{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:2H6HND2YXQ7KB2D7DZKCIEZQ4B","short_pith_number":"pith:2H6HND2Y","canonical_record":{"source":{"id":"1201.0636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-03T14:01:45Z","cross_cats_sorted":[],"title_canon_sha256":"c000693a35f66936c9ee08b9e0137b5381256ae58be1d458c1c3875c537180d0","abstract_canon_sha256":"1033a2b6f67a1aee9ab85b770049facd4de6660fdcd9f6572cdcedba3dab0bcf"},"schema_version":"1.0"},"canonical_sha256":"d1fc768f58bc3ea0e87f1e54241330e05ae58b3bf2452134d469696390a96588","source":{"kind":"arxiv","id":"1201.0636","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0636","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0636v1","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0636","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"2H6HND2YXQ7K","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2H6HND2YXQ7KB2D7","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2H6HND2Y","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:2H6HND2YXQ7KB2D7DZKCIEZQ4B","target":"record","payload":{"canonical_record":{"source":{"id":"1201.0636","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-03T14:01:45Z","cross_cats_sorted":[],"title_canon_sha256":"c000693a35f66936c9ee08b9e0137b5381256ae58be1d458c1c3875c537180d0","abstract_canon_sha256":"1033a2b6f67a1aee9ab85b770049facd4de6660fdcd9f6572cdcedba3dab0bcf"},"schema_version":"1.0"},"canonical_sha256":"d1fc768f58bc3ea0e87f1e54241330e05ae58b3bf2452134d469696390a96588","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:17.021614Z","signature_b64":"BKcPz+p/q7PidGANTlmPO/SS/uqTGtfrRRlVBbSWm5bPiaojedNvSUvW/q4Nysics/zBMULgNly8nV+Zk24fBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1fc768f58bc3ea0e87f1e54241330e05ae58b3bf2452134d469696390a96588","last_reissued_at":"2026-05-18T04:05:17.020875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:17.020875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.0636","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":"2026-05-18T04:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lgC7KRvYXd6sQ0mr7+3Iuo6acfilOeuQ2y4vxXj8hLtIZ/UL8gXn56EsLrM6rhm3+It4MfBbozfKqaSg/21ZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:05:21.661733Z"},"content_sha256":"8b4b571baaba45c88ab007656af6363feb66052aac6d44a806e3390eff569690","schema_version":"1.0","event_id":"sha256:8b4b571baaba45c88ab007656af6363feb66052aac6d44a806e3390eff569690"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:2H6HND2YXQ7KB2D7DZKCIEZQ4B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some new properties of composition operators associated with lens maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Li (LML), Herv\\'e Queff\\'elec (LPP), Luis Rodriguez-Piazza, Pascal Lef\\`evre (LML)","submitted_at":"2012-01-03T14:01:45Z","abstract_excerpt":"We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space $H^2$. The last ones are connected with Hardy-Orlicz and Bergman-Orlicz spaces $H^\\psi$ and $B^\\psi$, and provide a negative answer to the question of knowing if all composition operators which are weakly compact on a non-reflexive space are norm-compact."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0636","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":"2026-05-18T04:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Af7sy3rdKTBsz3HFoOHlwaD/gWjFkYW8K+/40QDhptPyKTO0FykSFhnupatJi8vwCkCudgTfV+QoJkAdj8VWDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T05:05:21.662400Z"},"content_sha256":"ec071e10f74a6b0fbd7382a8c5f6adfcf0a93ce92afc2319dd15aa02d6e18a22","schema_version":"1.0","event_id":"sha256:ec071e10f74a6b0fbd7382a8c5f6adfcf0a93ce92afc2319dd15aa02d6e18a22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2H6HND2YXQ7KB2D7DZKCIEZQ4B/bundle.json","state_url":"https://pith.science/pith/2H6HND2YXQ7KB2D7DZKCIEZQ4B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2H6HND2YXQ7KB2D7DZKCIEZQ4B/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":"2026-06-09T05:05:21Z","links":{"resolver":"https://pith.science/pith/2H6HND2YXQ7KB2D7DZKCIEZQ4B","bundle":"https://pith.science/pith/2H6HND2YXQ7KB2D7DZKCIEZQ4B/bundle.json","state":"https://pith.science/pith/2H6HND2YXQ7KB2D7DZKCIEZQ4B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2H6HND2YXQ7KB2D7DZKCIEZQ4B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:2H6HND2YXQ7KB2D7DZKCIEZQ4B","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":"1033a2b6f67a1aee9ab85b770049facd4de6660fdcd9f6572cdcedba3dab0bcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-03T14:01:45Z","title_canon_sha256":"c000693a35f66936c9ee08b9e0137b5381256ae58be1d458c1c3875c537180d0"},"schema_version":"1.0","source":{"id":"1201.0636","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.0636","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"1201.0636v1","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.0636","created_at":"2026-05-18T04:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"2H6HND2YXQ7K","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"2H6HND2YXQ7KB2D7","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"2H6HND2Y","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:ec071e10f74a6b0fbd7382a8c5f6adfcf0a93ce92afc2319dd15aa02d6e18a22","target":"graph","created_at":"2026-05-18T04:05:17Z","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"},"paper":{"abstract_excerpt":"We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space $H^2$. The last ones are connected with Hardy-Orlicz and Bergman-Orlicz spaces $H^\\psi$ and $B^\\psi$, and provide a negative answer to the question of knowing if all composition operators which are weakly compact on a non-reflexive space are norm-compact.","authors_text":"Daniel Li (LML), Herv\\'e Queff\\'elec (LPP), Luis Rodriguez-Piazza, Pascal Lef\\`evre (LML)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-03T14:01:45Z","title":"Some new properties of composition operators associated with lens maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0636","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":"sha256:8b4b571baaba45c88ab007656af6363feb66052aac6d44a806e3390eff569690","target":"record","created_at":"2026-05-18T04:05:17Z","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":"1033a2b6f67a1aee9ab85b770049facd4de6660fdcd9f6572cdcedba3dab0bcf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2012-01-03T14:01:45Z","title_canon_sha256":"c000693a35f66936c9ee08b9e0137b5381256ae58be1d458c1c3875c537180d0"},"schema_version":"1.0","source":{"id":"1201.0636","kind":"arxiv","version":1}},"canonical_sha256":"d1fc768f58bc3ea0e87f1e54241330e05ae58b3bf2452134d469696390a96588","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1fc768f58bc3ea0e87f1e54241330e05ae58b3bf2452134d469696390a96588","first_computed_at":"2026-05-18T04:05:17.020875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:17.020875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BKcPz+p/q7PidGANTlmPO/SS/uqTGtfrRRlVBbSWm5bPiaojedNvSUvW/q4Nysics/zBMULgNly8nV+Zk24fBA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:17.021614Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.0636","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8b4b571baaba45c88ab007656af6363feb66052aac6d44a806e3390eff569690","sha256:ec071e10f74a6b0fbd7382a8c5f6adfcf0a93ce92afc2319dd15aa02d6e18a22"],"state_sha256":"0dff2d85fd05ec18b7f2655996b5c5418f6659f1a30bd0d768cf2ea70cfe6b39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"++ifADmiIJW1k8CD7acvwiGLBftqxCpZJsjktK7A2tVaUki/TJM1U3lzsOkYumM2Lgxc+Lkfndcs0CXEixuCBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T05:05:21.666789Z","bundle_sha256":"8babb9141aca57d96d85845a1759a9e79fc9a3b8322a08f13f7ce5e61a6b9b86"}}