{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QV3AEZNNC325HX5ICT4C6XZDZ4","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":"c50f17667b2a37fbf79d875d3bbc9f0efe42e3b387fa8a5c42f13cec043c31f0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-17T14:59:10Z","title_canon_sha256":"3549e1a19de03697f36599f36e9a0084f86840e2a3f01e4008f6194785c0fb21"},"schema_version":"1.0","source":{"id":"1105.3404","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.3404","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"arxiv_version","alias_value":"1105.3404v4","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.3404","created_at":"2026-05-18T00:51:58Z"},{"alias_kind":"pith_short_12","alias_value":"QV3AEZNNC325","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QV3AEZNNC325HX5I","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QV3AEZNN","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:c1750ed60332cb9f481833455a0ce5c6e2fb04355dca49a4c6065cdc56a3b338","target":"graph","created_at":"2026-05-18T00:51:58Z","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 article the degenerate warped products of singular semi-Riemannian manifolds are studied. They were used recently by the author to handle singularities occurring in General Relativity, in black holes and at the big-bang. One main result presented here is that a degenerate warped product of semi-regular semi-Riemannian manifolds with the warping function satisfying a certain condition is a semi-regular semi-Riemannian manifold. The connection and the Riemann curvature of the warped product are expressed in terms of those of the factor manifolds. Examples of singular semi-Riemannian mani","authors_text":"Ovidiu Cristinel Stoica","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-17T14:59:10Z","title":"The Geometry of Warped Product Singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.3404","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:abbae8996a572570fd786cc5d4f9f48c8addd1206c160e9f9d74da72f00be3cc","target":"record","created_at":"2026-05-18T00:51:58Z","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":"c50f17667b2a37fbf79d875d3bbc9f0efe42e3b387fa8a5c42f13cec043c31f0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-05-17T14:59:10Z","title_canon_sha256":"3549e1a19de03697f36599f36e9a0084f86840e2a3f01e4008f6194785c0fb21"},"schema_version":"1.0","source":{"id":"1105.3404","kind":"arxiv","version":4}},"canonical_sha256":"85760265ad16f5d3dfa814f82f5f23cf2f3b5e14eda975e3c2cad1826b3cb2b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85760265ad16f5d3dfa814f82f5f23cf2f3b5e14eda975e3c2cad1826b3cb2b0","first_computed_at":"2026-05-18T00:51:58.650728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:58.650728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f699dky9q7vMSMsYoHvFaxKKY8upwcs8LDIQGreHZaUVrgMh/Fq9hf/yunIFAs4jUBJGUmmS1L4IIizHlijGAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:58.651218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.3404","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:abbae8996a572570fd786cc5d4f9f48c8addd1206c160e9f9d74da72f00be3cc","sha256:c1750ed60332cb9f481833455a0ce5c6e2fb04355dca49a4c6065cdc56a3b338"],"state_sha256":"cb122c73bb45c14ab7fc36d730ee3143b4f1bb6fc6b5e606c8da32ab558f1259"}