{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LBZDK7ZFBLFYCRQRP4WEPF6DZM","short_pith_number":"pith:LBZDK7ZF","canonical_record":{"source":{"id":"1704.05490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-04-18T18:33:21Z","cross_cats_sorted":[],"title_canon_sha256":"02332a297817bde759bb5a8414f9ebf2e732c7ae0fbcbcc545d3667483f61d5e","abstract_canon_sha256":"c3a863e766fad48e577831601fbb29371839f8df19d47378f60d94272e49273f"},"schema_version":"1.0"},"canonical_sha256":"5872357f250acb8146117f2c4797c3cb1e3a4ff38fda0ad98cee4ff1151fda11","source":{"kind":"arxiv","id":"1704.05490","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05490","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05490v1","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05490","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"LBZDK7ZFBLFY","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LBZDK7ZFBLFYCRQR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LBZDK7ZF","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LBZDK7ZFBLFYCRQRP4WEPF6DZM","target":"record","payload":{"canonical_record":{"source":{"id":"1704.05490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-04-18T18:33:21Z","cross_cats_sorted":[],"title_canon_sha256":"02332a297817bde759bb5a8414f9ebf2e732c7ae0fbcbcc545d3667483f61d5e","abstract_canon_sha256":"c3a863e766fad48e577831601fbb29371839f8df19d47378f60d94272e49273f"},"schema_version":"1.0"},"canonical_sha256":"5872357f250acb8146117f2c4797c3cb1e3a4ff38fda0ad98cee4ff1151fda11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:07.301062Z","signature_b64":"nYHOeW/utF27dfClBE0tcqyehTbalgrgcHpfjt5MMJTXfPBBnGa+qMTMHLOPLQp1l+4mgHVrga/UQhDjVuhyBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5872357f250acb8146117f2c4797c3cb1e3a4ff38fda0ad98cee4ff1151fda11","last_reissued_at":"2026-05-18T00:46:07.300641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:07.300641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.05490","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":"2026-05-18T00:46:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RvdePC6gz3MUT9xya9AxFrzu65gb5UkjiUfSvm/bD+Ru7lSyFbvi9ZqHhSy7F5fECK/bigOqAX5OoibevOrnBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:31:06.676719Z"},"content_sha256":"3edb0a44924b29f97ef7b45ef34b302b9d369548312b7181f507bfce16b734f0","schema_version":"1.0","event_id":"sha256:3edb0a44924b29f97ef7b45ef34b302b9d369548312b7181f507bfce16b734f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LBZDK7ZFBLFYCRQRP4WEPF6DZM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive Scalar Curvature and Minimal Hypersurface Singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Richard Schoen, Shing-Tung Yau","submitted_at":"2017-04-18T18:33:21Z","abstract_excerpt":"In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption. It also includes statements about the structure of compact manifolds of positive scalar curvature extending the work of \\cite{sy1} to all dimensions. The technical work in this paper is to construct minimal slicings and associated weight functions in the presence of small singular sets and to show that the singular sets do not become too large in the lower dimensional"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05490","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":"2026-05-18T00:46:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j0S8+YnUmKtmJ7U4e5bj/H1CRZu+ypD6N0wO4MWk9dL5QBYDoUlcEkX+42UhsnPBvOSYOiG6fFTpTUgNCm8OBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T19:31:06.677058Z"},"content_sha256":"19ca6d551becf350aff6f2fca1dd001140e6ddbf5354245a9867e9bff8cbba8d","schema_version":"1.0","event_id":"sha256:19ca6d551becf350aff6f2fca1dd001140e6ddbf5354245a9867e9bff8cbba8d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LBZDK7ZFBLFYCRQRP4WEPF6DZM/bundle.json","state_url":"https://pith.science/pith/LBZDK7ZFBLFYCRQRP4WEPF6DZM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LBZDK7ZFBLFYCRQRP4WEPF6DZM/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":"2026-05-30T19:31:06Z","links":{"resolver":"https://pith.science/pith/LBZDK7ZFBLFYCRQRP4WEPF6DZM","bundle":"https://pith.science/pith/LBZDK7ZFBLFYCRQRP4WEPF6DZM/bundle.json","state":"https://pith.science/pith/LBZDK7ZFBLFYCRQRP4WEPF6DZM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LBZDK7ZFBLFYCRQRP4WEPF6DZM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LBZDK7ZFBLFYCRQRP4WEPF6DZM","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":"c3a863e766fad48e577831601fbb29371839f8df19d47378f60d94272e49273f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-04-18T18:33:21Z","title_canon_sha256":"02332a297817bde759bb5a8414f9ebf2e732c7ae0fbcbcc545d3667483f61d5e"},"schema_version":"1.0","source":{"id":"1704.05490","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.05490","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1704.05490v1","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05490","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"LBZDK7ZFBLFY","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LBZDK7ZFBLFYCRQR","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LBZDK7ZF","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:19ca6d551becf350aff6f2fca1dd001140e6ddbf5354245a9867e9bff8cbba8d","target":"graph","created_at":"2026-05-18T00:46:07Z","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 develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption. It also includes statements about the structure of compact manifolds of positive scalar curvature extending the work of \\cite{sy1} to all dimensions. The technical work in this paper is to construct minimal slicings and associated weight functions in the presence of small singular sets and to show that the singular sets do not become too large in the lower dimensional","authors_text":"Richard Schoen, Shing-Tung Yau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-04-18T18:33:21Z","title":"Positive Scalar Curvature and Minimal Hypersurface Singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05490","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":"sha256:3edb0a44924b29f97ef7b45ef34b302b9d369548312b7181f507bfce16b734f0","target":"record","created_at":"2026-05-18T00:46:07Z","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":"c3a863e766fad48e577831601fbb29371839f8df19d47378f60d94272e49273f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-04-18T18:33:21Z","title_canon_sha256":"02332a297817bde759bb5a8414f9ebf2e732c7ae0fbcbcc545d3667483f61d5e"},"schema_version":"1.0","source":{"id":"1704.05490","kind":"arxiv","version":1}},"canonical_sha256":"5872357f250acb8146117f2c4797c3cb1e3a4ff38fda0ad98cee4ff1151fda11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5872357f250acb8146117f2c4797c3cb1e3a4ff38fda0ad98cee4ff1151fda11","first_computed_at":"2026-05-18T00:46:07.300641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:07.300641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nYHOeW/utF27dfClBE0tcqyehTbalgrgcHpfjt5MMJTXfPBBnGa+qMTMHLOPLQp1l+4mgHVrga/UQhDjVuhyBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:07.301062Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.05490","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3edb0a44924b29f97ef7b45ef34b302b9d369548312b7181f507bfce16b734f0","sha256:19ca6d551becf350aff6f2fca1dd001140e6ddbf5354245a9867e9bff8cbba8d"],"state_sha256":"62777ac6e8bc576eaba31b7fba9192a46f63c10816067487365ae4c090c3a2f7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xMalm9gfGKenjZh1CMdMknh54MqCd5su/9u+AjzwEbnvgootI/p8iaoLAvJ3vhJ+fPgXOnvJveTEds2R2O44AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T19:31:06.679054Z","bundle_sha256":"c4855b8b725018098625d28726b06c7e1469c5fb60310d3af6e9bf393463d63c"}}