{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:HOYHGCCLWFXZNRJI2DSAYTHIJW","short_pith_number":"pith:HOYHGCCL","canonical_record":{"source":{"id":"1404.3514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-14T09:47:08Z","cross_cats_sorted":[],"title_canon_sha256":"2df9ac0d6972a4f1fa8f0927467bcad873ac67e3ae37da7d60e24efabe2f313f","abstract_canon_sha256":"ade78192fca6248f7caf9ea3fa9b7e336358b48831c8cdbe7e3eb6afbc81c5ce"},"schema_version":"1.0"},"canonical_sha256":"3bb073084bb16f96c528d0e40c4ce84d8652e6f25321cb675673fe9f0f5682e3","source":{"kind":"arxiv","id":"1404.3514","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3514","created_at":"2026-05-18T02:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3514v1","created_at":"2026-05-18T02:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3514","created_at":"2026-05-18T02:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"HOYHGCCLWFXZ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HOYHGCCLWFXZNRJI","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HOYHGCCL","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:HOYHGCCLWFXZNRJI2DSAYTHIJW","target":"record","payload":{"canonical_record":{"source":{"id":"1404.3514","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-14T09:47:08Z","cross_cats_sorted":[],"title_canon_sha256":"2df9ac0d6972a4f1fa8f0927467bcad873ac67e3ae37da7d60e24efabe2f313f","abstract_canon_sha256":"ade78192fca6248f7caf9ea3fa9b7e336358b48831c8cdbe7e3eb6afbc81c5ce"},"schema_version":"1.0"},"canonical_sha256":"3bb073084bb16f96c528d0e40c4ce84d8652e6f25321cb675673fe9f0f5682e3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:15.040253Z","signature_b64":"XB/JnXbctTOhtLkDKA8P7sJUabue429ff/BbW8JFONHGq+MhOfaDWsqHPe4K11PFHpoOQG7gHbWcndrl4aj+BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3bb073084bb16f96c528d0e40c4ce84d8652e6f25321cb675673fe9f0f5682e3","last_reissued_at":"2026-05-18T02:54:15.039819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:15.039819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.3514","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":"2026-05-18T02:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TuqFbIwv9DR5jPy4jdcUt6O1m/5DrKTB5kgtWOlgx6QuF/ZLUoxWeWffsZISsau3e9J0ffDJFk0CNrsK/EvSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:28:16.161243Z"},"content_sha256":"56dd6e88c7b850917816c27e1c6fbb0a865fbdde5667a0d4749988fda1ad8e34","schema_version":"1.0","event_id":"sha256:56dd6e88c7b850917816c27e1c6fbb0a865fbdde5667a0d4749988fda1ad8e34"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:HOYHGCCLWFXZNRJI2DSAYTHIJW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isometric and invertible composition operators on weighted Bergman spaces of Dirichlet series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Maxime Bailleul","submitted_at":"2014-04-14T09:47:08Z","abstract_excerpt":"We show that a composition operator on weighted Bergman spaces $\\mathcal{A}_{\\mu}^p$ is invertible if and only if it is Fredholm if and only if it is an isometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3514","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":"2026-05-18T02:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pn+hYCUxit3yeA5J+4VGgdgB+nHCOtAO/UCs+Pj/hxNTs5LCiBaLDuV+IzLmZHXF2sK1eTCaSuUODiq5Xd3ABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T04:28:16.161646Z"},"content_sha256":"5424728b8a5df4157c9a89bc51862a0b67ff9de0b612d9fd8ecf660a89233f09","schema_version":"1.0","event_id":"sha256:5424728b8a5df4157c9a89bc51862a0b67ff9de0b612d9fd8ecf660a89233f09"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HOYHGCCLWFXZNRJI2DSAYTHIJW/bundle.json","state_url":"https://pith.science/pith/HOYHGCCLWFXZNRJI2DSAYTHIJW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HOYHGCCLWFXZNRJI2DSAYTHIJW/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":"2026-06-27T04:28:16Z","links":{"resolver":"https://pith.science/pith/HOYHGCCLWFXZNRJI2DSAYTHIJW","bundle":"https://pith.science/pith/HOYHGCCLWFXZNRJI2DSAYTHIJW/bundle.json","state":"https://pith.science/pith/HOYHGCCLWFXZNRJI2DSAYTHIJW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HOYHGCCLWFXZNRJI2DSAYTHIJW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:HOYHGCCLWFXZNRJI2DSAYTHIJW","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":"ade78192fca6248f7caf9ea3fa9b7e336358b48831c8cdbe7e3eb6afbc81c5ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-14T09:47:08Z","title_canon_sha256":"2df9ac0d6972a4f1fa8f0927467bcad873ac67e3ae37da7d60e24efabe2f313f"},"schema_version":"1.0","source":{"id":"1404.3514","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3514","created_at":"2026-05-18T02:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3514v1","created_at":"2026-05-18T02:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3514","created_at":"2026-05-18T02:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"HOYHGCCLWFXZ","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"HOYHGCCLWFXZNRJI","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"HOYHGCCL","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:5424728b8a5df4157c9a89bc51862a0b67ff9de0b612d9fd8ecf660a89233f09","target":"graph","created_at":"2026-05-18T02:54:15Z","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 show that a composition operator on weighted Bergman spaces $\\mathcal{A}_{\\mu}^p$ is invertible if and only if it is Fredholm if and only if it is an isometry.","authors_text":"Maxime Bailleul","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-14T09:47:08Z","title":"Isometric and invertible composition operators on weighted Bergman spaces of Dirichlet series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3514","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":"sha256:56dd6e88c7b850917816c27e1c6fbb0a865fbdde5667a0d4749988fda1ad8e34","target":"record","created_at":"2026-05-18T02:54:15Z","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":"ade78192fca6248f7caf9ea3fa9b7e336358b48831c8cdbe7e3eb6afbc81c5ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-14T09:47:08Z","title_canon_sha256":"2df9ac0d6972a4f1fa8f0927467bcad873ac67e3ae37da7d60e24efabe2f313f"},"schema_version":"1.0","source":{"id":"1404.3514","kind":"arxiv","version":1}},"canonical_sha256":"3bb073084bb16f96c528d0e40c4ce84d8652e6f25321cb675673fe9f0f5682e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bb073084bb16f96c528d0e40c4ce84d8652e6f25321cb675673fe9f0f5682e3","first_computed_at":"2026-05-18T02:54:15.039819Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:15.039819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XB/JnXbctTOhtLkDKA8P7sJUabue429ff/BbW8JFONHGq+MhOfaDWsqHPe4K11PFHpoOQG7gHbWcndrl4aj+BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:15.040253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3514","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:56dd6e88c7b850917816c27e1c6fbb0a865fbdde5667a0d4749988fda1ad8e34","sha256:5424728b8a5df4157c9a89bc51862a0b67ff9de0b612d9fd8ecf660a89233f09"],"state_sha256":"f19809b7233393592f0dadab59f394898615cb612124664098bd7fc4a29b697f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VXi4enc8sAY5lbW0rh7/MO97cWd9ojninTzReXDur1YRqTGinr7BGBGLi3je1xGcdNVBFEs/YodQdQ16RZAUCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T04:28:16.163630Z","bundle_sha256":"51ba27c22c7041282deaf6bd7d455125a0c6ca8f7e3951ef7699d5a0ea62667b"}}