{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:75JKDX3J2EEJBKCUJWLTCTM4LW","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":"5bc7f51b5b98f711c6c42cac872e4c35a0ef0bcd40a387169c31b91de18fe839","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-14T18:50:42Z","title_canon_sha256":"6e5a0855bb42e72137a54c7517cc6f2fa7f536b26fe440fb5e4b3337b4528cf4"},"schema_version":"1.0","source":{"id":"1505.03833","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.03833","created_at":"2026-05-18T01:17:05Z"},{"alias_kind":"arxiv_version","alias_value":"1505.03833v2","created_at":"2026-05-18T01:17:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.03833","created_at":"2026-05-18T01:17:05Z"},{"alias_kind":"pith_short_12","alias_value":"75JKDX3J2EEJ","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"75JKDX3J2EEJBKCU","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"75JKDX3J","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:16e538436b5fe5b6d9f52e34bc6f1f1f05caa3006c138cf54bda816c20212433","target":"graph","created_at":"2026-05-18T01:17:05Z","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 consider $M = B\\times_{f}F$ warped product gradient Ricci solitons. We proved that the potential function depends only on the base and the fiber $F$ is necessarily Einstein manifold. We provide all such solutions in the case of steady gradient Ricci solitons when the base is conformal to an $n$-dimensional pseudo-Euclidean space, invariant under the action of an $(n-1)$-dimensional translation group and the fiber $F$ is Ricci-flat.","authors_text":"M\\'arcio Lemes de Sousa, Romildo Pina","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-14T18:50:42Z","title":"On Warped product gradient Ricci Soliton"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.03833","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:d81630e0d43014d07415fdcf65612f5f28e11728f4f6d33c1cf765f955192264","target":"record","created_at":"2026-05-18T01:17:05Z","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":"5bc7f51b5b98f711c6c42cac872e4c35a0ef0bcd40a387169c31b91de18fe839","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-05-14T18:50:42Z","title_canon_sha256":"6e5a0855bb42e72137a54c7517cc6f2fa7f536b26fe440fb5e4b3337b4528cf4"},"schema_version":"1.0","source":{"id":"1505.03833","kind":"arxiv","version":2}},"canonical_sha256":"ff52a1df69d10890a8544d97314d9c5d84f5c74ef291634188fec7a547c7bc15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff52a1df69d10890a8544d97314d9c5d84f5c74ef291634188fec7a547c7bc15","first_computed_at":"2026-05-18T01:17:05.377683Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:05.377683Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ubFNwIYPTgPCpcLhOSMu3t1NvpdafsHOSXo619nMjqblkABchFG9ANMV3RILXwTJLQkw8jy+sT1AVgh83F/AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:05.378296Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.03833","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d81630e0d43014d07415fdcf65612f5f28e11728f4f6d33c1cf765f955192264","sha256:16e538436b5fe5b6d9f52e34bc6f1f1f05caa3006c138cf54bda816c20212433"],"state_sha256":"28dfc8a2fcecca8a2d6e6811377aa94d2ad0612a7978bd9149f41782e936ebed"}