{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:X5NZSLK2FFTMW2POD5BYHBHWOC","short_pith_number":"pith:X5NZSLK2","canonical_record":{"source":{"id":"1107.4408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-22T01:29:00Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"e6233d7ba8f986c6dc12cf964d4e69f75663717a561b20a9b8fc7d2c36c11201","abstract_canon_sha256":"b41881d4427096d478b5c66ac7dbf41642f2d6bdf67b0c5031f3b8a0ede22471"},"schema_version":"1.0"},"canonical_sha256":"bf5b992d5a2966cb69ee1f438384f670bc3c4622e78dbfac56d22d758b9f0375","source":{"kind":"arxiv","id":"1107.4408","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4408","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4408v1","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4408","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"X5NZSLK2FFTM","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"X5NZSLK2FFTMW2PO","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"X5NZSLK2","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:X5NZSLK2FFTMW2POD5BYHBHWOC","target":"record","payload":{"canonical_record":{"source":{"id":"1107.4408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-22T01:29:00Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"e6233d7ba8f986c6dc12cf964d4e69f75663717a561b20a9b8fc7d2c36c11201","abstract_canon_sha256":"b41881d4427096d478b5c66ac7dbf41642f2d6bdf67b0c5031f3b8a0ede22471"},"schema_version":"1.0"},"canonical_sha256":"bf5b992d5a2966cb69ee1f438384f670bc3c4622e78dbfac56d22d758b9f0375","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:25.593116Z","signature_b64":"yM1sK5mh3P8ntc+P3GU0GD4FDeyCuUtRcsm7xmiiUglzMkJLOI3rCNc1/0BjPkvWo1bWzRP5r6Jw2/ovscFoCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf5b992d5a2966cb69ee1f438384f670bc3c4622e78dbfac56d22d758b9f0375","last_reissued_at":"2026-05-18T02:29:25.592744Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:25.592744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.4408","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":"2026-05-18T02:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WzGiEuO2o7ilmaB7wlJMhKO91kQf0RnTX4R+DpdlZGRz4sDcJqyIJQxX90sQdfJO0Q9+8IkuAAvJDxH5BT+BBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:35:10.526018Z"},"content_sha256":"17387afa4e74fbf01298a2fb8cc167e5d54c80a58d51d3bba74f816229989808","schema_version":"1.0","event_id":"sha256:17387afa4e74fbf01298a2fb8cc167e5d54c80a58d51d3bba74f816229989808"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:X5NZSLK2FFTMW2POD5BYHBHWOC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vanishing Mean Oscillation Spaces Associated with Operators Satisfying Davies-Gaffney Estimates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Dachun Yang, Wen Yuan, Yiyu Liang","submitted_at":"2011-07-22T01:29:00Z","abstract_excerpt":"Let $(\\mathcal{X}, d, \\mu)$ be a metric measure space, $L$ a linear operator which has a bounded $H_\\infty$ functional calculus and satisfies the Davies-Gaffney estimate, $\\Phi$ a concave function on $(0,\\infty)$ of critical lower type $p_\\Phi^-\\in(0,1]$ and $\\rho(t)\\equiv t^{-1}/\\Phi^{-1}(t^{-1})$ for all $t\\in(0,\\infty)$. In this paper, the authors introduce the generalized VMO space ${\\mathrm {VMO}}_{\\rho,L}({\\mathcal X})$ associated with $L$, and establish its characterization via the tent space. As applications, the authors show that $({\\mathrm {VMO}}_{\\rho,L}({\\mathcal X}))^*=B_{\\Phi,L^*"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4408","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":"2026-05-18T02:29:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DTTCnzzW4XPKV9ldpTIaZe+4DcJMTSi9cBhEYWW/S9wa20FAFwctrG+pDu9bqoRns8d61wE/o33VIW7UezMrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:35:10.526613Z"},"content_sha256":"315d2c1706f6537ced664eacde478620826b15b038bf13a299f2c64ef7c276ea","schema_version":"1.0","event_id":"sha256:315d2c1706f6537ced664eacde478620826b15b038bf13a299f2c64ef7c276ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X5NZSLK2FFTMW2POD5BYHBHWOC/bundle.json","state_url":"https://pith.science/pith/X5NZSLK2FFTMW2POD5BYHBHWOC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X5NZSLK2FFTMW2POD5BYHBHWOC/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":"2026-05-30T23:35:10Z","links":{"resolver":"https://pith.science/pith/X5NZSLK2FFTMW2POD5BYHBHWOC","bundle":"https://pith.science/pith/X5NZSLK2FFTMW2POD5BYHBHWOC/bundle.json","state":"https://pith.science/pith/X5NZSLK2FFTMW2POD5BYHBHWOC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X5NZSLK2FFTMW2POD5BYHBHWOC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:X5NZSLK2FFTMW2POD5BYHBHWOC","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":"b41881d4427096d478b5c66ac7dbf41642f2d6bdf67b0c5031f3b8a0ede22471","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-22T01:29:00Z","title_canon_sha256":"e6233d7ba8f986c6dc12cf964d4e69f75663717a561b20a9b8fc7d2c36c11201"},"schema_version":"1.0","source":{"id":"1107.4408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4408","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4408v1","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4408","created_at":"2026-05-18T02:29:25Z"},{"alias_kind":"pith_short_12","alias_value":"X5NZSLK2FFTM","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"X5NZSLK2FFTMW2PO","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"X5NZSLK2","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:315d2c1706f6537ced664eacde478620826b15b038bf13a299f2c64ef7c276ea","target":"graph","created_at":"2026-05-18T02:29:25Z","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":"Let $(\\mathcal{X}, d, \\mu)$ be a metric measure space, $L$ a linear operator which has a bounded $H_\\infty$ functional calculus and satisfies the Davies-Gaffney estimate, $\\Phi$ a concave function on $(0,\\infty)$ of critical lower type $p_\\Phi^-\\in(0,1]$ and $\\rho(t)\\equiv t^{-1}/\\Phi^{-1}(t^{-1})$ for all $t\\in(0,\\infty)$. In this paper, the authors introduce the generalized VMO space ${\\mathrm {VMO}}_{\\rho,L}({\\mathcal X})$ associated with $L$, and establish its characterization via the tent space. As applications, the authors show that $({\\mathrm {VMO}}_{\\rho,L}({\\mathcal X}))^*=B_{\\Phi,L^*","authors_text":"Dachun Yang, Wen Yuan, Yiyu Liang","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-22T01:29:00Z","title":"Vanishing Mean Oscillation Spaces Associated with Operators Satisfying Davies-Gaffney Estimates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4408","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":"sha256:17387afa4e74fbf01298a2fb8cc167e5d54c80a58d51d3bba74f816229989808","target":"record","created_at":"2026-05-18T02:29:25Z","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":"b41881d4427096d478b5c66ac7dbf41642f2d6bdf67b0c5031f3b8a0ede22471","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-07-22T01:29:00Z","title_canon_sha256":"e6233d7ba8f986c6dc12cf964d4e69f75663717a561b20a9b8fc7d2c36c11201"},"schema_version":"1.0","source":{"id":"1107.4408","kind":"arxiv","version":1}},"canonical_sha256":"bf5b992d5a2966cb69ee1f438384f670bc3c4622e78dbfac56d22d758b9f0375","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf5b992d5a2966cb69ee1f438384f670bc3c4622e78dbfac56d22d758b9f0375","first_computed_at":"2026-05-18T02:29:25.592744Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:25.592744Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yM1sK5mh3P8ntc+P3GU0GD4FDeyCuUtRcsm7xmiiUglzMkJLOI3rCNc1/0BjPkvWo1bWzRP5r6Jw2/ovscFoCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:25.593116Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:17387afa4e74fbf01298a2fb8cc167e5d54c80a58d51d3bba74f816229989808","sha256:315d2c1706f6537ced664eacde478620826b15b038bf13a299f2c64ef7c276ea"],"state_sha256":"c4c344a0c7182551a1a9bd034a7a825a58acb373bc475505e8e46ea0caf4a1f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QySxanvFWmYzCUCzaiGBldKws3Wcu+i+NCYLVvBZvwIZNksLqMVi1qqN1sbKRaX7FSAQWm6H6X5zOv+6B73/BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:35:10.530343Z","bundle_sha256":"9bfcddd358024d513639944b61fa47a37205bc0e80489b0929fa4869f9df592e"}}