{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:4WPCUHM27K3FUFBXVHUKCL44TD","short_pith_number":"pith:4WPCUHM2","canonical_record":{"source":{"id":"2012.10962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-12-20T16:15:01Z","cross_cats_sorted":[],"title_canon_sha256":"2438df6967fdbfd00a5516bc8b08fbafda2e065143564557b39ad68851a46f32","abstract_canon_sha256":"f73f7e13c6bba115ed9d69ab63135c08c44338fc1bc615505ff851fba3acc19d"},"schema_version":"1.0"},"canonical_sha256":"e59e2a1d9afab65a1437a9e8a12f9c98e6418cf2eb9c83dc5fa076349a54ff5e","source":{"kind":"arxiv","id":"2012.10962","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.10962","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"2012.10962v2","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.10962","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"4WPCUHM27K3F","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"pith_short_16","alias_value":"4WPCUHM27K3FUFBX","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"pith_short_8","alias_value":"4WPCUHM2","created_at":"2026-06-23T02:13:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:4WPCUHM27K3FUFBXVHUKCL44TD","target":"record","payload":{"canonical_record":{"source":{"id":"2012.10962","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-12-20T16:15:01Z","cross_cats_sorted":[],"title_canon_sha256":"2438df6967fdbfd00a5516bc8b08fbafda2e065143564557b39ad68851a46f32","abstract_canon_sha256":"f73f7e13c6bba115ed9d69ab63135c08c44338fc1bc615505ff851fba3acc19d"},"schema_version":"1.0"},"canonical_sha256":"e59e2a1d9afab65a1437a9e8a12f9c98e6418cf2eb9c83dc5fa076349a54ff5e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:11.401986Z","signature_b64":"6+gzLKOtuA2vqzCA1CSgHxArLlV/FMq+ra5E44g2bZfLMaBLeHOR/w1G8oI2uSAvqENA3OiRMAj36kpKS9uMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e59e2a1d9afab65a1437a9e8a12f9c98e6418cf2eb9c83dc5fa076349a54ff5e","last_reissued_at":"2026-06-23T02:13:11.401598Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:11.401598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2012.10962","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":"2026-06-23T02:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2IxvuxM78elObx1/fq4ahYp27hQB2Apgnetf+mv0lFcdN4wrt6Q+JOFiJtNUoLA/yu7h8qnViUHM+oVd07qDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:57:35.939386Z"},"content_sha256":"b430bb2eafef41d8763790148e4370a16ade7b54472bf3c5c5bacd80b61f78ff","schema_version":"1.0","event_id":"sha256:b430bb2eafef41d8763790148e4370a16ade7b54472bf3c5c5bacd80b61f78ff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:4WPCUHM27K3FUFBXVHUKCL44TD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conditional positive definiteness as a bridge between k-hyponormality and n-contractivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Chafiq Benhida, George R. Exner, Raul E. Curto","submitted_at":"2020-12-20T16:15:01Z","abstract_excerpt":"For sequences $\\alpha \\equiv \\{\\alpha_n\\}_{n=0}^{\\infty}$ of positive real numbers, called weights, we study the weighted shift operators $W_{\\alpha}$ having the property of moment infinite divisibility ($\\mathcal{MID}$); that is, for any $p > 0$, the Schur power $W_{\\alpha}^p$ is subnormal. We first prove that $W_{\\alpha}$ is $\\mathcal{MID}$ if and only if certain infinite matrices $\\log M_{\\gamma}(0)$ and $\\log M_{\\gamma}(1)$ are conditionally positive definite (CPD). Here $\\gamma$ is the sequence of moments associated with $\\alpha$, $M_{\\gamma}(0),M_{\\gamma}(1)$ are the canonical Hankel mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.10962","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.10962/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":"2026-06-23T02:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UiEOuESvlEkKiTLjimBU67HU2jrW+xsYzcjv4Ea/pNzjuuFksVR1E0q/4vX54GSWsxsaNNozvAGIuVnG1jNgCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:57:35.939759Z"},"content_sha256":"f410b96aac17043c81aa42a723e2d23a16561f204de4426e69eb78cdfbb531f5","schema_version":"1.0","event_id":"sha256:f410b96aac17043c81aa42a723e2d23a16561f204de4426e69eb78cdfbb531f5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4WPCUHM27K3FUFBXVHUKCL44TD/bundle.json","state_url":"https://pith.science/pith/4WPCUHM27K3FUFBXVHUKCL44TD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4WPCUHM27K3FUFBXVHUKCL44TD/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":"2026-06-27T00:57:35Z","links":{"resolver":"https://pith.science/pith/4WPCUHM27K3FUFBXVHUKCL44TD","bundle":"https://pith.science/pith/4WPCUHM27K3FUFBXVHUKCL44TD/bundle.json","state":"https://pith.science/pith/4WPCUHM27K3FUFBXVHUKCL44TD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4WPCUHM27K3FUFBXVHUKCL44TD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4WPCUHM27K3FUFBXVHUKCL44TD","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":"f73f7e13c6bba115ed9d69ab63135c08c44338fc1bc615505ff851fba3acc19d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-12-20T16:15:01Z","title_canon_sha256":"2438df6967fdbfd00a5516bc8b08fbafda2e065143564557b39ad68851a46f32"},"schema_version":"1.0","source":{"id":"2012.10962","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2012.10962","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"2012.10962v2","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.10962","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"4WPCUHM27K3F","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"pith_short_16","alias_value":"4WPCUHM27K3FUFBX","created_at":"2026-06-23T02:13:11Z"},{"alias_kind":"pith_short_8","alias_value":"4WPCUHM2","created_at":"2026-06-23T02:13:11Z"}],"graph_snapshots":[{"event_id":"sha256:f410b96aac17043c81aa42a723e2d23a16561f204de4426e69eb78cdfbb531f5","target":"graph","created_at":"2026-06-23T02:13:11Z","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/2012.10962/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For sequences $\\alpha \\equiv \\{\\alpha_n\\}_{n=0}^{\\infty}$ of positive real numbers, called weights, we study the weighted shift operators $W_{\\alpha}$ having the property of moment infinite divisibility ($\\mathcal{MID}$); that is, for any $p > 0$, the Schur power $W_{\\alpha}^p$ is subnormal. We first prove that $W_{\\alpha}$ is $\\mathcal{MID}$ if and only if certain infinite matrices $\\log M_{\\gamma}(0)$ and $\\log M_{\\gamma}(1)$ are conditionally positive definite (CPD). Here $\\gamma$ is the sequence of moments associated with $\\alpha$, $M_{\\gamma}(0),M_{\\gamma}(1)$ are the canonical Hankel mat","authors_text":"Chafiq Benhida, George R. Exner, Raul E. Curto","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-12-20T16:15:01Z","title":"Conditional positive definiteness as a bridge between k-hyponormality and n-contractivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.10962","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:b430bb2eafef41d8763790148e4370a16ade7b54472bf3c5c5bacd80b61f78ff","target":"record","created_at":"2026-06-23T02:13:11Z","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":"f73f7e13c6bba115ed9d69ab63135c08c44338fc1bc615505ff851fba3acc19d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2020-12-20T16:15:01Z","title_canon_sha256":"2438df6967fdbfd00a5516bc8b08fbafda2e065143564557b39ad68851a46f32"},"schema_version":"1.0","source":{"id":"2012.10962","kind":"arxiv","version":2}},"canonical_sha256":"e59e2a1d9afab65a1437a9e8a12f9c98e6418cf2eb9c83dc5fa076349a54ff5e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e59e2a1d9afab65a1437a9e8a12f9c98e6418cf2eb9c83dc5fa076349a54ff5e","first_computed_at":"2026-06-23T02:13:11.401598Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:11.401598Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6+gzLKOtuA2vqzCA1CSgHxArLlV/FMq+ra5E44g2bZfLMaBLeHOR/w1G8oI2uSAvqENA3OiRMAj36kpKS9uMDg==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:11.401986Z","signed_message":"canonical_sha256_bytes"},"source_id":"2012.10962","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b430bb2eafef41d8763790148e4370a16ade7b54472bf3c5c5bacd80b61f78ff","sha256:f410b96aac17043c81aa42a723e2d23a16561f204de4426e69eb78cdfbb531f5"],"state_sha256":"d8b77d4a67dec1fa17b9b83000e6453a8c5c652b3d9ae0266eb3eb1752a53d8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r3J+wnTIXz22BPAp2HHmhXQza3Z37nKQd+LWQfF6X5umu9aolLqijifp2BUvp9J712Ej6Eg7nNqutor+1fYnCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T00:57:35.941715Z","bundle_sha256":"00d63ff34a45759003b95f84e73cb7c8599c6a92be65485dd3eb33f8a0a0abd5"}}