{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:XSCVUFZHC37WKIDRV7IGKJWYN2","short_pith_number":"pith:XSCVUFZH","canonical_record":{"source":{"id":"2104.12220","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2021-04-25T18:04:00Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"d3dd30ae56a762677ec45a04f14ddc47d26057332721fc7b4af058e69150082f","abstract_canon_sha256":"c85a4db36922a882fb79742fa846a16ac6ef211a61c041575904dcb2c9f5abe1"},"schema_version":"1.0"},"canonical_sha256":"bc855a172716ff652071afd06526d86e9c3957275cbb147638e6a807cfdd04ab","source":{"kind":"arxiv","id":"2104.12220","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.12220","created_at":"2026-07-05T04:50:10Z"},{"alias_kind":"arxiv_version","alias_value":"2104.12220v2","created_at":"2026-07-05T04:50:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.12220","created_at":"2026-07-05T04:50:10Z"},{"alias_kind":"pith_short_12","alias_value":"XSCVUFZHC37W","created_at":"2026-07-05T04:50:10Z"},{"alias_kind":"pith_short_16","alias_value":"XSCVUFZHC37WKIDR","created_at":"2026-07-05T04:50:10Z"},{"alias_kind":"pith_short_8","alias_value":"XSCVUFZH","created_at":"2026-07-05T04:50:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:XSCVUFZHC37WKIDRV7IGKJWYN2","target":"record","payload":{"canonical_record":{"source":{"id":"2104.12220","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2021-04-25T18:04:00Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"d3dd30ae56a762677ec45a04f14ddc47d26057332721fc7b4af058e69150082f","abstract_canon_sha256":"c85a4db36922a882fb79742fa846a16ac6ef211a61c041575904dcb2c9f5abe1"},"schema_version":"1.0"},"canonical_sha256":"bc855a172716ff652071afd06526d86e9c3957275cbb147638e6a807cfdd04ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:50:10.282426Z","signature_b64":"vSzSbJruTs4ubCUvmDYYHbBEsw8W+cMbX639nnyUjdTozTYo0ZT/7r/b7S8jQ83XU1C/+Chot525cG6D9EqTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bc855a172716ff652071afd06526d86e9c3957275cbb147638e6a807cfdd04ab","last_reissued_at":"2026-07-05T04:50:10.282025Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:50:10.282025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.12220","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":"2026-07-05T04:50:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b95mss70iEsgyawR8jKBo8IEBJuUMjYHCkQ7ox/5yMhpg4PsBeXriLNYfHIAGk97sRpZtnaC2/nEt6unG5lICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T03:46:36.092431Z"},"content_sha256":"8a61f86c64e6ef005cab2c8deb6e87d8b6ee689d828f196dd5e87ca8c0d7559e","schema_version":"1.0","event_id":"sha256:8a61f86c64e6ef005cab2c8deb6e87d8b6ee689d828f196dd5e87ca8c0d7559e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:XSCVUFZHC37WKIDRV7IGKJWYN2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invertible and isometric weighted composition operators","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Alejandro Mas, Dragan Vukoti\\'c","submitted_at":"2021-04-25T18:04:00Z","abstract_excerpt":"We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces. For the spaces of analytic functions in the disk whose norm is given in terms of a natural seminorm (such as the typical spaces given in terms of derivatives), we describe all surjective weighted composition operators that are isometric. This generalizes a number of known results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.12220","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.12220/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:50:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XhYfPmTQKMUCbrKy/jt3CDfOr3XMr6RnBnjNB3exQ+ELPm5Au47MN2tZzvrSoEvmKw9cBjPzDugUOTb5ArEyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T03:46:36.092808Z"},"content_sha256":"6d9934729d6737f6ccfaf7a3884891fb260482e515d421653a5aa844980e2886","schema_version":"1.0","event_id":"sha256:6d9934729d6737f6ccfaf7a3884891fb260482e515d421653a5aa844980e2886"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XSCVUFZHC37WKIDRV7IGKJWYN2/bundle.json","state_url":"https://pith.science/pith/XSCVUFZHC37WKIDRV7IGKJWYN2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XSCVUFZHC37WKIDRV7IGKJWYN2/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":"2026-07-07T03:46:36Z","links":{"resolver":"https://pith.science/pith/XSCVUFZHC37WKIDRV7IGKJWYN2","bundle":"https://pith.science/pith/XSCVUFZHC37WKIDRV7IGKJWYN2/bundle.json","state":"https://pith.science/pith/XSCVUFZHC37WKIDRV7IGKJWYN2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XSCVUFZHC37WKIDRV7IGKJWYN2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XSCVUFZHC37WKIDRV7IGKJWYN2","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":"c85a4db36922a882fb79742fa846a16ac6ef211a61c041575904dcb2c9f5abe1","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2021-04-25T18:04:00Z","title_canon_sha256":"d3dd30ae56a762677ec45a04f14ddc47d26057332721fc7b4af058e69150082f"},"schema_version":"1.0","source":{"id":"2104.12220","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.12220","created_at":"2026-07-05T04:50:10Z"},{"alias_kind":"arxiv_version","alias_value":"2104.12220v2","created_at":"2026-07-05T04:50:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.12220","created_at":"2026-07-05T04:50:10Z"},{"alias_kind":"pith_short_12","alias_value":"XSCVUFZHC37W","created_at":"2026-07-05T04:50:10Z"},{"alias_kind":"pith_short_16","alias_value":"XSCVUFZHC37WKIDR","created_at":"2026-07-05T04:50:10Z"},{"alias_kind":"pith_short_8","alias_value":"XSCVUFZH","created_at":"2026-07-05T04:50:10Z"}],"graph_snapshots":[{"event_id":"sha256:6d9934729d6737f6ccfaf7a3884891fb260482e515d421653a5aa844980e2886","target":"graph","created_at":"2026-07-05T04:50:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2104.12220/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider abstract Banach spaces of analytic functions on general bounded domains that satisfy only a minimum number of axioms. We describe all invertible (equivalently, surjective) weighted composition operators acting on such spaces. For the spaces of analytic functions in the disk whose norm is given in terms of a natural seminorm (such as the typical spaces given in terms of derivatives), we describe all surjective weighted composition operators that are isometric. This generalizes a number of known results.","authors_text":"Alejandro Mas, Dragan Vukoti\\'c","cross_cats":["math.CV"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2021-04-25T18:04:00Z","title":"Invertible and isometric weighted composition operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.12220","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":"sha256:8a61f86c64e6ef005cab2c8deb6e87d8b6ee689d828f196dd5e87ca8c0d7559e","target":"record","created_at":"2026-07-05T04:50:10Z","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":"c85a4db36922a882fb79742fa846a16ac6ef211a61c041575904dcb2c9f5abe1","cross_cats_sorted":["math.CV"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2021-04-25T18:04:00Z","title_canon_sha256":"d3dd30ae56a762677ec45a04f14ddc47d26057332721fc7b4af058e69150082f"},"schema_version":"1.0","source":{"id":"2104.12220","kind":"arxiv","version":2}},"canonical_sha256":"bc855a172716ff652071afd06526d86e9c3957275cbb147638e6a807cfdd04ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc855a172716ff652071afd06526d86e9c3957275cbb147638e6a807cfdd04ab","first_computed_at":"2026-07-05T04:50:10.282025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:50:10.282025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vSzSbJruTs4ubCUvmDYYHbBEsw8W+cMbX639nnyUjdTozTYo0ZT/7r/b7S8jQ83XU1C/+Chot525cG6D9EqTBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:50:10.282426Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.12220","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a61f86c64e6ef005cab2c8deb6e87d8b6ee689d828f196dd5e87ca8c0d7559e","sha256:6d9934729d6737f6ccfaf7a3884891fb260482e515d421653a5aa844980e2886"],"state_sha256":"f0f31fb49edd67914321fa9c0b85d6ad82ad4d69b1cf4b031a284aa5e68dddfa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X3lBHui6kfl3z3QCw1zZy2xOUMRoz7tsl30sNbFz6izuKCydsmvwIZnxmOrFcrDrzlt1MBiXQ/pN+xef211CCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T03:46:36.094749Z","bundle_sha256":"e9ccc729d4e5edef895b4c1c03c088200660b70501aa64bb91d580a796c5f689"}}