{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:BUDOKELJFXIS3BW2L3LMLPRGZU","short_pith_number":"pith:BUDOKELJ","canonical_record":{"source":{"id":"1511.04566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-14T14:51:37Z","cross_cats_sorted":[],"title_canon_sha256":"b80aff749f798ae22d735b87b67134120293d81142af594832fc4e59e378e67a","abstract_canon_sha256":"4ed9f0e72084262427741b6ef959239fdf1f360759a546ded0f6de48a01b6e8f"},"schema_version":"1.0"},"canonical_sha256":"0d06e511692dd12d86da5ed6c5be26cd2345f6a9bb1fbd5e2771e7c48ed08e62","source":{"kind":"arxiv","id":"1511.04566","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04566","created_at":"2026-05-18T01:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04566v1","created_at":"2026-05-18T01:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04566","created_at":"2026-05-18T01:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"BUDOKELJFXIS","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BUDOKELJFXIS3BW2","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BUDOKELJ","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:BUDOKELJFXIS3BW2L3LMLPRGZU","target":"record","payload":{"canonical_record":{"source":{"id":"1511.04566","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-14T14:51:37Z","cross_cats_sorted":[],"title_canon_sha256":"b80aff749f798ae22d735b87b67134120293d81142af594832fc4e59e378e67a","abstract_canon_sha256":"4ed9f0e72084262427741b6ef959239fdf1f360759a546ded0f6de48a01b6e8f"},"schema_version":"1.0"},"canonical_sha256":"0d06e511692dd12d86da5ed6c5be26cd2345f6a9bb1fbd5e2771e7c48ed08e62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:52.322762Z","signature_b64":"YYO12MLnRBpZBI8uQ+3kOsYjWjo4iEuljpDWOOjECk7PDxYObNudU1PdjucmgqpP1brT6X5rUmql/Cdv7zwsDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0d06e511692dd12d86da5ed6c5be26cd2345f6a9bb1fbd5e2771e7c48ed08e62","last_reissued_at":"2026-05-18T01:26:52.322161Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:52.322161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.04566","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":"2026-05-18T01:26:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xqZSPwVpmj/epJbYZJFTyW5uLMYCuAcoyhvaQJ0s06LyKtmxRymiyvJ5k4RFDRZ9Infuvq0XzJ8Aa/O0PKw5CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:20:02.252676Z"},"content_sha256":"562dd1742e2afeb1d01b53c87dda18bae9c95ed5f4cde83db98b4c90598fba5c","schema_version":"1.0","event_id":"sha256:562dd1742e2afeb1d01b53c87dda18bae9c95ed5f4cde83db98b4c90598fba5c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:BUDOKELJFXIS3BW2L3LMLPRGZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On DeTurck uniqueness theorems for Ricci tensor","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Sergey Stepanov","submitted_at":"2015-11-14T14:51:37Z","abstract_excerpt":"In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold $M$ and a symmetric 2-tensor $r$, construct a metric on $M$ whose Ricci tensor equals $r$. In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with non-negative section curvature. In addition, we extended our result to complete non-compact Riemanni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04566","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":"2026-05-18T01:26:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b5bGQqDGjKuvQUBE+8lyz9RAAIfzIF177rNqpbJCOnOBG2yJDA/RHig6LPl3etz4n7ylpGgwsARfS5ResrMYCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:20:02.253379Z"},"content_sha256":"6f18d6c52e0c4f94d4e16cf1cb20fdffa488dc82e98e06214c7ca36f4ce241ef","schema_version":"1.0","event_id":"sha256:6f18d6c52e0c4f94d4e16cf1cb20fdffa488dc82e98e06214c7ca36f4ce241ef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BUDOKELJFXIS3BW2L3LMLPRGZU/bundle.json","state_url":"https://pith.science/pith/BUDOKELJFXIS3BW2L3LMLPRGZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BUDOKELJFXIS3BW2L3LMLPRGZU/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":"2026-06-06T16:20:02Z","links":{"resolver":"https://pith.science/pith/BUDOKELJFXIS3BW2L3LMLPRGZU","bundle":"https://pith.science/pith/BUDOKELJFXIS3BW2L3LMLPRGZU/bundle.json","state":"https://pith.science/pith/BUDOKELJFXIS3BW2L3LMLPRGZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BUDOKELJFXIS3BW2L3LMLPRGZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:BUDOKELJFXIS3BW2L3LMLPRGZU","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":"4ed9f0e72084262427741b6ef959239fdf1f360759a546ded0f6de48a01b6e8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-14T14:51:37Z","title_canon_sha256":"b80aff749f798ae22d735b87b67134120293d81142af594832fc4e59e378e67a"},"schema_version":"1.0","source":{"id":"1511.04566","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.04566","created_at":"2026-05-18T01:26:52Z"},{"alias_kind":"arxiv_version","alias_value":"1511.04566v1","created_at":"2026-05-18T01:26:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.04566","created_at":"2026-05-18T01:26:52Z"},{"alias_kind":"pith_short_12","alias_value":"BUDOKELJFXIS","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"BUDOKELJFXIS3BW2","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"BUDOKELJ","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:6f18d6c52e0c4f94d4e16cf1cb20fdffa488dc82e98e06214c7ca36f4ce241ef","target":"graph","created_at":"2026-05-18T01:26:52Z","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 Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold $M$ and a symmetric 2-tensor $r$, construct a metric on $M$ whose Ricci tensor equals $r$. In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with non-negative section curvature. In addition, we extended our result to complete non-compact Riemanni","authors_text":"Sergey Stepanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-14T14:51:37Z","title":"On DeTurck uniqueness theorems for Ricci tensor"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.04566","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":"sha256:562dd1742e2afeb1d01b53c87dda18bae9c95ed5f4cde83db98b4c90598fba5c","target":"record","created_at":"2026-05-18T01:26:52Z","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":"4ed9f0e72084262427741b6ef959239fdf1f360759a546ded0f6de48a01b6e8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-11-14T14:51:37Z","title_canon_sha256":"b80aff749f798ae22d735b87b67134120293d81142af594832fc4e59e378e67a"},"schema_version":"1.0","source":{"id":"1511.04566","kind":"arxiv","version":1}},"canonical_sha256":"0d06e511692dd12d86da5ed6c5be26cd2345f6a9bb1fbd5e2771e7c48ed08e62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d06e511692dd12d86da5ed6c5be26cd2345f6a9bb1fbd5e2771e7c48ed08e62","first_computed_at":"2026-05-18T01:26:52.322161Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:52.322161Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YYO12MLnRBpZBI8uQ+3kOsYjWjo4iEuljpDWOOjECk7PDxYObNudU1PdjucmgqpP1brT6X5rUmql/Cdv7zwsDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:52.322762Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.04566","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:562dd1742e2afeb1d01b53c87dda18bae9c95ed5f4cde83db98b4c90598fba5c","sha256:6f18d6c52e0c4f94d4e16cf1cb20fdffa488dc82e98e06214c7ca36f4ce241ef"],"state_sha256":"f4a58e9bd36eabdf63aaab5ff7edc1a72402c2b388f9b2956e6137761acd1776"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1tEng3YlFR7t/YE1M8syMl4IED+HTzrqqDTEwHkdzZUxrCOTDu2W/xajGXWvOkFj62NeSoE//3YnBVqXGm7zBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:20:02.256182Z","bundle_sha256":"38577c1bc884d126d10c5c5fe404a397b79252139b1c0a8fc9af306f350a3033"}}