{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FE45UUIIAPQ2JRMYBUN7ANJXUJ","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":"643460528aadb24449eafad0431340b0253697917b1be91e8c7a8649c42a0f44","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T15:04:45Z","title_canon_sha256":"fae7d7b1496834a530079e5814d15c7c4f63eac1439684c258860c78528508d0"},"schema_version":"1.0","source":{"id":"2607.27007","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.27007","created_at":"2026-07-30T01:23:18Z"},{"alias_kind":"arxiv_version","alias_value":"2607.27007v1","created_at":"2026-07-30T01:23:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.27007","created_at":"2026-07-30T01:23:18Z"},{"alias_kind":"pith_short_12","alias_value":"FE45UUIIAPQ2","created_at":"2026-07-30T01:23:18Z"},{"alias_kind":"pith_short_16","alias_value":"FE45UUIIAPQ2JRMY","created_at":"2026-07-30T01:23:18Z"},{"alias_kind":"pith_short_8","alias_value":"FE45UUII","created_at":"2026-07-30T01:23:18Z"}],"graph_snapshots":[{"event_id":"sha256:2e66c2b8367cfeb24d0b1234afef5fd3737f705951ebe2982e2e3098a3e3c7fe","target":"graph","created_at":"2026-07-30T01:23:18Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.27007/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"On spin manifolds, we give a proof of Brendle and Wang's refined positive mass theorem using the Dirac operator method. In the course of this proof, we discuss the origin of the special coefficient appearing in Brendle and Wang's spectral positivity condition for scalar curvature from the perspective of spin geometry.","authors_text":"Xiangsheng Wang","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T15:04:45Z","title":"The positive mass theorem under a spectral scalar curvature bound on spin manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27007","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:db3b4aec8ebc3370eac6507ea238b414370a8a5dccf422c7743ce7b87aa69c28","target":"record","created_at":"2026-07-30T01:23:18Z","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":"643460528aadb24449eafad0431340b0253697917b1be91e8c7a8649c42a0f44","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-29T15:04:45Z","title_canon_sha256":"fae7d7b1496834a530079e5814d15c7c4f63eac1439684c258860c78528508d0"},"schema_version":"1.0","source":{"id":"2607.27007","kind":"arxiv","version":1}},"canonical_sha256":"2939da510803e1a4c5980d1bf03537a258b6880b513c0a9c7efc911ded8340b4","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2939da510803e1a4c5980d1bf03537a258b6880b513c0a9c7efc911ded8340b4","first_computed_at":"2026-07-30T01:23:18.952461Z","kind":"pith_receipt","last_reissued_at":"2026-07-30T01:23:18.952461Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.27007","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:db3b4aec8ebc3370eac6507ea238b414370a8a5dccf422c7743ce7b87aa69c28","sha256:2e66c2b8367cfeb24d0b1234afef5fd3737f705951ebe2982e2e3098a3e3c7fe"],"state_sha256":"523100c1a06b75f8b76735f9b6d0206e4c24f4b4930985ca694a9329ccfa1070"}