{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:PRW4JEUB6ERXPKLJ2ADM266IY7","short_pith_number":"pith:PRW4JEUB","canonical_record":{"source":{"id":"1904.06992","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-15T12:23:06Z","cross_cats_sorted":[],"title_canon_sha256":"1bf7baf61b06b0ca1d091c23cc1e75f91496dfe1ada3000e2ef5864431acc170","abstract_canon_sha256":"ac19aa494474fc3478c4ad6386e03640e006ed7c23f3de83111d6b760662d068"},"schema_version":"1.0"},"canonical_sha256":"7c6dc49281f12377a969d006cd7bc8c7d7972350076a0a75d92550b277237863","source":{"kind":"arxiv","id":"1904.06992","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06992","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06992v1","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06992","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"PRW4JEUB6ERX","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PRW4JEUB6ERXPKLJ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PRW4JEUB","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:PRW4JEUB6ERXPKLJ2ADM266IY7","target":"record","payload":{"canonical_record":{"source":{"id":"1904.06992","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-15T12:23:06Z","cross_cats_sorted":[],"title_canon_sha256":"1bf7baf61b06b0ca1d091c23cc1e75f91496dfe1ada3000e2ef5864431acc170","abstract_canon_sha256":"ac19aa494474fc3478c4ad6386e03640e006ed7c23f3de83111d6b760662d068"},"schema_version":"1.0"},"canonical_sha256":"7c6dc49281f12377a969d006cd7bc8c7d7972350076a0a75d92550b277237863","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:35.545044Z","signature_b64":"dgjH2uFZ+3I5LisUTLS74U4cYgwiKzZprTiVPofC1wj+cos4SJ2dnEQNFMwjn6rw3C+MRla4RXDFjCfF4eXiAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c6dc49281f12377a969d006cd7bc8c7d7972350076a0a75d92550b277237863","last_reissued_at":"2026-05-17T23:48:35.544493Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:35.544493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.06992","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":"2026-05-17T23:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uNT/kI3ZqWDghbQAGtQSnzgCOW2TooseraWjXCnpuwCeSsR7xjVM+1RbbPpQWaB5Rv74+MtqKuQTk+eNGGa8Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:10:27.181444Z"},"content_sha256":"525ae051a26868652239f773529060e10619175218948f4f1009657596ebbd85","schema_version":"1.0","event_id":"sha256:525ae051a26868652239f773529060e10619175218948f4f1009657596ebbd85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:PRW4JEUB6ERXPKLJ2ADM266IY7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compactification, and beyond, of composition operators on Hardy spaces by weights","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":"2019-04-15T12:23:06Z","abstract_excerpt":"We study when multiplication by a weight can turn a non-compact composition operator on H 2 into a compact operator, and when it can be in Schatten classes. The q-summing case in H p is considered. We also study when this multiplication can turn a compact composition operator into a non-compact one. MSC 2010 primary: 47B33 ; secondary: 46B28"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06992","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":"2026-05-17T23:48:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b4NY9uaspSWpz1cuZ1wX/Z/pTyvNIJoq9t2GXwA5MVNhrJRlNKBLj0yaIwSpCWUEyT/UdKEQ38pQVM32TLb2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T09:10:27.181783Z"},"content_sha256":"b66146f9e09538546260393172a082b7fc0644ebe575903c20d1b9c700e41cc9","schema_version":"1.0","event_id":"sha256:b66146f9e09538546260393172a082b7fc0644ebe575903c20d1b9c700e41cc9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PRW4JEUB6ERXPKLJ2ADM266IY7/bundle.json","state_url":"https://pith.science/pith/PRW4JEUB6ERXPKLJ2ADM266IY7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PRW4JEUB6ERXPKLJ2ADM266IY7/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":"2026-06-09T09:10:27Z","links":{"resolver":"https://pith.science/pith/PRW4JEUB6ERXPKLJ2ADM266IY7","bundle":"https://pith.science/pith/PRW4JEUB6ERXPKLJ2ADM266IY7/bundle.json","state":"https://pith.science/pith/PRW4JEUB6ERXPKLJ2ADM266IY7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PRW4JEUB6ERXPKLJ2ADM266IY7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:PRW4JEUB6ERXPKLJ2ADM266IY7","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":"ac19aa494474fc3478c4ad6386e03640e006ed7c23f3de83111d6b760662d068","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-15T12:23:06Z","title_canon_sha256":"1bf7baf61b06b0ca1d091c23cc1e75f91496dfe1ada3000e2ef5864431acc170"},"schema_version":"1.0","source":{"id":"1904.06992","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.06992","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.06992v1","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.06992","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"PRW4JEUB6ERX","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"PRW4JEUB6ERXPKLJ","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"PRW4JEUB","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:b66146f9e09538546260393172a082b7fc0644ebe575903c20d1b9c700e41cc9","target":"graph","created_at":"2026-05-17T23:48:35Z","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 when multiplication by a weight can turn a non-compact composition operator on H 2 into a compact operator, and when it can be in Schatten classes. The q-summing case in H p is considered. We also study when this multiplication can turn a compact composition operator into a non-compact one. MSC 2010 primary: 47B33 ; secondary: 46B28","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":"2019-04-15T12:23:06Z","title":"Compactification, and beyond, of composition operators on Hardy spaces by weights"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.06992","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":"sha256:525ae051a26868652239f773529060e10619175218948f4f1009657596ebbd85","target":"record","created_at":"2026-05-17T23:48:35Z","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":"ac19aa494474fc3478c4ad6386e03640e006ed7c23f3de83111d6b760662d068","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-15T12:23:06Z","title_canon_sha256":"1bf7baf61b06b0ca1d091c23cc1e75f91496dfe1ada3000e2ef5864431acc170"},"schema_version":"1.0","source":{"id":"1904.06992","kind":"arxiv","version":1}},"canonical_sha256":"7c6dc49281f12377a969d006cd7bc8c7d7972350076a0a75d92550b277237863","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c6dc49281f12377a969d006cd7bc8c7d7972350076a0a75d92550b277237863","first_computed_at":"2026-05-17T23:48:35.544493Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:35.544493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dgjH2uFZ+3I5LisUTLS74U4cYgwiKzZprTiVPofC1wj+cos4SJ2dnEQNFMwjn6rw3C+MRla4RXDFjCfF4eXiAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:35.545044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.06992","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:525ae051a26868652239f773529060e10619175218948f4f1009657596ebbd85","sha256:b66146f9e09538546260393172a082b7fc0644ebe575903c20d1b9c700e41cc9"],"state_sha256":"4e4c6b2e927d515b4252478622faf166fe36fd9231fde700a2082cb49037aa03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vER1Yu+aPzvDjIbNdbVT1O5/sLSri7SFZcqeH7NSBRhFPE0MJfXbu/VAix0yxpd0szpz17CzEh1MBktR+HTAAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T09:10:27.184718Z","bundle_sha256":"202bf9a5c00d441d9f088b637257c0b406caf137e44b9be6020e3d91e54ace56"}}