{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:2RZCBTOAFFANNLCDBHSMGZ7ASF","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":"86afe2106cdbb528def2325dcc9d744744c0cdd0bd3ccc467fb07d6f88cd8519","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-31T08:59:48Z","title_canon_sha256":"76ea89b6ea28358775646bd460d99b3f276d01d5a1d2db068cef533e3e00e260"},"schema_version":"1.0","source":{"id":"2606.01108","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.01108","created_at":"2026-06-02T02:04:23Z"},{"alias_kind":"arxiv_version","alias_value":"2606.01108v1","created_at":"2026-06-02T02:04:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01108","created_at":"2026-06-02T02:04:23Z"},{"alias_kind":"pith_short_12","alias_value":"2RZCBTOAFFAN","created_at":"2026-06-02T02:04:23Z"},{"alias_kind":"pith_short_16","alias_value":"2RZCBTOAFFANNLCD","created_at":"2026-06-02T02:04:23Z"},{"alias_kind":"pith_short_8","alias_value":"2RZCBTOA","created_at":"2026-06-02T02:04:23Z"}],"graph_snapshots":[{"event_id":"sha256:60ddbe0b93909d4e59c2ccd67bf0a80eba81a68db986a28367f2e6f013b2f7d7","target":"graph","created_at":"2026-06-02T02:04:23Z","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/2606.01108/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove an integral type Gauss-Green formula on non-collapsed RCD spaces using the strong locality of the Laplacian and an eigenfunction approximation method. As applications, we generalize Colding's monotonicity formulas and prove an asymptotic formula linking the mean curvature of a hypersurface at a given point to the volume of small balls centered at that point.","authors_text":"Zhangkai Huang","cross_cats":["math.MG"],"headline":"","license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-31T08:59:48Z","title":"Integral type Gauss-Green formula on non-collapsed RCD spaces and its applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01108","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":"sha256:98b9491f8e82267882cf9ebc92b272142fa85946b7fd0a4f175fcd2f2dc297f5","target":"record","created_at":"2026-06-02T02:04:23Z","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":"86afe2106cdbb528def2325dcc9d744744c0cdd0bd3ccc467fb07d6f88cd8519","cross_cats_sorted":["math.MG"],"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2026-05-31T08:59:48Z","title_canon_sha256":"76ea89b6ea28358775646bd460d99b3f276d01d5a1d2db068cef533e3e00e260"},"schema_version":"1.0","source":{"id":"2606.01108","kind":"arxiv","version":1}},"canonical_sha256":"d47220cdc02940d6ac4309e4c367e0916bad23a08511b7ec233f723ac8b313b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d47220cdc02940d6ac4309e4c367e0916bad23a08511b7ec233f723ac8b313b5","first_computed_at":"2026-06-02T02:04:23.700900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T02:04:23.700900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u9MFS8+kH5xfirS+0iR9Wq4PNwQY+K83V3quH6BY/crBEwc472IWpIYZAaqIGE00nRwNv4T01yWLoaQwk0K1Bw==","signature_status":"signed_v1","signed_at":"2026-06-02T02:04:23.701435Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.01108","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98b9491f8e82267882cf9ebc92b272142fa85946b7fd0a4f175fcd2f2dc297f5","sha256:60ddbe0b93909d4e59c2ccd67bf0a80eba81a68db986a28367f2e6f013b2f7d7"],"state_sha256":"e025c8729ff730c5aefd3f5640878239a69ee85739c5881d27100bf4dc74bf06"}