{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5QJCU5W76E43PHYUKLILWAIS4D","short_pith_number":"pith:5QJCU5W7","canonical_record":{"source":{"id":"1802.04026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T13:16:46Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"5a7cb324cb7e58e9503c250e099a946ae498abbbd8494a9d031681c1f8179350","abstract_canon_sha256":"8d824d7e090e23cf251e70162e1480e33530f341a72f72604b14d7b1cb831f01"},"schema_version":"1.0"},"canonical_sha256":"ec122a76dff139b79f1452d0bb0112e0cda040f43ba688beba45c384bf3c1fd4","source":{"kind":"arxiv","id":"1802.04026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04026","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04026v1","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04026","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"pith_short_12","alias_value":"5QJCU5W76E43","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5QJCU5W76E43PHYU","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5QJCU5W7","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5QJCU5W76E43PHYUKLILWAIS4D","target":"record","payload":{"canonical_record":{"source":{"id":"1802.04026","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T13:16:46Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"5a7cb324cb7e58e9503c250e099a946ae498abbbd8494a9d031681c1f8179350","abstract_canon_sha256":"8d824d7e090e23cf251e70162e1480e33530f341a72f72604b14d7b1cb831f01"},"schema_version":"1.0"},"canonical_sha256":"ec122a76dff139b79f1452d0bb0112e0cda040f43ba688beba45c384bf3c1fd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:49.690782Z","signature_b64":"hTg6HKnNZli+D0iioTDkvE8GbyQKlV8xXG4zXpYxK2Jcpz4KkOsGb/GIgfAEofJRkqmV7T/myoBBnAl3WnRgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ec122a76dff139b79f1452d0bb0112e0cda040f43ba688beba45c384bf3c1fd4","last_reissued_at":"2026-05-18T00:23:49.689812Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:49.689812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1802.04026","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":"2026-05-18T00:23:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cld3sBTla2TjPpWBA8GZ99zzYHtKkud2US4OCmX/KJuEV6yZfVd0TuDi7+0IPA58C0ZtAqQCRCkIG77Zg0ENDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:32:12.620492Z"},"content_sha256":"fe79a09953e467fd40f6053e63a7720c30bff69317dbfc0b3c0045a694de65b4","schema_version":"1.0","event_id":"sha256:fe79a09953e467fd40f6053e63a7720c30bff69317dbfc0b3c0045a694de65b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5QJCU5W76E43PHYUKLILWAIS4D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multipliers between range spaces of co-analytic Toeplitz operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Andreas Hartmann (IMB), Emmanuel Fricain (LPP), William Ross, William T. Ross","submitted_at":"2018-02-12T13:16:46Z","abstract_excerpt":"In this paper we discuss the multipliers between range spaces of co-analytic Toeplitz operators."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04026","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":"2026-05-18T00:23:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xt0MWvbJqwMzbNFGkLUEs2o3S8sxHd/syilCm+58dGGD3PlZeoofxB4TrGiAcpPVeBAWNS7MxDIK1PDPZ8FxDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T10:32:12.620837Z"},"content_sha256":"09f19e3331ee05d83268218ef869fb95126f80e27d9e70856fbce213c98e103c","schema_version":"1.0","event_id":"sha256:09f19e3331ee05d83268218ef869fb95126f80e27d9e70856fbce213c98e103c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5QJCU5W76E43PHYUKLILWAIS4D/bundle.json","state_url":"https://pith.science/pith/5QJCU5W76E43PHYUKLILWAIS4D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5QJCU5W76E43PHYUKLILWAIS4D/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":"2026-06-01T10:32:12Z","links":{"resolver":"https://pith.science/pith/5QJCU5W76E43PHYUKLILWAIS4D","bundle":"https://pith.science/pith/5QJCU5W76E43PHYUKLILWAIS4D/bundle.json","state":"https://pith.science/pith/5QJCU5W76E43PHYUKLILWAIS4D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5QJCU5W76E43PHYUKLILWAIS4D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5QJCU5W76E43PHYUKLILWAIS4D","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":"8d824d7e090e23cf251e70162e1480e33530f341a72f72604b14d7b1cb831f01","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T13:16:46Z","title_canon_sha256":"5a7cb324cb7e58e9503c250e099a946ae498abbbd8494a9d031681c1f8179350"},"schema_version":"1.0","source":{"id":"1802.04026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.04026","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"arxiv_version","alias_value":"1802.04026v1","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.04026","created_at":"2026-05-18T00:23:49Z"},{"alias_kind":"pith_short_12","alias_value":"5QJCU5W76E43","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5QJCU5W76E43PHYU","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5QJCU5W7","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:09f19e3331ee05d83268218ef869fb95126f80e27d9e70856fbce213c98e103c","target":"graph","created_at":"2026-05-18T00:23:49Z","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":"In this paper we discuss the multipliers between range spaces of co-analytic Toeplitz operators.","authors_text":"Andreas Hartmann (IMB), Emmanuel Fricain (LPP), William Ross, William T. Ross","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T13:16:46Z","title":"Multipliers between range spaces of co-analytic Toeplitz operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04026","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:fe79a09953e467fd40f6053e63a7720c30bff69317dbfc0b3c0045a694de65b4","target":"record","created_at":"2026-05-18T00:23:49Z","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":"8d824d7e090e23cf251e70162e1480e33530f341a72f72604b14d7b1cb831f01","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-02-12T13:16:46Z","title_canon_sha256":"5a7cb324cb7e58e9503c250e099a946ae498abbbd8494a9d031681c1f8179350"},"schema_version":"1.0","source":{"id":"1802.04026","kind":"arxiv","version":1}},"canonical_sha256":"ec122a76dff139b79f1452d0bb0112e0cda040f43ba688beba45c384bf3c1fd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec122a76dff139b79f1452d0bb0112e0cda040f43ba688beba45c384bf3c1fd4","first_computed_at":"2026-05-18T00:23:49.689812Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:49.689812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hTg6HKnNZli+D0iioTDkvE8GbyQKlV8xXG4zXpYxK2Jcpz4KkOsGb/GIgfAEofJRkqmV7T/myoBBnAl3WnRgCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:49.690782Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.04026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe79a09953e467fd40f6053e63a7720c30bff69317dbfc0b3c0045a694de65b4","sha256:09f19e3331ee05d83268218ef869fb95126f80e27d9e70856fbce213c98e103c"],"state_sha256":"707aeb42ed7ccd8e7143ee8c53c709ed5879a64dae0b74e43bf3a76fbd7f24f1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eZRapwDwFiJk9DAQlLy3g8KudP09rvORS5/l6gfpvWcQCv3jq0dpvjLBXajsMYiXnTCGDPITywxxlLMXcVD4Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T10:32:12.622814Z","bundle_sha256":"f9f41b4d813c33d7ee4f4b6729eb3f3199525cfa34844fb9e599ccb5d4bb82ad"}}