{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GMXQZEFOIEI4FODEV4V6XCW5CT","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":"1b03b595ab1e511eb141b774e8ec042cdf6b646acd8c93ad52f2657564802995","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2015-07-16T23:54:09Z","title_canon_sha256":"ce539e2dfb04202f56b9fec752184c93e19da9e9cadf4df1f9f2f2badc314ba0"},"schema_version":"1.0","source":{"id":"1507.04802","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04802","created_at":"2026-05-18T00:52:53Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04802v3","created_at":"2026-05-18T00:52:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04802","created_at":"2026-05-18T00:52:53Z"},{"alias_kind":"pith_short_12","alias_value":"GMXQZEFOIEI4","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GMXQZEFOIEI4FODE","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GMXQZEFO","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:f2af6cd2a24d02a9c4b58bdfe14acc0cdfa37ede003c995bd780289daa6c204e","target":"graph","created_at":"2026-05-18T00:52:53Z","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 analyze the asymptotic behavior of $\\kappa$-noncollapsed and positively curved steady Ricci solitons and prove that any $n$-dimensional $\\kappa$-noncollapsed steady K\\\"ahler-Ricci soliton with non-negative sectional curvature must be flat.","authors_text":"Xiaohua Zhu, Yuxing Deng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2015-07-16T23:54:09Z","title":"Asymptotic behavior of positively curved steady Ricci Solitons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04802","kind":"arxiv","version":3},"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":"sha256:1af99da7c892f47165c724d0e646a66a383450603868057c6fc7fb401c536a04","target":"record","created_at":"2026-05-18T00:52:53Z","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":"1b03b595ab1e511eb141b774e8ec042cdf6b646acd8c93ad52f2657564802995","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2015-07-16T23:54:09Z","title_canon_sha256":"ce539e2dfb04202f56b9fec752184c93e19da9e9cadf4df1f9f2f2badc314ba0"},"schema_version":"1.0","source":{"id":"1507.04802","kind":"arxiv","version":3}},"canonical_sha256":"332f0c90ae4111c2b864af2beb8add14d8c08cdc2eb7c42759a25b7a341eefe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"332f0c90ae4111c2b864af2beb8add14d8c08cdc2eb7c42759a25b7a341eefe5","first_computed_at":"2026-05-18T00:52:53.152926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:53.152926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7IbYtYNDpb9JQPI8IxAoE2waSsMEKGvZWN63IWvFM/JoWWxwgOqkTM73kihC9cXEvaSDSmaR/CNiFpTqFG0OBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:53.153715Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04802","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1af99da7c892f47165c724d0e646a66a383450603868057c6fc7fb401c536a04","sha256:f2af6cd2a24d02a9c4b58bdfe14acc0cdfa37ede003c995bd780289daa6c204e"],"state_sha256":"c97912b29acade34ddb40b575dd480f45ac513c54f5dd343dc8ffb42d20ff9f2"}