{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:OPA3YX7UXN5UCKAOSK73OZL3J2","short_pith_number":"pith:OPA3YX7U","canonical_record":{"source":{"id":"2403.04089","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-06T22:34:01Z","cross_cats_sorted":[],"title_canon_sha256":"2be34722a3af918be33efbb8489d51a8845a8696d76c6e7e941d0bf9b89b09a2","abstract_canon_sha256":"3ba026db199132221d88c66f907db460d0877a262474cb722a3a33a6813c4135"},"schema_version":"1.0"},"canonical_sha256":"73c1bc5ff4bb7b41280e92bfb7657b4e8b0e47616ab98b938e7f805cc39b4727","source":{"kind":"arxiv","id":"2403.04089","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.04089","created_at":"2026-07-05T08:22:22Z"},{"alias_kind":"arxiv_version","alias_value":"2403.04089v2","created_at":"2026-07-05T08:22:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.04089","created_at":"2026-07-05T08:22:22Z"},{"alias_kind":"pith_short_12","alias_value":"OPA3YX7UXN5U","created_at":"2026-07-05T08:22:22Z"},{"alias_kind":"pith_short_16","alias_value":"OPA3YX7UXN5UCKAO","created_at":"2026-07-05T08:22:22Z"},{"alias_kind":"pith_short_8","alias_value":"OPA3YX7U","created_at":"2026-07-05T08:22:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:OPA3YX7UXN5UCKAOSK73OZL3J2","target":"record","payload":{"canonical_record":{"source":{"id":"2403.04089","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-06T22:34:01Z","cross_cats_sorted":[],"title_canon_sha256":"2be34722a3af918be33efbb8489d51a8845a8696d76c6e7e941d0bf9b89b09a2","abstract_canon_sha256":"3ba026db199132221d88c66f907db460d0877a262474cb722a3a33a6813c4135"},"schema_version":"1.0"},"canonical_sha256":"73c1bc5ff4bb7b41280e92bfb7657b4e8b0e47616ab98b938e7f805cc39b4727","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:22:22.589731Z","signature_b64":"oP3LdmzA7hdGYzcrKgmlMamFQcpMg8/6yAH6NKRnFCWUNf0tpQ/ZgvMlpGLNaV7CgnANOR2VGSjJ76yN23BDAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"73c1bc5ff4bb7b41280e92bfb7657b4e8b0e47616ab98b938e7f805cc39b4727","last_reissued_at":"2026-07-05T08:22:22.589245Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:22:22.589245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2403.04089","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:22:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gB7LCBy4CMticZ/5rodDqIYtrbpiIgpP7wgQDQZKs/LQcjygUqaVCnUQOggjKHy5n0XRXMs0No4TeWcRQ3jBCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:35:40.854663Z"},"content_sha256":"27b820897019ddd091c16520e5b62c58677ea7c34907795adfada46d55a76fb8","schema_version":"1.0","event_id":"sha256:27b820897019ddd091c16520e5b62c58677ea7c34907795adfada46d55a76fb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:OPA3YX7UXN5UCKAOSK73OZL3J2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A family of K\\\"ahler flying wing steady Ricci solitons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Pak-Yeung Chan, Ronan J. Conlon, Yi Lai","submitted_at":"2024-03-06T22:34:01Z","abstract_excerpt":"In $1996$, H.-D. Cao constructed a $U(n)$-invariant steady gradient K\\\"ahler-Ricci soliton on $\\mathbb{C}^{n}$ and asked whether every steady gradient K\\\"ahler-Ricci soliton of positive curvature on $\\mathbb{C}^{n}$ is necessarily $U(n)$-invariant (and hence unique up to scaling). Recently, Apostolov-Cifarelli answered this question in the negative for $n=2$. Here, we construct a family of $U(1)\\times U(n-1)$-invariant, but not $U(n)$-invariant, complete steady gradient K\\\"ahler-Ricci solitons with strictly positive curvature operator on real $(1,\\,1)$-forms (in particular, with strictly posit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.04089","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2403.04089/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:22:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7znmMpPt5CHG6LqXvPHQH5MZo4DSvdEc0N2hgUUela1cdgyKPMJb1+CFoNtq6j6aNqgMHFa2qlfBPIM7/LBWBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T05:35:40.855238Z"},"content_sha256":"20b8557b6e277ef6e2157c5c9d5f4cf1921aa4c10883b477f04d79e15aa5b573","schema_version":"1.0","event_id":"sha256:20b8557b6e277ef6e2157c5c9d5f4cf1921aa4c10883b477f04d79e15aa5b573"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OPA3YX7UXN5UCKAOSK73OZL3J2/bundle.json","state_url":"https://pith.science/pith/OPA3YX7UXN5UCKAOSK73OZL3J2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OPA3YX7UXN5UCKAOSK73OZL3J2/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":"2026-08-13T05:35:40Z","links":{"resolver":"https://pith.science/pith/OPA3YX7UXN5UCKAOSK73OZL3J2","bundle":"https://pith.science/pith/OPA3YX7UXN5UCKAOSK73OZL3J2/bundle.json","state":"https://pith.science/pith/OPA3YX7UXN5UCKAOSK73OZL3J2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OPA3YX7UXN5UCKAOSK73OZL3J2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:OPA3YX7UXN5UCKAOSK73OZL3J2","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":"3ba026db199132221d88c66f907db460d0877a262474cb722a3a33a6813c4135","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-06T22:34:01Z","title_canon_sha256":"2be34722a3af918be33efbb8489d51a8845a8696d76c6e7e941d0bf9b89b09a2"},"schema_version":"1.0","source":{"id":"2403.04089","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2403.04089","created_at":"2026-07-05T08:22:22Z"},{"alias_kind":"arxiv_version","alias_value":"2403.04089v2","created_at":"2026-07-05T08:22:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2403.04089","created_at":"2026-07-05T08:22:22Z"},{"alias_kind":"pith_short_12","alias_value":"OPA3YX7UXN5U","created_at":"2026-07-05T08:22:22Z"},{"alias_kind":"pith_short_16","alias_value":"OPA3YX7UXN5UCKAO","created_at":"2026-07-05T08:22:22Z"},{"alias_kind":"pith_short_8","alias_value":"OPA3YX7U","created_at":"2026-07-05T08:22:22Z"}],"graph_snapshots":[{"event_id":"sha256:20b8557b6e277ef6e2157c5c9d5f4cf1921aa4c10883b477f04d79e15aa5b573","target":"graph","created_at":"2026-07-05T08:22:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2403.04089/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In $1996$, H.-D. Cao constructed a $U(n)$-invariant steady gradient K\\\"ahler-Ricci soliton on $\\mathbb{C}^{n}$ and asked whether every steady gradient K\\\"ahler-Ricci soliton of positive curvature on $\\mathbb{C}^{n}$ is necessarily $U(n)$-invariant (and hence unique up to scaling). Recently, Apostolov-Cifarelli answered this question in the negative for $n=2$. Here, we construct a family of $U(1)\\times U(n-1)$-invariant, but not $U(n)$-invariant, complete steady gradient K\\\"ahler-Ricci solitons with strictly positive curvature operator on real $(1,\\,1)$-forms (in particular, with strictly posit","authors_text":"Pak-Yeung Chan, Ronan J. Conlon, Yi Lai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-06T22:34:01Z","title":"A family of K\\\"ahler flying wing steady Ricci solitons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2403.04089","kind":"arxiv","version":2},"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":"sha256:27b820897019ddd091c16520e5b62c58677ea7c34907795adfada46d55a76fb8","target":"record","created_at":"2026-07-05T08:22:22Z","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":"3ba026db199132221d88c66f907db460d0877a262474cb722a3a33a6813c4135","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-03-06T22:34:01Z","title_canon_sha256":"2be34722a3af918be33efbb8489d51a8845a8696d76c6e7e941d0bf9b89b09a2"},"schema_version":"1.0","source":{"id":"2403.04089","kind":"arxiv","version":2}},"canonical_sha256":"73c1bc5ff4bb7b41280e92bfb7657b4e8b0e47616ab98b938e7f805cc39b4727","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"73c1bc5ff4bb7b41280e92bfb7657b4e8b0e47616ab98b938e7f805cc39b4727","first_computed_at":"2026-07-05T08:22:22.589245Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:22:22.589245Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oP3LdmzA7hdGYzcrKgmlMamFQcpMg8/6yAH6NKRnFCWUNf0tpQ/ZgvMlpGLNaV7CgnANOR2VGSjJ76yN23BDAg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:22:22.589731Z","signed_message":"canonical_sha256_bytes"},"source_id":"2403.04089","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27b820897019ddd091c16520e5b62c58677ea7c34907795adfada46d55a76fb8","sha256:20b8557b6e277ef6e2157c5c9d5f4cf1921aa4c10883b477f04d79e15aa5b573"],"state_sha256":"4b5de19c5c868f6f449128f74d053a79665aadb7e1e478c4bed1e08df5746cc5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IqUwX7D+QdnlaK/lR2eZfF6BxR5na6n7VR/I5Ep9Uw6ZVsixKgGY7HToWY2wxkBkLsna0bCtujXtOROSTHFPBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T05:35:40.860396Z","bundle_sha256":"3eda6f4ef58be268e7fe82805c133d2a702ea3f90ae8272cf556517b4f3992c2"}}