{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:V76EQLTVFDD4CXSN5L72CFBNGA","short_pith_number":"pith:V76EQLTV","canonical_record":{"source":{"id":"1809.01315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-05T04:03:55Z","cross_cats_sorted":[],"title_canon_sha256":"31b76e457532315d7fca363b817ffb3c083765e4229a7735d07a8b18fda19bac","abstract_canon_sha256":"2108e48215a5025f657574f68fc8999cf821775dd0fc83d294f5bcc792fa6e7d"},"schema_version":"1.0"},"canonical_sha256":"affc482e7528c7c15e4deaffa1142d3037a3282d5632d1c010d4f2dfd32973a1","source":{"kind":"arxiv","id":"1809.01315","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.01315","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"1809.01315v1","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01315","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"V76EQLTVFDD4","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"V76EQLTVFDD4CXSN","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"V76EQLTV","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:V76EQLTVFDD4CXSN5L72CFBNGA","target":"record","payload":{"canonical_record":{"source":{"id":"1809.01315","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-05T04:03:55Z","cross_cats_sorted":[],"title_canon_sha256":"31b76e457532315d7fca363b817ffb3c083765e4229a7735d07a8b18fda19bac","abstract_canon_sha256":"2108e48215a5025f657574f68fc8999cf821775dd0fc83d294f5bcc792fa6e7d"},"schema_version":"1.0"},"canonical_sha256":"affc482e7528c7c15e4deaffa1142d3037a3282d5632d1c010d4f2dfd32973a1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:28.048059Z","signature_b64":"z2b4LGfX32p0Zq1T5vVbxWonLyEGI498PERwrhxa1vCxKz9cslzd4CkthBQAy3ocm7sBcZE4vroBZoz0hmOpCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"affc482e7528c7c15e4deaffa1142d3037a3282d5632d1c010d4f2dfd32973a1","last_reissued_at":"2026-05-18T00:06:28.047470Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:28.047470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.01315","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":"2026-05-18T00:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VLk5tI/Ltp0YjEACPb4VKwALl2ZlOITY1DqSAkHjO+UyR8HI9h+xCvZdxIrB80HA6GD6kz3tRU6tWfaRwpqLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:21:06.679913Z"},"content_sha256":"87a8d91944e1c68fea633ed5e4ac7a27e2c82463c4374ae6ae6199c03fae0059","schema_version":"1.0","event_id":"sha256:87a8d91944e1c68fea633ed5e4ac7a27e2c82463c4374ae6ae6199c03fae0059"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:V76EQLTVFDD4CXSN5L72CFBNGA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Splitting of operator for frame inequalities in Hilbert spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Dongwei Li","submitted_at":"2018-09-05T04:03:55Z","abstract_excerpt":"In this paper, we obtain a new type of inequalities for frames, which are parametrized by a parameter \\lambda\\in R . By suitable choices of {\\lambda}, one obtains the previous results as special cases. Our new proof also makes the underlying mathematical structure that gives rise to these inequalities more transparent than previous approaches: Our proof shows that the main point is the splitting S = S1 + S2 of the positive denite frame operator S into the two positive semidenite operators S1 and S2 ."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01315","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":"2026-05-18T00:06:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mfx/DgweKOjy4E52Q38VvD19RfCBl68QJw9HIHeKq+IlHU/fI5mZw9tLRXcBKxsBzryXZTTx4uEnJSWSWCALBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:21:06.680600Z"},"content_sha256":"7441d4471a23204af7a5e5a906f674e1d84ef41ffb37d8d0ef42f463ab02c6d7","schema_version":"1.0","event_id":"sha256:7441d4471a23204af7a5e5a906f674e1d84ef41ffb37d8d0ef42f463ab02c6d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V76EQLTVFDD4CXSN5L72CFBNGA/bundle.json","state_url":"https://pith.science/pith/V76EQLTVFDD4CXSN5L72CFBNGA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V76EQLTVFDD4CXSN5L72CFBNGA/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":"2026-05-26T07:21:06Z","links":{"resolver":"https://pith.science/pith/V76EQLTVFDD4CXSN5L72CFBNGA","bundle":"https://pith.science/pith/V76EQLTVFDD4CXSN5L72CFBNGA/bundle.json","state":"https://pith.science/pith/V76EQLTVFDD4CXSN5L72CFBNGA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V76EQLTVFDD4CXSN5L72CFBNGA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:V76EQLTVFDD4CXSN5L72CFBNGA","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":"2108e48215a5025f657574f68fc8999cf821775dd0fc83d294f5bcc792fa6e7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-05T04:03:55Z","title_canon_sha256":"31b76e457532315d7fca363b817ffb3c083765e4229a7735d07a8b18fda19bac"},"schema_version":"1.0","source":{"id":"1809.01315","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.01315","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"1809.01315v1","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01315","created_at":"2026-05-18T00:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"V76EQLTVFDD4","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"V76EQLTVFDD4CXSN","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"V76EQLTV","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:7441d4471a23204af7a5e5a906f674e1d84ef41ffb37d8d0ef42f463ab02c6d7","target":"graph","created_at":"2026-05-18T00:06:28Z","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":"In this paper, we obtain a new type of inequalities for frames, which are parametrized by a parameter \\lambda\\in R . By suitable choices of {\\lambda}, one obtains the previous results as special cases. Our new proof also makes the underlying mathematical structure that gives rise to these inequalities more transparent than previous approaches: Our proof shows that the main point is the splitting S = S1 + S2 of the positive denite frame operator S into the two positive semidenite operators S1 and S2 .","authors_text":"Dongwei Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-05T04:03:55Z","title":"Splitting of operator for frame inequalities in Hilbert spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01315","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":"sha256:87a8d91944e1c68fea633ed5e4ac7a27e2c82463c4374ae6ae6199c03fae0059","target":"record","created_at":"2026-05-18T00:06:28Z","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":"2108e48215a5025f657574f68fc8999cf821775dd0fc83d294f5bcc792fa6e7d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-09-05T04:03:55Z","title_canon_sha256":"31b76e457532315d7fca363b817ffb3c083765e4229a7735d07a8b18fda19bac"},"schema_version":"1.0","source":{"id":"1809.01315","kind":"arxiv","version":1}},"canonical_sha256":"affc482e7528c7c15e4deaffa1142d3037a3282d5632d1c010d4f2dfd32973a1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"affc482e7528c7c15e4deaffa1142d3037a3282d5632d1c010d4f2dfd32973a1","first_computed_at":"2026-05-18T00:06:28.047470Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:28.047470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z2b4LGfX32p0Zq1T5vVbxWonLyEGI498PERwrhxa1vCxKz9cslzd4CkthBQAy3ocm7sBcZE4vroBZoz0hmOpCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:28.048059Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.01315","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87a8d91944e1c68fea633ed5e4ac7a27e2c82463c4374ae6ae6199c03fae0059","sha256:7441d4471a23204af7a5e5a906f674e1d84ef41ffb37d8d0ef42f463ab02c6d7"],"state_sha256":"06a11bf384d2d6f70ad970337ea39c4fcc192b211e254b0a409fc45c7212a4af"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FDKRTOsOg+jfDdmBDMAR8PXO3HKR7Jy3MEsdrWGHT/58ZwYbznkZM1XCRTMgQszmIBYzVclcmgSHkcbbK1qaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:21:06.684126Z","bundle_sha256":"776e2f3d17e6719120ac1ef6063963d28fae2001e8c6f927453a1aba96a430d0"}}