{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:IQL4EQ5R4ASQFVCQJI4KSPI4ZN","short_pith_number":"pith:IQL4EQ5R","canonical_record":{"source":{"id":"1612.03970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-12T23:34:05Z","cross_cats_sorted":[],"title_canon_sha256":"1e6a0e6d342194f3ae1240146bf6938106a15212db5fcb1274d6643d9dbd77cb","abstract_canon_sha256":"d0f7bd4dc8c88fda6c24119befc0aa1e4930d1afdd0e7977757c1a925d1e753b"},"schema_version":"1.0"},"canonical_sha256":"4417c243b1e02502d4504a38a93d1ccb727cfecf874a701cc10e17096ad21cb8","source":{"kind":"arxiv","id":"1612.03970","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03970","created_at":"2026-05-17T23:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03970v1","created_at":"2026-05-17T23:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03970","created_at":"2026-05-17T23:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"IQL4EQ5R4ASQ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IQL4EQ5R4ASQFVCQ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IQL4EQ5R","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:IQL4EQ5R4ASQFVCQJI4KSPI4ZN","target":"record","payload":{"canonical_record":{"source":{"id":"1612.03970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-12T23:34:05Z","cross_cats_sorted":[],"title_canon_sha256":"1e6a0e6d342194f3ae1240146bf6938106a15212db5fcb1274d6643d9dbd77cb","abstract_canon_sha256":"d0f7bd4dc8c88fda6c24119befc0aa1e4930d1afdd0e7977757c1a925d1e753b"},"schema_version":"1.0"},"canonical_sha256":"4417c243b1e02502d4504a38a93d1ccb727cfecf874a701cc10e17096ad21cb8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:18.196048Z","signature_b64":"s0pI5OvgKR9JnJgWPO0ras3CbV61OZF4GjC9OpFQJykgJrWj2Izkx8k2TaW+xOnpMU2iRcDzC1q1bydWLZNVDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4417c243b1e02502d4504a38a93d1ccb727cfecf874a701cc10e17096ad21cb8","last_reissued_at":"2026-05-17T23:59:18.195474Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:18.195474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.03970","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":"2026-05-17T23:59:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N7DIevfmraTSeTg37FYyx7is59B4OhX/s7IOo1Jkyf8F1ObL6K/Ajv9EAsmeXDRXouusnhHq8ZPlRaRyCtoMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T00:19:22.243876Z"},"content_sha256":"c745280fd66e3e7e658d13a3c39aba705800c357163caf65f91e04f51b2f1b85","schema_version":"1.0","event_id":"sha256:c745280fd66e3e7e658d13a3c39aba705800c357163caf65f91e04f51b2f1b85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:IQL4EQ5R4ASQFVCQJI4KSPI4ZN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singular values of weighted composition operators and second quantization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"James E. Tener, Mihai Putinar","submitted_at":"2016-12-12T23:34:05Z","abstract_excerpt":"We study a semigroup of weighted composition operators on the Hardy space of the disk $H^2(\\mathbb{D})$, and more generally on the Hardy space $H^2(U)$ attached to a simply connected domain $U$ with smooth boundary. Motivated by conformal field theory, we establish bounds on the singular values (approximation numbers) of these weighted composition operators. As a byproduct we obtain estimates on the singular values of the restriction operator (embedding operator) $H^2(V) \\to H^2(U)$ when $U \\subset V$ and the boundary of $U$ touches that of $V$. Moreover, using the connection between the weigh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03970","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":"2026-05-17T23:59:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i+Q16LTdzFVFBhcoJsnND2T00+CQ+JfXFsHtL4PpX/M3WldBKzZez2ehRVwQ2MF5h3uAOcjHUDt6yqmepI1HBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T00:19:22.244510Z"},"content_sha256":"c421e3d044f25eb4292ceb5f9a8fead151f77f9c867fcc778d24755d88a42f5a","schema_version":"1.0","event_id":"sha256:c421e3d044f25eb4292ceb5f9a8fead151f77f9c867fcc778d24755d88a42f5a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IQL4EQ5R4ASQFVCQJI4KSPI4ZN/bundle.json","state_url":"https://pith.science/pith/IQL4EQ5R4ASQFVCQJI4KSPI4ZN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IQL4EQ5R4ASQFVCQJI4KSPI4ZN/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":"2026-05-22T00:19:22Z","links":{"resolver":"https://pith.science/pith/IQL4EQ5R4ASQFVCQJI4KSPI4ZN","bundle":"https://pith.science/pith/IQL4EQ5R4ASQFVCQJI4KSPI4ZN/bundle.json","state":"https://pith.science/pith/IQL4EQ5R4ASQFVCQJI4KSPI4ZN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IQL4EQ5R4ASQFVCQJI4KSPI4ZN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:IQL4EQ5R4ASQFVCQJI4KSPI4ZN","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":"d0f7bd4dc8c88fda6c24119befc0aa1e4930d1afdd0e7977757c1a925d1e753b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-12T23:34:05Z","title_canon_sha256":"1e6a0e6d342194f3ae1240146bf6938106a15212db5fcb1274d6643d9dbd77cb"},"schema_version":"1.0","source":{"id":"1612.03970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.03970","created_at":"2026-05-17T23:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"1612.03970v1","created_at":"2026-05-17T23:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.03970","created_at":"2026-05-17T23:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"IQL4EQ5R4ASQ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"IQL4EQ5R4ASQFVCQ","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"IQL4EQ5R","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:c421e3d044f25eb4292ceb5f9a8fead151f77f9c867fcc778d24755d88a42f5a","target":"graph","created_at":"2026-05-17T23:59:18Z","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 study a semigroup of weighted composition operators on the Hardy space of the disk $H^2(\\mathbb{D})$, and more generally on the Hardy space $H^2(U)$ attached to a simply connected domain $U$ with smooth boundary. Motivated by conformal field theory, we establish bounds on the singular values (approximation numbers) of these weighted composition operators. As a byproduct we obtain estimates on the singular values of the restriction operator (embedding operator) $H^2(V) \\to H^2(U)$ when $U \\subset V$ and the boundary of $U$ touches that of $V$. Moreover, using the connection between the weigh","authors_text":"James E. Tener, Mihai Putinar","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-12T23:34:05Z","title":"Singular values of weighted composition operators and second quantization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03970","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:c745280fd66e3e7e658d13a3c39aba705800c357163caf65f91e04f51b2f1b85","target":"record","created_at":"2026-05-17T23:59:18Z","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":"d0f7bd4dc8c88fda6c24119befc0aa1e4930d1afdd0e7977757c1a925d1e753b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2016-12-12T23:34:05Z","title_canon_sha256":"1e6a0e6d342194f3ae1240146bf6938106a15212db5fcb1274d6643d9dbd77cb"},"schema_version":"1.0","source":{"id":"1612.03970","kind":"arxiv","version":1}},"canonical_sha256":"4417c243b1e02502d4504a38a93d1ccb727cfecf874a701cc10e17096ad21cb8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4417c243b1e02502d4504a38a93d1ccb727cfecf874a701cc10e17096ad21cb8","first_computed_at":"2026-05-17T23:59:18.195474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:59:18.195474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s0pI5OvgKR9JnJgWPO0ras3CbV61OZF4GjC9OpFQJykgJrWj2Izkx8k2TaW+xOnpMU2iRcDzC1q1bydWLZNVDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:59:18.196048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.03970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c745280fd66e3e7e658d13a3c39aba705800c357163caf65f91e04f51b2f1b85","sha256:c421e3d044f25eb4292ceb5f9a8fead151f77f9c867fcc778d24755d88a42f5a"],"state_sha256":"fe566fb8dd3fea0a458532aa61a00901030164cad35bfa469d48ba9d5d1ce980"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uj8uj3VxgB/YgRVNgd8uQ+3A2GzLBb8hARI+40UJ/jpIBuNwOMTuti2gPGsAdgkxlDGxHw6CoXAaKNzl/ZwsDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T00:19:22.248169Z","bundle_sha256":"3b3199e12dcf68e172c39362ee40d293d75b0c1478ffa4c3d52582228e8e4f18"}}