{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Q7QRWXAKVU4QCWYPRCNRH3YFH2","short_pith_number":"pith:Q7QRWXAK","canonical_record":{"source":{"id":"2608.13550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-13T17:59:28Z","cross_cats_sorted":[],"title_canon_sha256":"328f83b5da73d645963147b4c80c928cac1b52a036335a1ea38c2791d16b898b","abstract_canon_sha256":"6a3e420be027733a55ff3fbd4d902dd124ea4a9468c7c65cf92543ba5765f69e"},"schema_version":"1.0"},"canonical_sha256":"87e11b5c0aad39015b0f889b13ef053e840f5cad76c2ad34988737dbf4eb8e6c","source":{"kind":"arxiv","id":"2608.13550","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13550","created_at":"2026-08-14T01:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13550v1","created_at":"2026-08-14T01:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13550","created_at":"2026-08-14T01:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"Q7QRWXAKVU4Q","created_at":"2026-08-14T01:25:02Z"},{"alias_kind":"pith_short_16","alias_value":"Q7QRWXAKVU4QCWYP","created_at":"2026-08-14T01:25:02Z"},{"alias_kind":"pith_short_8","alias_value":"Q7QRWXAK","created_at":"2026-08-14T01:25:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Q7QRWXAKVU4QCWYPRCNRH3YFH2","target":"record","payload":{"canonical_record":{"source":{"id":"2608.13550","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-13T17:59:28Z","cross_cats_sorted":[],"title_canon_sha256":"328f83b5da73d645963147b4c80c928cac1b52a036335a1ea38c2791d16b898b","abstract_canon_sha256":"6a3e420be027733a55ff3fbd4d902dd124ea4a9468c7c65cf92543ba5765f69e"},"schema_version":"1.0"},"canonical_sha256":"87e11b5c0aad39015b0f889b13ef053e840f5cad76c2ad34988737dbf4eb8e6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-14T01:25:02.877196Z","signature_b64":"ruz7pf3lTg5a36U+O8THeZwzJE62dTquQisipf2IrzvkPsrubUcHUGmbeDk7ToKcDtfXKgScgSOSgA/4N348AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"87e11b5c0aad39015b0f889b13ef053e840f5cad76c2ad34988737dbf4eb8e6c","last_reissued_at":"2026-08-14T01:25:02.874999Z","signature_status":"signed_v1","first_computed_at":"2026-08-14T01:25:02.874999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.13550","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":"2026-08-14T01:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gN3/J0pmW9657QVR7/DI+Znreizm3aq1FfQeLHy66xUKo2d/iloDKs/PF2ZyrKMOmyAn3v6va6QPBV6IcIQqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T11:30:24.445770Z"},"content_sha256":"0088f07a65acadd591727e1c010d4afff354304f90577921bf4e3f685ac3dce9","schema_version":"1.0","event_id":"sha256:0088f07a65acadd591727e1c010d4afff354304f90577921bf4e3f685ac3dce9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Q7QRWXAKVU4QCWYPRCNRH3YFH2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive Toeplitz operators on pluriharmonic Fock space: Schatten class criteria and sharp norm comparisons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sam Looi","submitted_at":"2026-08-13T17:59:28Z","abstract_excerpt":"Let $\\mu$ be a positive Borel measure on $\\C^n$. For every $0<p<\\infty$, we prove that the Toeplitz operator $T_\\mu^{\\mathrm{ph}}$ induced by $\\mu$ on pluriharmonic Fock space belongs to $\\Sp_p$ if and only if $z\\mapsto\\mu(B(z,r))$ belongs to $L^p(\\C^n)$ for one, or equivalently every, $r>0$; this is also equivalent to Schatten membership of the corresponding holomorphic Toeplitz operator $T_\\mu$. For $n\\geq2$, this settles a conjecture of Jaguzovi\\'c and Vujadinovi\\'c, and the result includes the range $0<p<1$ in every dimension. Moreover, \\[\n  \\norm{T_\\mu}_{\\Sp_p}^p\n  \\leq\\norm{T_\\mu^{\\mathr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13550","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.13550/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":"2026-08-14T01:25:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BEtNkQj1Pra2qvMiL2if297Ue2LVJa0VPBmRoFhc/2Y7ssF6SzOZAZ7XEaKx5t1NotnkeTqUx5EiiAbfZtEBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T11:30:24.446270Z"},"content_sha256":"a20a5f70efecda3f065ba1d3a2822598338bd2d3462831c057fede7d0a376b6b","schema_version":"1.0","event_id":"sha256:a20a5f70efecda3f065ba1d3a2822598338bd2d3462831c057fede7d0a376b6b"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:Q7QRWXAKVU4QCWYPRCNRH3YFH2","target":"integrity","payload":{"note":"DOI in the printed bibliography is fragmented by whitespace or line breaks. A longer candidate (10.1007/s11785-021-01115-5) was visible in the surrounding text but could not be confirmed against doi.org as printed.","snippet":"D. Vujadinović,Carleson measures for harmonic Fock spaces in the plane, Complex Anal. Oper. Theory15(2021), no. 4, Paper No. 72, 11 pp. doi:10.1007/s11785-021- 01115-5","arxiv_id":"2608.13550","detector":"doi_compliance","evidence":{"ref_index":17,"verdict_class":"incontrovertible","resolved_title":null,"printed_excerpt":"10.1007/s11785-021-","reconstructed_doi":"10.1007/s11785-021-01115-5"},"severity":"advisory","ref_index":17,"audited_at":"2026-08-14T04:28:15.470963Z","event_type":"pith.integrity.v1","detected_doi":"10.1007/s11785-021-01115-5","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"f80826ea75bd0b0e03da8c0ea3431bc3f1313530c17a2f04d7af1a51093cb856","paper_version":1,"verdict_class":"incontrovertible","resolved_title":null,"detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":19481,"payload_sha256":"c6374f1f01e0d3e3f1e3179486d8e82e7550586ae0f8f247187bb6d129cb3b27","signature_b64":"mUJCgIr7L7b2wniBadJTCiUhyGqdAzqIKCmJdA7pjGxfT4LoSXyS2wtJf1jaV3QlM3A7rPJK1Nffq8eJiCO2Cw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-14T04:28:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hgmK4RhqkZCHf87/3aKUg3JFAET3YQjlKKS4JkUiWb1MWCHA/t51ZvU0utDVs277CNBOhGbzsZ41n7eexQX0Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T11:30:24.450102Z"},"content_sha256":"e37d31e35ed4740d0a8b0b7e501e500163791ee91db27b45e1c5b9f0ec7ae9d5","schema_version":"1.0","event_id":"sha256:e37d31e35ed4740d0a8b0b7e501e500163791ee91db27b45e1c5b9f0ec7ae9d5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q7QRWXAKVU4QCWYPRCNRH3YFH2/bundle.json","state_url":"https://pith.science/pith/Q7QRWXAKVU4QCWYPRCNRH3YFH2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q7QRWXAKVU4QCWYPRCNRH3YFH2/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":"2026-08-15T11:30:24Z","links":{"resolver":"https://pith.science/pith/Q7QRWXAKVU4QCWYPRCNRH3YFH2","bundle":"https://pith.science/pith/Q7QRWXAKVU4QCWYPRCNRH3YFH2/bundle.json","state":"https://pith.science/pith/Q7QRWXAKVU4QCWYPRCNRH3YFH2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q7QRWXAKVU4QCWYPRCNRH3YFH2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Q7QRWXAKVU4QCWYPRCNRH3YFH2","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"6a3e420be027733a55ff3fbd4d902dd124ea4a9468c7c65cf92543ba5765f69e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-13T17:59:28Z","title_canon_sha256":"328f83b5da73d645963147b4c80c928cac1b52a036335a1ea38c2791d16b898b"},"schema_version":"1.0","source":{"id":"2608.13550","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.13550","created_at":"2026-08-14T01:25:02Z"},{"alias_kind":"arxiv_version","alias_value":"2608.13550v1","created_at":"2026-08-14T01:25:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.13550","created_at":"2026-08-14T01:25:02Z"},{"alias_kind":"pith_short_12","alias_value":"Q7QRWXAKVU4Q","created_at":"2026-08-14T01:25:02Z"},{"alias_kind":"pith_short_16","alias_value":"Q7QRWXAKVU4QCWYP","created_at":"2026-08-14T01:25:02Z"},{"alias_kind":"pith_short_8","alias_value":"Q7QRWXAK","created_at":"2026-08-14T01:25:02Z"}],"graph_snapshots":[{"event_id":"sha256:a20a5f70efecda3f065ba1d3a2822598338bd2d3462831c057fede7d0a376b6b","target":"graph","created_at":"2026-08-14T01:25:02Z","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/2608.13550/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\mu$ be a positive Borel measure on $\\C^n$. For every $0<p<\\infty$, we prove that the Toeplitz operator $T_\\mu^{\\mathrm{ph}}$ induced by $\\mu$ on pluriharmonic Fock space belongs to $\\Sp_p$ if and only if $z\\mapsto\\mu(B(z,r))$ belongs to $L^p(\\C^n)$ for one, or equivalently every, $r>0$; this is also equivalent to Schatten membership of the corresponding holomorphic Toeplitz operator $T_\\mu$. For $n\\geq2$, this settles a conjecture of Jaguzovi\\'c and Vujadinovi\\'c, and the result includes the range $0<p<1$ in every dimension. Moreover, \\[\n  \\norm{T_\\mu}_{\\Sp_p}^p\n  \\leq\\norm{T_\\mu^{\\mathr","authors_text":"Sam Looi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-13T17:59:28Z","title":"Positive Toeplitz operators on pluriharmonic Fock space: Schatten class criteria and sharp norm comparisons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.13550","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":"sha256:0088f07a65acadd591727e1c010d4afff354304f90577921bf4e3f685ac3dce9","target":"record","created_at":"2026-08-14T01:25:02Z","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":"6a3e420be027733a55ff3fbd4d902dd124ea4a9468c7c65cf92543ba5765f69e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-08-13T17:59:28Z","title_canon_sha256":"328f83b5da73d645963147b4c80c928cac1b52a036335a1ea38c2791d16b898b"},"schema_version":"1.0","source":{"id":"2608.13550","kind":"arxiv","version":1}},"canonical_sha256":"87e11b5c0aad39015b0f889b13ef053e840f5cad76c2ad34988737dbf4eb8e6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87e11b5c0aad39015b0f889b13ef053e840f5cad76c2ad34988737dbf4eb8e6c","first_computed_at":"2026-08-14T01:25:02.874999Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-14T01:25:02.874999Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ruz7pf3lTg5a36U+O8THeZwzJE62dTquQisipf2IrzvkPsrubUcHUGmbeDk7ToKcDtfXKgScgSOSgA/4N348AA==","signature_status":"signed_v1","signed_at":"2026-08-14T01:25:02.877196Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.13550","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0088f07a65acadd591727e1c010d4afff354304f90577921bf4e3f685ac3dce9","sha256:a20a5f70efecda3f065ba1d3a2822598338bd2d3462831c057fede7d0a376b6b","sha256:e37d31e35ed4740d0a8b0b7e501e500163791ee91db27b45e1c5b9f0ec7ae9d5"],"state_sha256":"69f98578770ba8da4253681e801da9c21f2bacb9dcc97cf5b718085d63ab6339"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZvUIUF6Lv6MpQtpQ+NGapZCT7QnjFuHvQ+vXPEPqCeE/9hhXw2UKrISWvfWUvVjrBrMj9WgOIYUfZdbmj4JzCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T11:30:24.452397Z","bundle_sha256":"41504a1ca2a2b250059e09a607a6a15074f453500668ddf4d26cd504c6a41092"}}