{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:X7ZSMRMP652BISPNCF3GRHSOR6","short_pith_number":"pith:X7ZSMRMP","canonical_record":{"source":{"id":"1404.5753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-23T09:16:56Z","cross_cats_sorted":[],"title_canon_sha256":"e0e336cfefd35d06e45494d90cd56b6ec95d47008e430fd9a35527e6208e3010","abstract_canon_sha256":"d143e8ec08054680a87b70618ecdebabc0a0d6f239404798b71423df9d583f0b"},"schema_version":"1.0"},"canonical_sha256":"bff326458ff7741449ed1176689e4e8f952d887469da71bd4cdd1f6e343879ea","source":{"kind":"arxiv","id":"1404.5753","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5753","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5753v1","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5753","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"pith_short_12","alias_value":"X7ZSMRMP652B","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X7ZSMRMP652BISPN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X7ZSMRMP","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:X7ZSMRMP652BISPNCF3GRHSOR6","target":"record","payload":{"canonical_record":{"source":{"id":"1404.5753","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-23T09:16:56Z","cross_cats_sorted":[],"title_canon_sha256":"e0e336cfefd35d06e45494d90cd56b6ec95d47008e430fd9a35527e6208e3010","abstract_canon_sha256":"d143e8ec08054680a87b70618ecdebabc0a0d6f239404798b71423df9d583f0b"},"schema_version":"1.0"},"canonical_sha256":"bff326458ff7741449ed1176689e4e8f952d887469da71bd4cdd1f6e343879ea","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:28.026027Z","signature_b64":"sb0QFD42NvApLk/2ETVgYYCTWCf9JVHaJOH4r9nRHb5QPPcRbo/o3pSXYZP3nL6RTSmsQ7cKpjiIyq8SB5ZDDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bff326458ff7741449ed1176689e4e8f952d887469da71bd4cdd1f6e343879ea","last_reissued_at":"2026-05-18T02:53:28.025395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:28.025395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.5753","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":"2026-05-18T02:53:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4FGRSSYHiiVn4vpQ/ios/xHp06Qn2w5iiPY5dDhHUiGYcmslzpr9KTEFUOgnR1GN8A7B6GNpHwa465RtdtoHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:33:57.689363Z"},"content_sha256":"942637a2394320df5e337763716a8f94aadc72f0653396c202ae106732a404de","schema_version":"1.0","event_id":"sha256:942637a2394320df5e337763716a8f94aadc72f0653396c202ae106732a404de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:X7ZSMRMP652BISPNCF3GRHSOR6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundedness for Gevrey and Gelfand-Shilov kernels to positive operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Joachim Toft, Yuanyuan Chen","submitted_at":"2014-04-23T09:16:56Z","abstract_excerpt":"We study properties of positive operators on Gelfand-Shilov spaces, and distributions which are positive with respect to non-commutative convolutions. We prove that boundedness of kernels $K \\in \\maclD_s^{\\prime}$ to positive operators, are completely determined by the behaviour of $K$ alone the diagonal. We also prove that positive elements $a$ in $\\mascS^{\\prime}$ with respect to twisted convolutions, having Gevrey class property of order $s\\geq 1/2$ at the origin, then $a$ belongs to the Gelfand-Shilov space $\\maclS_s$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5753","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":"2026-05-18T02:53:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QiOgkAkrQL6nv1euWMnM+LSw+AYYdrbx2L1f4Yiwkhz1LNnwvVb2zwE6RIfeLuFN6l4ckpo/vqBSVpeP7WtNAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T23:33:57.689708Z"},"content_sha256":"e00c30ca4c5d115595d6e02908b8a61668ed35b8e7b5a3399f8375cba0081e22","schema_version":"1.0","event_id":"sha256:e00c30ca4c5d115595d6e02908b8a61668ed35b8e7b5a3399f8375cba0081e22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X7ZSMRMP652BISPNCF3GRHSOR6/bundle.json","state_url":"https://pith.science/pith/X7ZSMRMP652BISPNCF3GRHSOR6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X7ZSMRMP652BISPNCF3GRHSOR6/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":"2026-06-30T23:33:57Z","links":{"resolver":"https://pith.science/pith/X7ZSMRMP652BISPNCF3GRHSOR6","bundle":"https://pith.science/pith/X7ZSMRMP652BISPNCF3GRHSOR6/bundle.json","state":"https://pith.science/pith/X7ZSMRMP652BISPNCF3GRHSOR6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X7ZSMRMP652BISPNCF3GRHSOR6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:X7ZSMRMP652BISPNCF3GRHSOR6","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":"d143e8ec08054680a87b70618ecdebabc0a0d6f239404798b71423df9d583f0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-23T09:16:56Z","title_canon_sha256":"e0e336cfefd35d06e45494d90cd56b6ec95d47008e430fd9a35527e6208e3010"},"schema_version":"1.0","source":{"id":"1404.5753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5753","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5753v1","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5753","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"pith_short_12","alias_value":"X7ZSMRMP652B","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"X7ZSMRMP652BISPN","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"X7ZSMRMP","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:e00c30ca4c5d115595d6e02908b8a61668ed35b8e7b5a3399f8375cba0081e22","target":"graph","created_at":"2026-05-18T02:53:28Z","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":"We study properties of positive operators on Gelfand-Shilov spaces, and distributions which are positive with respect to non-commutative convolutions. We prove that boundedness of kernels $K \\in \\maclD_s^{\\prime}$ to positive operators, are completely determined by the behaviour of $K$ alone the diagonal. We also prove that positive elements $a$ in $\\mascS^{\\prime}$ with respect to twisted convolutions, having Gevrey class property of order $s\\geq 1/2$ at the origin, then $a$ belongs to the Gelfand-Shilov space $\\maclS_s$.","authors_text":"Joachim Toft, Yuanyuan Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-23T09:16:56Z","title":"Boundedness for Gevrey and Gelfand-Shilov kernels to positive operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5753","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":"sha256:942637a2394320df5e337763716a8f94aadc72f0653396c202ae106732a404de","target":"record","created_at":"2026-05-18T02:53:28Z","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":"d143e8ec08054680a87b70618ecdebabc0a0d6f239404798b71423df9d583f0b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-04-23T09:16:56Z","title_canon_sha256":"e0e336cfefd35d06e45494d90cd56b6ec95d47008e430fd9a35527e6208e3010"},"schema_version":"1.0","source":{"id":"1404.5753","kind":"arxiv","version":1}},"canonical_sha256":"bff326458ff7741449ed1176689e4e8f952d887469da71bd4cdd1f6e343879ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bff326458ff7741449ed1176689e4e8f952d887469da71bd4cdd1f6e343879ea","first_computed_at":"2026-05-18T02:53:28.025395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:28.025395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sb0QFD42NvApLk/2ETVgYYCTWCf9JVHaJOH4r9nRHb5QPPcRbo/o3pSXYZP3nL6RTSmsQ7cKpjiIyq8SB5ZDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:28.026027Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:942637a2394320df5e337763716a8f94aadc72f0653396c202ae106732a404de","sha256:e00c30ca4c5d115595d6e02908b8a61668ed35b8e7b5a3399f8375cba0081e22"],"state_sha256":"ff4c5f5fabccd3a955cf151aadd1744331550632a965e3676190668bd2776785"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r22HBwY06vuqpJUanwTPXarNgwj3IhqVtpFOAOKkpB+CAbSrwXLN4+kYgrutqG11+ZiKgQNdMcnt0k/fRD5tAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T23:33:57.692134Z","bundle_sha256":"14d29ac5cc1192cd32b70c6b18cdad5e9c7adf0828fdb9a7444bafcfce72d07c"}}