{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CKS6FYP7SYO4XM7GGPJJG4RCM6","short_pith_number":"pith:CKS6FYP7","canonical_record":{"source":{"id":"1705.09627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-26T15:55:49Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"860285fb9a3d769a011d3fab4baed810435b1d4832910a9ad679c718d0e60f39","abstract_canon_sha256":"bddebf40c06b2de73eb0cc3b142726bf9c55c4ea04f4c2f0e3960c6fa7d72629"},"schema_version":"1.0"},"canonical_sha256":"12a5e2e1ff961dcbb3e633d293722267a236408d55686a512585a54be7c2a705","source":{"kind":"arxiv","id":"1705.09627","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09627","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09627v1","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09627","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"CKS6FYP7SYO4","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CKS6FYP7SYO4XM7G","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CKS6FYP7","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CKS6FYP7SYO4XM7GGPJJG4RCM6","target":"record","payload":{"canonical_record":{"source":{"id":"1705.09627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-26T15:55:49Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"860285fb9a3d769a011d3fab4baed810435b1d4832910a9ad679c718d0e60f39","abstract_canon_sha256":"bddebf40c06b2de73eb0cc3b142726bf9c55c4ea04f4c2f0e3960c6fa7d72629"},"schema_version":"1.0"},"canonical_sha256":"12a5e2e1ff961dcbb3e633d293722267a236408d55686a512585a54be7c2a705","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:38.199433Z","signature_b64":"Sl/DqFG8agnuREscXMfZPtH9i0i7S5PgU7llxUS30SLZUdVPytI+wh96t6rJQJZFQwZfXBKKTmzzYo2VGz+eAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"12a5e2e1ff961dcbb3e633d293722267a236408d55686a512585a54be7c2a705","last_reissued_at":"2026-05-18T00:43:38.198964Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:38.198964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.09627","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":"2026-05-18T00:43:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DjHl2n6N8A7JwhMd/RIO8yOyPsm3PzNWyXEL65HFNSAAbrmp/rPJmET9B8HVaU+K0XCBrJqbPBgdXj66U0nUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:37:21.534686Z"},"content_sha256":"0ffeae82a7b67af62749b9fbf500b3849c6edb73779dfb89cb43981d21f99cdd","schema_version":"1.0","event_id":"sha256:0ffeae82a7b67af62749b9fbf500b3849c6edb73779dfb89cb43981d21f99cdd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CKS6FYP7SYO4XM7GGPJJG4RCM6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Scalar curvature flow on S^n to a prescribed sign-changing function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Hong Zhang","submitted_at":"2017-05-26T15:55:49Z","abstract_excerpt":"In this paper, we consider the problem of prescribing scalar curvature on n-sphere. Assume that the candidate curvature function $f$, which is allowed to change sign, satisfies some kind of Morse index or symmetry condition. By studying the well-known scalar curvature flow, we are able to prove that the flow converges to a metric with the prescribed function $f$ as its scalar curvature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09627","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":"2026-05-18T00:43:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GKeocNQLa+KTcj0SxRYUS4rEO/EsnvpdxsRcszgxz0PRGSyTy0ZPi+v2wHhMmAXKpYM2CxLVF5HpCpp+q9Z+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:37:21.535252Z"},"content_sha256":"55d705eddd2b4ad86b2afbbeef0c4abd66efa34bd7d5d83501fa356b5d386fcd","schema_version":"1.0","event_id":"sha256:55d705eddd2b4ad86b2afbbeef0c4abd66efa34bd7d5d83501fa356b5d386fcd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CKS6FYP7SYO4XM7GGPJJG4RCM6/bundle.json","state_url":"https://pith.science/pith/CKS6FYP7SYO4XM7GGPJJG4RCM6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CKS6FYP7SYO4XM7GGPJJG4RCM6/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":"2026-06-04T02:37:21Z","links":{"resolver":"https://pith.science/pith/CKS6FYP7SYO4XM7GGPJJG4RCM6","bundle":"https://pith.science/pith/CKS6FYP7SYO4XM7GGPJJG4RCM6/bundle.json","state":"https://pith.science/pith/CKS6FYP7SYO4XM7GGPJJG4RCM6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CKS6FYP7SYO4XM7GGPJJG4RCM6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CKS6FYP7SYO4XM7GGPJJG4RCM6","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":"bddebf40c06b2de73eb0cc3b142726bf9c55c4ea04f4c2f0e3960c6fa7d72629","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-26T15:55:49Z","title_canon_sha256":"860285fb9a3d769a011d3fab4baed810435b1d4832910a9ad679c718d0e60f39"},"schema_version":"1.0","source":{"id":"1705.09627","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.09627","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"arxiv_version","alias_value":"1705.09627v1","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.09627","created_at":"2026-05-18T00:43:38Z"},{"alias_kind":"pith_short_12","alias_value":"CKS6FYP7SYO4","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CKS6FYP7SYO4XM7G","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CKS6FYP7","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:55d705eddd2b4ad86b2afbbeef0c4abd66efa34bd7d5d83501fa356b5d386fcd","target":"graph","created_at":"2026-05-18T00:43:38Z","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 the problem of prescribing scalar curvature on n-sphere. Assume that the candidate curvature function $f$, which is allowed to change sign, satisfies some kind of Morse index or symmetry condition. By studying the well-known scalar curvature flow, we are able to prove that the flow converges to a metric with the prescribed function $f$ as its scalar curvature.","authors_text":"Hong Zhang","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-26T15:55:49Z","title":"Scalar curvature flow on S^n to a prescribed sign-changing function"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.09627","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":"sha256:0ffeae82a7b67af62749b9fbf500b3849c6edb73779dfb89cb43981d21f99cdd","target":"record","created_at":"2026-05-18T00:43:38Z","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":"bddebf40c06b2de73eb0cc3b142726bf9c55c4ea04f4c2f0e3960c6fa7d72629","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-05-26T15:55:49Z","title_canon_sha256":"860285fb9a3d769a011d3fab4baed810435b1d4832910a9ad679c718d0e60f39"},"schema_version":"1.0","source":{"id":"1705.09627","kind":"arxiv","version":1}},"canonical_sha256":"12a5e2e1ff961dcbb3e633d293722267a236408d55686a512585a54be7c2a705","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12a5e2e1ff961dcbb3e633d293722267a236408d55686a512585a54be7c2a705","first_computed_at":"2026-05-18T00:43:38.198964Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:38.198964Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Sl/DqFG8agnuREscXMfZPtH9i0i7S5PgU7llxUS30SLZUdVPytI+wh96t6rJQJZFQwZfXBKKTmzzYo2VGz+eAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:38.199433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.09627","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ffeae82a7b67af62749b9fbf500b3849c6edb73779dfb89cb43981d21f99cdd","sha256:55d705eddd2b4ad86b2afbbeef0c4abd66efa34bd7d5d83501fa356b5d386fcd"],"state_sha256":"06513e5369fcceb0436394c5c5e42b4110b6908e52ed610538e59f4b00fc2d23"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9WvyAAIEulzqtYh8Ovrmeub6QQdErf7DQYWSssx51tKeuQPlcO4srlWEDw0vtMwOy0N5f80Z4v9fuGkuyHSAAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T02:37:21.539826Z","bundle_sha256":"7d629e149c0a40f3c831ab4549f13694a1ba74a4a2543dfb312110d46e209265"}}