{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:H5HEZLD475IMPX3GSB4R7PTPDE","short_pith_number":"pith:H5HEZLD4","canonical_record":{"source":{"id":"1501.05985","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.CV","submitted_at":"2015-01-24T00:22:15Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"7b2af49d85e2427b6ef124ae07d7944dd7cd696aed1e66b863316cc705f20a6d","abstract_canon_sha256":"d74b6d4f4a5442e0bc0d1e47db5f7279f722107c32534c1f1d9fe355697f112b"},"schema_version":"1.0"},"canonical_sha256":"3f4e4cac7cff50c7df6690791fbe6f1928c45f4c35599efd59097d4465322803","source":{"kind":"arxiv","id":"1501.05985","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05985","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05985v1","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05985","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"H5HEZLD475IM","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H5HEZLD475IMPX3G","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H5HEZLD4","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:H5HEZLD475IMPX3GSB4R7PTPDE","target":"record","payload":{"canonical_record":{"source":{"id":"1501.05985","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.CV","submitted_at":"2015-01-24T00:22:15Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"7b2af49d85e2427b6ef124ae07d7944dd7cd696aed1e66b863316cc705f20a6d","abstract_canon_sha256":"d74b6d4f4a5442e0bc0d1e47db5f7279f722107c32534c1f1d9fe355697f112b"},"schema_version":"1.0"},"canonical_sha256":"3f4e4cac7cff50c7df6690791fbe6f1928c45f4c35599efd59097d4465322803","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:22.139725Z","signature_b64":"qPNa6UbjlHHo1sTyGz1rnwo3cODsQ0mBtwBCz/A5r0u0XLloSGcP5K8gfTzIjbyJdfjq1Rje4oyaudjNqgGVCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f4e4cac7cff50c7df6690791fbe6f1928c45f4c35599efd59097d4465322803","last_reissued_at":"2026-05-18T00:42:22.139111Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:22.139111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.05985","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":"2026-05-18T00:42:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y7GCmZtn0g50KNzw6Og96khuS5krKFUc3DZjSjIy03lTbH1Rxzl7c55aygteNk+9k7LYYDVcc1Ki+XAnTKlUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T04:06:42.854729Z"},"content_sha256":"85afc6658b763beeb9770bbbaf7d990f424ff5d723616a2421bdd1129f3ab071","schema_version":"1.0","event_id":"sha256:85afc6658b763beeb9770bbbaf7d990f424ff5d723616a2421bdd1129f3ab071"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:H5HEZLD475IMPX3GSB4R7PTPDE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Invariant subspaces of the shift plus complex Volterra operator","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"Bhupendra Paudyal, \\v{Z}eljko \\v{C}u\\v{c}kovi\\'c","submitted_at":"2015-01-24T00:22:15Z","abstract_excerpt":"The lattice of closed invariant subspaces of the Volterra operator acting on $L^2(0,1)$ was completely described by Sarason. On the other hand, he explicitly found the lattice of closed invariant subspaces of the shift plus Volterra operator on $L^2(0,1)$. Inspired by Sarason's results, we find the lattice of closed invariant subspaces of the shift plus complex Volterra operator acting on the Hardy space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05985","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":"2026-05-18T00:42:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4atNxT9vgC0j6JRDy2XEMcf/UB3XwFHtZKfVIpMR+1/KUW+IU3uhSPAy6RTo41l/IQR5ecxG2prf8YBcp7LAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T04:06:42.855067Z"},"content_sha256":"f606959a21cec1e5f61a4006d88b7fc6f787c6be35e0dd2dafa8b8aa6da5f04c","schema_version":"1.0","event_id":"sha256:f606959a21cec1e5f61a4006d88b7fc6f787c6be35e0dd2dafa8b8aa6da5f04c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H5HEZLD475IMPX3GSB4R7PTPDE/bundle.json","state_url":"https://pith.science/pith/H5HEZLD475IMPX3GSB4R7PTPDE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H5HEZLD475IMPX3GSB4R7PTPDE/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":"2026-07-02T04:06:42Z","links":{"resolver":"https://pith.science/pith/H5HEZLD475IMPX3GSB4R7PTPDE","bundle":"https://pith.science/pith/H5HEZLD475IMPX3GSB4R7PTPDE/bundle.json","state":"https://pith.science/pith/H5HEZLD475IMPX3GSB4R7PTPDE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H5HEZLD475IMPX3GSB4R7PTPDE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:H5HEZLD475IMPX3GSB4R7PTPDE","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":"d74b6d4f4a5442e0bc0d1e47db5f7279f722107c32534c1f1d9fe355697f112b","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.CV","submitted_at":"2015-01-24T00:22:15Z","title_canon_sha256":"7b2af49d85e2427b6ef124ae07d7944dd7cd696aed1e66b863316cc705f20a6d"},"schema_version":"1.0","source":{"id":"1501.05985","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.05985","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"arxiv_version","alias_value":"1501.05985v1","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.05985","created_at":"2026-05-18T00:42:22Z"},{"alias_kind":"pith_short_12","alias_value":"H5HEZLD475IM","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"H5HEZLD475IMPX3G","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"H5HEZLD4","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:f606959a21cec1e5f61a4006d88b7fc6f787c6be35e0dd2dafa8b8aa6da5f04c","target":"graph","created_at":"2026-05-18T00:42:22Z","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":"The lattice of closed invariant subspaces of the Volterra operator acting on $L^2(0,1)$ was completely described by Sarason. On the other hand, he explicitly found the lattice of closed invariant subspaces of the shift plus Volterra operator on $L^2(0,1)$. Inspired by Sarason's results, we find the lattice of closed invariant subspaces of the shift plus complex Volterra operator acting on the Hardy space","authors_text":"Bhupendra Paudyal, \\v{Z}eljko \\v{C}u\\v{c}kovi\\'c","cross_cats":["math.FA"],"headline":"","license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.CV","submitted_at":"2015-01-24T00:22:15Z","title":"Invariant subspaces of the shift plus complex Volterra operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.05985","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":"sha256:85afc6658b763beeb9770bbbaf7d990f424ff5d723616a2421bdd1129f3ab071","target":"record","created_at":"2026-05-18T00:42:22Z","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":"d74b6d4f4a5442e0bc0d1e47db5f7279f722107c32534c1f1d9fe355697f112b","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.CV","submitted_at":"2015-01-24T00:22:15Z","title_canon_sha256":"7b2af49d85e2427b6ef124ae07d7944dd7cd696aed1e66b863316cc705f20a6d"},"schema_version":"1.0","source":{"id":"1501.05985","kind":"arxiv","version":1}},"canonical_sha256":"3f4e4cac7cff50c7df6690791fbe6f1928c45f4c35599efd59097d4465322803","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f4e4cac7cff50c7df6690791fbe6f1928c45f4c35599efd59097d4465322803","first_computed_at":"2026-05-18T00:42:22.139111Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:22.139111Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qPNa6UbjlHHo1sTyGz1rnwo3cODsQ0mBtwBCz/A5r0u0XLloSGcP5K8gfTzIjbyJdfjq1Rje4oyaudjNqgGVCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:22.139725Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.05985","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85afc6658b763beeb9770bbbaf7d990f424ff5d723616a2421bdd1129f3ab071","sha256:f606959a21cec1e5f61a4006d88b7fc6f787c6be35e0dd2dafa8b8aa6da5f04c"],"state_sha256":"71d148585b182eb7ef59d6be3a178f0939cb6adf285fb2ac9b34f47ff60b1177"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w3WQqV70dbDXjcJ7CGSD1whY5t3DSnBAS9a6pa8tBNVyV/xq5NB9PN4cQi8hVgWGxuQEhSldPSOxpbXRynExCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T04:06:42.857031Z","bundle_sha256":"c4d34d2c5876d7f0d9884dd2aaf567f2d8cda79506271d4cd4bb29a84f106370"}}