{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NIG6WBH7LGJJFIIWO55ODI43Z2","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":"7ff081f695531892eb50077be3889c1100cf92770a14c01aafcc7342c672990a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-25T01:28:28Z","title_canon_sha256":"c86584b5eeefa9876f22b2590ba0940d92e49e22feea107e0221003d67687abf"},"schema_version":"1.0","source":{"id":"2503.19254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2503.19254","created_at":"2026-07-05T10:38:51Z"},{"alias_kind":"arxiv_version","alias_value":"2503.19254v1","created_at":"2026-07-05T10:38:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2503.19254","created_at":"2026-07-05T10:38:51Z"},{"alias_kind":"pith_short_12","alias_value":"NIG6WBH7LGJJ","created_at":"2026-07-05T10:38:51Z"},{"alias_kind":"pith_short_16","alias_value":"NIG6WBH7LGJJFIIW","created_at":"2026-07-05T10:38:51Z"},{"alias_kind":"pith_short_8","alias_value":"NIG6WBH7","created_at":"2026-07-05T10:38:51Z"}],"graph_snapshots":[{"event_id":"sha256:9c57e7ff52973a4d4f3a0d15a830c05df4ba757da69cb386e9b222b186cf907e","target":"graph","created_at":"2026-07-05T10:38:51Z","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/2503.19254/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"By using the ABP method developed by Cabr\\'e and Brendle, we establish some Sobolev inequalities for compact domains and submanifolds in a complete Riemannian manifold with lower quadratic curvature decay","authors_text":"Han Luo, Lingen Lu, Tian Chong","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-25T01:28:28Z","title":"Sobolev Inequality In Manifolds With Lower Quadratic Curvature Decay"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.19254","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":"sha256:424097636087f7051213be531acbcc266ca7a68eb36d859b0562d768d6f37032","target":"record","created_at":"2026-07-05T10:38:51Z","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":"7ff081f695531892eb50077be3889c1100cf92770a14c01aafcc7342c672990a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2025-03-25T01:28:28Z","title_canon_sha256":"c86584b5eeefa9876f22b2590ba0940d92e49e22feea107e0221003d67687abf"},"schema_version":"1.0","source":{"id":"2503.19254","kind":"arxiv","version":1}},"canonical_sha256":"6a0deb04ff599292a116777ae1a39bce82869b9a43336a52d248f1adfd9729cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a0deb04ff599292a116777ae1a39bce82869b9a43336a52d248f1adfd9729cc","first_computed_at":"2026-07-05T10:38:51.789369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:38:51.789369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R2drmPL8ykJ4N5/nrmH9OW7hrFrlZKlrLT9CmMe7bmuqw5OIJcQdNG6KugPdyxBs1w/eXkJnxgBQEjB4+1DNAg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:38:51.789847Z","signed_message":"canonical_sha256_bytes"},"source_id":"2503.19254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:424097636087f7051213be531acbcc266ca7a68eb36d859b0562d768d6f37032","sha256:9c57e7ff52973a4d4f3a0d15a830c05df4ba757da69cb386e9b222b186cf907e"],"state_sha256":"976166029d10796b0c3d029b614c2dc8ee3988eb55f6b9a6adb59b59d5c276fc"}