{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:WR7ZZ4JB4PCF323M5AINQAK2ZG","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b5b3b1bad241fb67a136844d40ce9946a3a33feb2661b6c694b00f08e61afb53","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-27T19:12:52Z","title_canon_sha256":"0611f8738f2602c5e0990fb00e0bd8d91bbb172d75557fb28bd11e716acf0ba8"},"schema_version":"1.0","source":{"id":"2607.25015","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.25015","created_at":"2026-07-29T00:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"2607.25015v1","created_at":"2026-07-29T00:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.25015","created_at":"2026-07-29T00:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"WR7ZZ4JB4PCF","created_at":"2026-07-29T00:24:57Z"},{"alias_kind":"pith_short_16","alias_value":"WR7ZZ4JB4PCF323M","created_at":"2026-07-29T00:24:57Z"},{"alias_kind":"pith_short_8","alias_value":"WR7ZZ4JB","created_at":"2026-07-29T00:24:57Z"}],"graph_snapshots":[{"event_id":"sha256:76ff2c528d59fa5261767ac236ab85989b792b617f280b29058ea4c2c876f0ed","target":"graph","created_at":"2026-07-29T00:24:57Z","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/2607.25015/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that a contractible $3$-manifold admitting a complete Riemannian metric of nonnegative scalar curvature is diffeomorphic to $\\R^3$. We also prove that, if the interior $M_\\gamma$ of a compact handlebody of genus $\\gamma$ admits such a metric, then $\\gamma\\leq1$. This answers two open questions posed by Wang and Gromov, respectively.","authors_text":"Heng Zhang, Jiangcheng You","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-27T19:12:52Z","title":"Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.25015","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":"sha256:6a5aaf473e905c9baf65448654eb17aaeef5b03860e356207aa7f48f94ffef07","target":"record","created_at":"2026-07-29T00:24:57Z","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":"b5b3b1bad241fb67a136844d40ce9946a3a33feb2661b6c694b00f08e61afb53","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-27T19:12:52Z","title_canon_sha256":"0611f8738f2602c5e0990fb00e0bd8d91bbb172d75557fb28bd11e716acf0ba8"},"schema_version":"1.0","source":{"id":"2607.25015","kind":"arxiv","version":1}},"canonical_sha256":"b47f9cf121e3c45deb6ce810d8015ac9ad9aef41f3a114049dc7aed0ab45c883","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b47f9cf121e3c45deb6ce810d8015ac9ad9aef41f3a114049dc7aed0ab45c883","first_computed_at":"2026-07-29T00:24:57.810818Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-29T00:24:57.810818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Aoh3PDxoxcUKzqufF3/DSthspgnD8HvrRMJlM6Cozo0/hyNQEtcinGrneaWEE9tbMiSYVE31TufbmCbdg34FBw==","signature_status":"signed_v1","signed_at":"2026-07-29T00:24:57.811642Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.25015","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6a5aaf473e905c9baf65448654eb17aaeef5b03860e356207aa7f48f94ffef07","sha256:76ff2c528d59fa5261767ac236ab85989b792b617f280b29058ea4c2c876f0ed","sha256:4999eef3ff4a26e9319dacdebc1b78977ad1481a92431c42b9d0aca52864fb8e"],"state_sha256":"5800519866c6251962f5201cff08ac6830fa61b706e08bae28241f7c34fa7328"}