{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WYETHRFA6Q7KD534DBOT5UID76","short_pith_number":"pith:WYETHRFA","canonical_record":{"source":{"id":"1703.02792","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-08T11:21:18Z","cross_cats_sorted":[],"title_canon_sha256":"5baf8446eb5fd39a05c49633044f87606ef026ff09441c54c48c7db4cbe05a47","abstract_canon_sha256":"7413b2a0302e2758241cc8bf453c39f80d548102d3f59f69e211f0cb311e6d8e"},"schema_version":"1.0"},"canonical_sha256":"b60933c4a0f43ea1f77c185d3ed103ffae99de3038b9adab93928ac016d427b0","source":{"kind":"arxiv","id":"1703.02792","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02792","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02792v2","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02792","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"pith_short_12","alias_value":"WYETHRFA6Q7K","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WYETHRFA6Q7KD534","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WYETHRFA","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WYETHRFA6Q7KD534DBOT5UID76","target":"record","payload":{"canonical_record":{"source":{"id":"1703.02792","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-08T11:21:18Z","cross_cats_sorted":[],"title_canon_sha256":"5baf8446eb5fd39a05c49633044f87606ef026ff09441c54c48c7db4cbe05a47","abstract_canon_sha256":"7413b2a0302e2758241cc8bf453c39f80d548102d3f59f69e211f0cb311e6d8e"},"schema_version":"1.0"},"canonical_sha256":"b60933c4a0f43ea1f77c185d3ed103ffae99de3038b9adab93928ac016d427b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:35.145989Z","signature_b64":"J93vLWY8lvHhs/U7RVzX65O7bziEMCssPX4pcDLOLBCPEm+UNGT7MTRyi/a2acqaQxC/IXNwb1bI4/MU4kQqAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b60933c4a0f43ea1f77c185d3ed103ffae99de3038b9adab93928ac016d427b0","last_reissued_at":"2026-05-18T00:43:35.145566Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:35.145566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.02792","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":"2026-05-18T00:43:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U5G05M1nWRvjPSL4f4vRHu6sgJ/+xPmxfD04ATm8+NSnNNmtRXwEtcwIrta44MZO8IVKOdgJnTFp8MayrrP1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:54:16.696591Z"},"content_sha256":"efd11044c9f62d1e3393ce585dc62119f483346c36e0479a2a57fdd81cb9dc16","schema_version":"1.0","event_id":"sha256:efd11044c9f62d1e3393ce585dc62119f483346c36e0479a2a57fdd81cb9dc16"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WYETHRFA6Q7KD534DBOT5UID76","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On sum of two subnormal kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Soumitra Ghara, Surjit Kumar","submitted_at":"2017-03-08T11:21:18Z","abstract_excerpt":"We show, by means of a class of examples, that if $K_1$ and $K_2$ are two positive definite kernels on the unit disc such that the multiplication by the coordinate function on the corresponding reproducing kernel Hilbert space is subnormal, then the multiplication operator on the Hilbert space determined by their sum $K_1+K_2$ need not be subnormal. This settles a recent conjecture of Gregory T. Adams, Nathan S. Feldman and Paul J. McGuire in the negative. We also discuss some cases for which the answer is affirmative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02792","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":""},"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":"2026-05-18T00:43:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zAxjpNPcpTfGBQ+NfEWqwoNFZtEfr54glslBRXtsdbdh0OfkpSf3rtB2nmcW+WQJ+bQXS5h4Gc7wRkfD8JdkBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T22:54:16.696920Z"},"content_sha256":"c5de5b8063aa5fc202e782ce0ea824039331d469ab56ce989d14106ec9853f58","schema_version":"1.0","event_id":"sha256:c5de5b8063aa5fc202e782ce0ea824039331d469ab56ce989d14106ec9853f58"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WYETHRFA6Q7KD534DBOT5UID76/bundle.json","state_url":"https://pith.science/pith/WYETHRFA6Q7KD534DBOT5UID76/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WYETHRFA6Q7KD534DBOT5UID76/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":"2026-06-10T22:54:16Z","links":{"resolver":"https://pith.science/pith/WYETHRFA6Q7KD534DBOT5UID76","bundle":"https://pith.science/pith/WYETHRFA6Q7KD534DBOT5UID76/bundle.json","state":"https://pith.science/pith/WYETHRFA6Q7KD534DBOT5UID76/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WYETHRFA6Q7KD534DBOT5UID76/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WYETHRFA6Q7KD534DBOT5UID76","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":"7413b2a0302e2758241cc8bf453c39f80d548102d3f59f69e211f0cb311e6d8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-08T11:21:18Z","title_canon_sha256":"5baf8446eb5fd39a05c49633044f87606ef026ff09441c54c48c7db4cbe05a47"},"schema_version":"1.0","source":{"id":"1703.02792","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.02792","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"arxiv_version","alias_value":"1703.02792v2","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.02792","created_at":"2026-05-18T00:43:35Z"},{"alias_kind":"pith_short_12","alias_value":"WYETHRFA6Q7K","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WYETHRFA6Q7KD534","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WYETHRFA","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:c5de5b8063aa5fc202e782ce0ea824039331d469ab56ce989d14106ec9853f58","target":"graph","created_at":"2026-05-18T00:43:35Z","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 show, by means of a class of examples, that if $K_1$ and $K_2$ are two positive definite kernels on the unit disc such that the multiplication by the coordinate function on the corresponding reproducing kernel Hilbert space is subnormal, then the multiplication operator on the Hilbert space determined by their sum $K_1+K_2$ need not be subnormal. This settles a recent conjecture of Gregory T. Adams, Nathan S. Feldman and Paul J. McGuire in the negative. We also discuss some cases for which the answer is affirmative.","authors_text":"Soumitra Ghara, Surjit Kumar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-08T11:21:18Z","title":"On sum of two subnormal kernels"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.02792","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:efd11044c9f62d1e3393ce585dc62119f483346c36e0479a2a57fdd81cb9dc16","target":"record","created_at":"2026-05-18T00:43:35Z","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":"7413b2a0302e2758241cc8bf453c39f80d548102d3f59f69e211f0cb311e6d8e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-03-08T11:21:18Z","title_canon_sha256":"5baf8446eb5fd39a05c49633044f87606ef026ff09441c54c48c7db4cbe05a47"},"schema_version":"1.0","source":{"id":"1703.02792","kind":"arxiv","version":2}},"canonical_sha256":"b60933c4a0f43ea1f77c185d3ed103ffae99de3038b9adab93928ac016d427b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b60933c4a0f43ea1f77c185d3ed103ffae99de3038b9adab93928ac016d427b0","first_computed_at":"2026-05-18T00:43:35.145566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:35.145566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J93vLWY8lvHhs/U7RVzX65O7bziEMCssPX4pcDLOLBCPEm+UNGT7MTRyi/a2acqaQxC/IXNwb1bI4/MU4kQqAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:35.145989Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.02792","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:efd11044c9f62d1e3393ce585dc62119f483346c36e0479a2a57fdd81cb9dc16","sha256:c5de5b8063aa5fc202e782ce0ea824039331d469ab56ce989d14106ec9853f58"],"state_sha256":"4b48189a84ae637529965bf5cf6dda21ef23997158f81bf5ac4f0452a1ce47bc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GD7JyKgDWVbn5knZda0gAQFiz4d7pFfJ3eIkiyMSJTdqM8oz3QxCMOtk+h0czcXjG1zvwKrpLzmAuylr39lsAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T22:54:16.698784Z","bundle_sha256":"51f5cf9d8fd45296e129bd53a1bf212ad94633f74eda3d34fc0f0f9d964c9552"}}