{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:TCGKDEPCNJFAPNBOXMUVMW4RXF","short_pith_number":"pith:TCGKDEPC","canonical_record":{"source":{"id":"1708.05225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-17T12:16:51Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"cec7a24ed617ac3ee508f1b3c763ae77128f38d5da7332565d73957db161bd2e","abstract_canon_sha256":"87569c4222969cf2c6dd5e8322035cf97ba36a041c9eddf6cf34665e90cef2be"},"schema_version":"1.0"},"canonical_sha256":"988ca191e26a4a07b42ebb29565b91b97cc877c031bb403ff486b7fda41a48e3","source":{"kind":"arxiv","id":"1708.05225","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05225","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05225v1","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05225","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"pith_short_12","alias_value":"TCGKDEPCNJFA","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TCGKDEPCNJFAPNBO","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TCGKDEPC","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:TCGKDEPCNJFAPNBOXMUVMW4RXF","target":"record","payload":{"canonical_record":{"source":{"id":"1708.05225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-17T12:16:51Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"cec7a24ed617ac3ee508f1b3c763ae77128f38d5da7332565d73957db161bd2e","abstract_canon_sha256":"87569c4222969cf2c6dd5e8322035cf97ba36a041c9eddf6cf34665e90cef2be"},"schema_version":"1.0"},"canonical_sha256":"988ca191e26a4a07b42ebb29565b91b97cc877c031bb403ff486b7fda41a48e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:53.538668Z","signature_b64":"l2u5NQu7Kk4s9PfoDoz41Iyn8rR6HgEDnrYmVvAJFj2bxsf+YqOPn9vj6K0jd5wT56suX4UOdsbZ1HY9odFKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"988ca191e26a4a07b42ebb29565b91b97cc877c031bb403ff486b7fda41a48e3","last_reissued_at":"2026-05-18T00:37:53.538123Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:53.538123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.05225","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":"2026-05-18T00:37:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7XQGX9dPOtwt/0BnOk9eMSfdn/eSVyqTfCciYyYndKxPoHgLVdQ4BK2PV1sqwSFryyKcieHzCFbo0S/woWlbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:45:48.477355Z"},"content_sha256":"0ba5ba46e9b5c59adbf36238c2500f15ec0ab033611b9be8c86f972cac7aa606","schema_version":"1.0","event_id":"sha256:0ba5ba46e9b5c59adbf36238c2500f15ec0ab033611b9be8c86f972cac7aa606"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:TCGKDEPCNJFAPNBOXMUVMW4RXF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weighted Composition Operators Acting on Harmonic Hardy Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Congwen Liu, Lifang Zhou, Pengyan Hu, Taishun Liu","submitted_at":"2017-08-17T12:16:51Z","abstract_excerpt":"Suppose $n\\geq 3$ and let $B$ be the open unit ball in $\\mathbb{R}^n$. Let $\\varphi: B\\to B$ be a $C^2$ map whose Jacobian does not change sign, and let $\\psi$ be a $C^2$ function on $B$. We characterize bounded weighted composition operators $W_{\\varphi,\\psi}$ acting on harmonic Hardy spaces $h^p(B)$. In addition, we compute the operator norm of $W_{\\varphi,\\psi}$ on $h^p(B)$ when $\\varphi$ is a M\\\"obius transformation of $B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05225","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":"2026-05-18T00:37:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V5fRk/OWqA3GG5+MjW6hT3c5PPdWR/C4olItYVu0txwihxg9TjERKXdJ41jDCdtQKvms0rCoOG9L+8qYMZYsCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T21:45:48.477705Z"},"content_sha256":"3ada8e5087b94b80cdfafc6da88dcdf709a4676076f2ad2cae29f8d192d25197","schema_version":"1.0","event_id":"sha256:3ada8e5087b94b80cdfafc6da88dcdf709a4676076f2ad2cae29f8d192d25197"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TCGKDEPCNJFAPNBOXMUVMW4RXF/bundle.json","state_url":"https://pith.science/pith/TCGKDEPCNJFAPNBOXMUVMW4RXF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TCGKDEPCNJFAPNBOXMUVMW4RXF/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":"2026-06-03T21:45:48Z","links":{"resolver":"https://pith.science/pith/TCGKDEPCNJFAPNBOXMUVMW4RXF","bundle":"https://pith.science/pith/TCGKDEPCNJFAPNBOXMUVMW4RXF/bundle.json","state":"https://pith.science/pith/TCGKDEPCNJFAPNBOXMUVMW4RXF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TCGKDEPCNJFAPNBOXMUVMW4RXF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:TCGKDEPCNJFAPNBOXMUVMW4RXF","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":"87569c4222969cf2c6dd5e8322035cf97ba36a041c9eddf6cf34665e90cef2be","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-17T12:16:51Z","title_canon_sha256":"cec7a24ed617ac3ee508f1b3c763ae77128f38d5da7332565d73957db161bd2e"},"schema_version":"1.0","source":{"id":"1708.05225","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.05225","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"arxiv_version","alias_value":"1708.05225v1","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05225","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"pith_short_12","alias_value":"TCGKDEPCNJFA","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"TCGKDEPCNJFAPNBO","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"TCGKDEPC","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:3ada8e5087b94b80cdfafc6da88dcdf709a4676076f2ad2cae29f8d192d25197","target":"graph","created_at":"2026-05-18T00:37:53Z","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":"Suppose $n\\geq 3$ and let $B$ be the open unit ball in $\\mathbb{R}^n$. Let $\\varphi: B\\to B$ be a $C^2$ map whose Jacobian does not change sign, and let $\\psi$ be a $C^2$ function on $B$. We characterize bounded weighted composition operators $W_{\\varphi,\\psi}$ acting on harmonic Hardy spaces $h^p(B)$. In addition, we compute the operator norm of $W_{\\varphi,\\psi}$ on $h^p(B)$ when $\\varphi$ is a M\\\"obius transformation of $B$.","authors_text":"Congwen Liu, Lifang Zhou, Pengyan Hu, Taishun Liu","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-17T12:16:51Z","title":"Weighted Composition Operators Acting on Harmonic Hardy Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05225","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":"sha256:0ba5ba46e9b5c59adbf36238c2500f15ec0ab033611b9be8c86f972cac7aa606","target":"record","created_at":"2026-05-18T00:37:53Z","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":"87569c4222969cf2c6dd5e8322035cf97ba36a041c9eddf6cf34665e90cef2be","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2017-08-17T12:16:51Z","title_canon_sha256":"cec7a24ed617ac3ee508f1b3c763ae77128f38d5da7332565d73957db161bd2e"},"schema_version":"1.0","source":{"id":"1708.05225","kind":"arxiv","version":1}},"canonical_sha256":"988ca191e26a4a07b42ebb29565b91b97cc877c031bb403ff486b7fda41a48e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"988ca191e26a4a07b42ebb29565b91b97cc877c031bb403ff486b7fda41a48e3","first_computed_at":"2026-05-18T00:37:53.538123Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:53.538123Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l2u5NQu7Kk4s9PfoDoz41Iyn8rR6HgEDnrYmVvAJFj2bxsf+YqOPn9vj6K0jd5wT56suX4UOdsbZ1HY9odFKBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:53.538668Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.05225","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ba5ba46e9b5c59adbf36238c2500f15ec0ab033611b9be8c86f972cac7aa606","sha256:3ada8e5087b94b80cdfafc6da88dcdf709a4676076f2ad2cae29f8d192d25197"],"state_sha256":"0467782fa431d7110bfa97980e97c02e3b3e83e3d31daf379a74aa5d9b4210ed"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n1uHUEffkJn7wmea44Ms12bB8kNyqLUo+2XUUBw6UmotwCgWt1i/sNZDbh9hqdfikdWZ3/y6i40vgCAOOWEjDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T21:45:48.479562Z","bundle_sha256":"206bd0bca2a9cdf44ac77ad136af65a9cd61c65b41b57aef29fd339570921d6d"}}