","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"D76QGCRG4ZTRETTV","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"D76QGCRG","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:deddc69564d35bb8e8397d02b8093a1795ba1fa8fbae41bad0bff3fef5ba512f","target":"graph","created_at":"2026-05-18T00:29:12Z","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":"In this work we obtain sharp embedding inequalities for a family of conformally invariant integral extension operators. This family includes among others the classical Poisson extension operator and the extension operator with Riesz kernel. We show that the sharp constants in these inequalities are attained and classify the corresponding extremal functions. We also compute the limiting behavior at the boundary of the extensions of the extremal functions.","authors_text":"Mathew Gluck","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T03:05:25Z","title":"Subcritical approach to conformally invariant extension operators on the upper half space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11198","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":"sha256:147666111d21a96ceced04fa50b9a9f777b798b96a6515f43603e358255b9671","target":"record","created_at":"2026-05-18T00:29:12Z","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":"14852d69e50f196eef36531c667a1fc66208289e3b31df31a6347340f4c4c3f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-30T03:05:25Z","title_canon_sha256":"665c46809690fff1115183ff63b5c9c668bacb48d7c1ac9ac10d028ef5bd73f2"},"schema_version":"1.0","source":{"id":"1711.11198","kind":"arxiv","version":1}},"canonical_sha256":"1ffd030a26e667124e75004434501c81426ec41d64af56b9363d8e09764b9f10","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ffd030a26e667124e75004434501c81426ec41d64af56b9363d8e09764b9f10","first_computed_at":"2026-05-18T00:29:12.233677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:12.233677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x8TadTfQ64bmT8cRuYQwebil25BB4eCJHpHz7Jf/5Z3HenjzlVC6bq3oVzjYgs5vHYtCRTHxCeL+20ATtCL8AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:12.234192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.11198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:147666111d21a96ceced04fa50b9a9f777b798b96a6515f43603e358255b9671","sha256:deddc69564d35bb8e8397d02b8093a1795ba1fa8fbae41bad0bff3fef5ba512f"],"state_sha256":"dee9044d44146dbb2fa71d6597384cb8a41d2858e71768be5bc0ed88f3ed1fda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3834jG28QCxbUwtqlnSaKAhXCkfbXjHHNzgciQcJm9YIGv07xxaARplnDpXcG/FfrPV5Mk28U4sXyuXVI4YyAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T05:36:57.107788Z","bundle_sha256":"8e40421a5fbfdfb0a29a59b6d499760d7db57a1bd48f2292b5ee86a64f38de0b"}}