{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:6Q7D7YDL6IB2QEJT6LSDCR65MA","short_pith_number":"pith:6Q7D7YDL","canonical_record":{"source":{"id":"1101.5884","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-31T09:40:53Z","cross_cats_sorted":[],"title_canon_sha256":"4f5480ad2716d5edf9176949bb149fe1bfeedc1965d752a6e28eac06744d7e8a","abstract_canon_sha256":"0c99347c44c1fdf8ded937c1278182e07e6c74e003358bc6cfd26fe682613799"},"schema_version":"1.0"},"canonical_sha256":"f43e3fe06bf203a81133f2e43147dd601e08099f8dec050f26527e646b03e78d","source":{"kind":"arxiv","id":"1101.5884","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5884","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5884v4","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5884","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"6Q7D7YDL6IB2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6Q7D7YDL6IB2QEJT","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6Q7D7YDL","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:6Q7D7YDL6IB2QEJT6LSDCR65MA","target":"record","payload":{"canonical_record":{"source":{"id":"1101.5884","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-31T09:40:53Z","cross_cats_sorted":[],"title_canon_sha256":"4f5480ad2716d5edf9176949bb149fe1bfeedc1965d752a6e28eac06744d7e8a","abstract_canon_sha256":"0c99347c44c1fdf8ded937c1278182e07e6c74e003358bc6cfd26fe682613799"},"schema_version":"1.0"},"canonical_sha256":"f43e3fe06bf203a81133f2e43147dd601e08099f8dec050f26527e646b03e78d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:45.106909Z","signature_b64":"W4+Unh/gvjkDSslGqsOQKFWpY65pLr1kX245co/711pJCkMtpoTni73Zz7wqB8VP+TFY39Lw6QnEzGQsmycHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f43e3fe06bf203a81133f2e43147dd601e08099f8dec050f26527e646b03e78d","last_reissued_at":"2026-05-18T04:24:45.106546Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:45.106546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1101.5884","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ETAPIxZ6sfgAzJMZQTv5ZByVszI1CASF6UDzAdeupNqUdNmycoz8/yA+eeiQlfK2fGeg+PnO9LTwUTBfy02qAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:29:11.559074Z"},"content_sha256":"db926ae72359d9d61e4106cbf4472558084592d0b840106a6aa626b5b5b0692e","schema_version":"1.0","event_id":"sha256:db926ae72359d9d61e4106cbf4472558084592d0b840106a6aa626b5b5b0692e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:6Q7D7YDL6IB2QEJT6LSDCR65MA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Wilking's criterion for the Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"H. A. Gururaja, Harish Seshadri, Soma Maity","submitted_at":"2011-01-31T09:40:53Z","abstract_excerpt":"B Wilking has recently shown that one can associate a Ricci flow invariant cone of curvature operators $C(S)$, which are nonnegative in a suitable sense, to every $Ad_{SO(n,\\C)}$ invariant subset $S \\subset {\\bf so}(n,\\C)$. For curvature operators of a K\\\"ahler manifold of complex dimension $n$, one considers $Ad_{GL(n,\\C)}$ invariant subsets $S \\subset {\\bf gl}(n,\\C)$. In this article we show:\n  (i) If $S$ is an $Ad_{SO(n,\\C)}$ subset, then $C(S)$ is contained in the cone of curvature operators with nonnegative isotropic curvature and if $S$ is an $Ad_{GL(n,\\C)}$ subset, then $C(S)$ is contai"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5884","kind":"arxiv","version":4},"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":"2026-05-18T04:24:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VteEObBhRU7VhRGxBAoEbN0gIk5+QmS6KO8veqTYDVrgeq/xPpmRlxWXwwxRizUdpBGd3ptSwwZN67t8DsTvAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T09:29:11.559434Z"},"content_sha256":"d9290d57dfb6a12033f3e2ef785623ac1839a8103a1184375e3e870f0c84f836","schema_version":"1.0","event_id":"sha256:d9290d57dfb6a12033f3e2ef785623ac1839a8103a1184375e3e870f0c84f836"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6Q7D7YDL6IB2QEJT6LSDCR65MA/bundle.json","state_url":"https://pith.science/pith/6Q7D7YDL6IB2QEJT6LSDCR65MA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6Q7D7YDL6IB2QEJT6LSDCR65MA/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":"2026-06-22T09:29:11Z","links":{"resolver":"https://pith.science/pith/6Q7D7YDL6IB2QEJT6LSDCR65MA","bundle":"https://pith.science/pith/6Q7D7YDL6IB2QEJT6LSDCR65MA/bundle.json","state":"https://pith.science/pith/6Q7D7YDL6IB2QEJT6LSDCR65MA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6Q7D7YDL6IB2QEJT6LSDCR65MA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6Q7D7YDL6IB2QEJT6LSDCR65MA","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":"0c99347c44c1fdf8ded937c1278182e07e6c74e003358bc6cfd26fe682613799","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-31T09:40:53Z","title_canon_sha256":"4f5480ad2716d5edf9176949bb149fe1bfeedc1965d752a6e28eac06744d7e8a"},"schema_version":"1.0","source":{"id":"1101.5884","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.5884","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"arxiv_version","alias_value":"1101.5884v4","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.5884","created_at":"2026-05-18T04:24:45Z"},{"alias_kind":"pith_short_12","alias_value":"6Q7D7YDL6IB2","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6Q7D7YDL6IB2QEJT","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6Q7D7YDL","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:d9290d57dfb6a12033f3e2ef785623ac1839a8103a1184375e3e870f0c84f836","target":"graph","created_at":"2026-05-18T04:24:45Z","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":"B Wilking has recently shown that one can associate a Ricci flow invariant cone of curvature operators $C(S)$, which are nonnegative in a suitable sense, to every $Ad_{SO(n,\\C)}$ invariant subset $S \\subset {\\bf so}(n,\\C)$. For curvature operators of a K\\\"ahler manifold of complex dimension $n$, one considers $Ad_{GL(n,\\C)}$ invariant subsets $S \\subset {\\bf gl}(n,\\C)$. In this article we show:\n  (i) If $S$ is an $Ad_{SO(n,\\C)}$ subset, then $C(S)$ is contained in the cone of curvature operators with nonnegative isotropic curvature and if $S$ is an $Ad_{GL(n,\\C)}$ subset, then $C(S)$ is contai","authors_text":"H. A. Gururaja, Harish Seshadri, Soma Maity","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-31T09:40:53Z","title":"On Wilking's criterion for the Ricci flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5884","kind":"arxiv","version":4},"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:db926ae72359d9d61e4106cbf4472558084592d0b840106a6aa626b5b5b0692e","target":"record","created_at":"2026-05-18T04:24:45Z","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":"0c99347c44c1fdf8ded937c1278182e07e6c74e003358bc6cfd26fe682613799","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-01-31T09:40:53Z","title_canon_sha256":"4f5480ad2716d5edf9176949bb149fe1bfeedc1965d752a6e28eac06744d7e8a"},"schema_version":"1.0","source":{"id":"1101.5884","kind":"arxiv","version":4}},"canonical_sha256":"f43e3fe06bf203a81133f2e43147dd601e08099f8dec050f26527e646b03e78d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f43e3fe06bf203a81133f2e43147dd601e08099f8dec050f26527e646b03e78d","first_computed_at":"2026-05-18T04:24:45.106546Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:45.106546Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W4+Unh/gvjkDSslGqsOQKFWpY65pLr1kX245co/711pJCkMtpoTni73Zz7wqB8VP+TFY39Lw6QnEzGQsmycHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:45.106909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.5884","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db926ae72359d9d61e4106cbf4472558084592d0b840106a6aa626b5b5b0692e","sha256:d9290d57dfb6a12033f3e2ef785623ac1839a8103a1184375e3e870f0c84f836"],"state_sha256":"1c7b845765df7e21c9c4ae4059b5dffbbf1158bb3203700cfe84714dda8e1a4c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/3dTQrT2GbNSdrX3BR7fA94KhHB+9Ffz2DBxFoZn6LK2BHsoSt8Hoe/yLyi+9ySq4/wXoGqadhfLlGnElRITBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T09:29:11.561545Z","bundle_sha256":"3b8d032880f3c18d1339d4ac9df45608c94dd07cba2a8bd82c2b8ab4b5114dc8"}}