{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VY5XJB6HCRJ5XNLTHHK3P2HRA4","short_pith_number":"pith:VY5XJB6H","canonical_record":{"source":{"id":"1510.08128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-27T23:21:54Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"bbe987604c434a3ba49fe8b8cfb40eff8530fc83d1b0e0547db82b6baae5ee8d","abstract_canon_sha256":"994c2450a82a07f67ee2b0e8f12829b0736a720b6880db272e87bc53aa173352"},"schema_version":"1.0"},"canonical_sha256":"ae3b7487c71453dbb57339d5b7e8f10719f58ea35bb1b0e4bc7303b02b2c09c2","source":{"kind":"arxiv","id":"1510.08128","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08128","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08128v1","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08128","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"pith_short_12","alias_value":"VY5XJB6HCRJ5","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VY5XJB6HCRJ5XNLT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VY5XJB6H","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VY5XJB6HCRJ5XNLTHHK3P2HRA4","target":"record","payload":{"canonical_record":{"source":{"id":"1510.08128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-27T23:21:54Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"bbe987604c434a3ba49fe8b8cfb40eff8530fc83d1b0e0547db82b6baae5ee8d","abstract_canon_sha256":"994c2450a82a07f67ee2b0e8f12829b0736a720b6880db272e87bc53aa173352"},"schema_version":"1.0"},"canonical_sha256":"ae3b7487c71453dbb57339d5b7e8f10719f58ea35bb1b0e4bc7303b02b2c09c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:37.317664Z","signature_b64":"Vi8oSW1H6nTTN+VCT242yhfLjUtDOSm4KUp7Si8F28R2H1wHbEpN2u+ecGxjdcIRVgvwMk6hKJmvehFewS0rCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae3b7487c71453dbb57339d5b7e8f10719f58ea35bb1b0e4bc7303b02b2c09c2","last_reissued_at":"2026-05-18T01:28:37.316976Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:37.316976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.08128","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":"2026-05-18T01:28:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+++9SF89V3RhWOrTq/W+oUhzpmq8pikrdoRfBROwUuo5dFV2C04bYlbTPjpxDUCZQnwoqF2c81QLqmzrdvgDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T07:32:37.400972Z"},"content_sha256":"ce0a706563981435af593df950c8cb9e056a0b475b73db12054f394b35b0e783","schema_version":"1.0","event_id":"sha256:ce0a706563981435af593df950c8cb9e056a0b475b73db12054f394b35b0e783"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VY5XJB6HCRJ5XNLTHHK3P2HRA4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Gleason-Kahane-\\.Zelazko theorem for modules and applications to holomorphic function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.FA","authors_text":"Javad Mashreghi, Thomas Ransford","submitted_at":"2015-10-27T23:21:54Z","abstract_excerpt":"We generalize the Gleason-Kahane-\\.Zelazko theorem to modules. As an application, we show that every linear functional on a Hardy space that is non-zero on outer functions is a multiple of a point evaluation. A further consequence is that every linear endomorphism of a Hardy space that maps outer functions to nowhere-zero functions is a weighted composition operator. In neither case is continuity assumed. We also consider some extensions to other function spaces, including the Bergman, Dirichlet and Besov spaces, the little Bloch space and VMOA."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08128","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":"2026-05-18T01:28:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vkUG6PeL+OtzDepVVSHR990aV4KnOZRBapeOQTU2Q1E/g72c0QyuiVAUdLuVuRFl2divrh4sBpVGmCxdjazYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T07:32:37.401554Z"},"content_sha256":"990d3ef2748f0bb14f2e7f94793fb317343b3a3e0504cc677ae2ee39f52cfa02","schema_version":"1.0","event_id":"sha256:990d3ef2748f0bb14f2e7f94793fb317343b3a3e0504cc677ae2ee39f52cfa02"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VY5XJB6HCRJ5XNLTHHK3P2HRA4/bundle.json","state_url":"https://pith.science/pith/VY5XJB6HCRJ5XNLTHHK3P2HRA4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VY5XJB6HCRJ5XNLTHHK3P2HRA4/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":"2026-05-23T07:32:37Z","links":{"resolver":"https://pith.science/pith/VY5XJB6HCRJ5XNLTHHK3P2HRA4","bundle":"https://pith.science/pith/VY5XJB6HCRJ5XNLTHHK3P2HRA4/bundle.json","state":"https://pith.science/pith/VY5XJB6HCRJ5XNLTHHK3P2HRA4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VY5XJB6HCRJ5XNLTHHK3P2HRA4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VY5XJB6HCRJ5XNLTHHK3P2HRA4","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":"994c2450a82a07f67ee2b0e8f12829b0736a720b6880db272e87bc53aa173352","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-27T23:21:54Z","title_canon_sha256":"bbe987604c434a3ba49fe8b8cfb40eff8530fc83d1b0e0547db82b6baae5ee8d"},"schema_version":"1.0","source":{"id":"1510.08128","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08128","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08128v1","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08128","created_at":"2026-05-18T01:28:37Z"},{"alias_kind":"pith_short_12","alias_value":"VY5XJB6HCRJ5","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VY5XJB6HCRJ5XNLT","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VY5XJB6H","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:990d3ef2748f0bb14f2e7f94793fb317343b3a3e0504cc677ae2ee39f52cfa02","target":"graph","created_at":"2026-05-18T01:28:37Z","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 generalize the Gleason-Kahane-\\.Zelazko theorem to modules. As an application, we show that every linear functional on a Hardy space that is non-zero on outer functions is a multiple of a point evaluation. A further consequence is that every linear endomorphism of a Hardy space that maps outer functions to nowhere-zero functions is a weighted composition operator. In neither case is continuity assumed. We also consider some extensions to other function spaces, including the Bergman, Dirichlet and Besov spaces, the little Bloch space and VMOA.","authors_text":"Javad Mashreghi, Thomas Ransford","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-27T23:21:54Z","title":"A Gleason-Kahane-\\.Zelazko theorem for modules and applications to holomorphic function spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08128","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:ce0a706563981435af593df950c8cb9e056a0b475b73db12054f394b35b0e783","target":"record","created_at":"2026-05-18T01:28:37Z","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":"994c2450a82a07f67ee2b0e8f12829b0736a720b6880db272e87bc53aa173352","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-27T23:21:54Z","title_canon_sha256":"bbe987604c434a3ba49fe8b8cfb40eff8530fc83d1b0e0547db82b6baae5ee8d"},"schema_version":"1.0","source":{"id":"1510.08128","kind":"arxiv","version":1}},"canonical_sha256":"ae3b7487c71453dbb57339d5b7e8f10719f58ea35bb1b0e4bc7303b02b2c09c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae3b7487c71453dbb57339d5b7e8f10719f58ea35bb1b0e4bc7303b02b2c09c2","first_computed_at":"2026-05-18T01:28:37.316976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:37.316976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vi8oSW1H6nTTN+VCT242yhfLjUtDOSm4KUp7Si8F28R2H1wHbEpN2u+ecGxjdcIRVgvwMk6hKJmvehFewS0rCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:37.317664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08128","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce0a706563981435af593df950c8cb9e056a0b475b73db12054f394b35b0e783","sha256:990d3ef2748f0bb14f2e7f94793fb317343b3a3e0504cc677ae2ee39f52cfa02"],"state_sha256":"f693fa5b4af1adf15caefe7fa8b9cfaeb8f72c439e1ce4dac758ace08bd4cd1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bpeGG6KaXCQk1bl47SrsnYXER8peb859UTh7E+4XVOe7GFk/5sHbHqG1CInIPT4kxMNj5tBNqURGGCS+5nY9AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T07:32:37.405179Z","bundle_sha256":"e5d042a7b10e5b789def6754ac33dbbdb613eb40822a56cc7af1eff7600c9abc"}}