{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:DVY5KCFCX5JQEJRKWYACVHZVPO","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":"8295383c5aa7b7275cc9576798d5378916b307823a953d414de436b7a67f4bc8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-29T08:08:15Z","title_canon_sha256":"d24af7614d922abb01c129e2cd538af9d8f182573f6a8904626cad99b61e9f21"},"schema_version":"1.0","source":{"id":"2505.23222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.23222","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"arxiv_version","alias_value":"2505.23222v1","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.23222","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"pith_short_12","alias_value":"DVY5KCFCX5JQ","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"pith_short_16","alias_value":"DVY5KCFCX5JQEJRK","created_at":"2026-07-05T11:11:57Z"},{"alias_kind":"pith_short_8","alias_value":"DVY5KCFC","created_at":"2026-07-05T11:11:57Z"}],"graph_snapshots":[{"event_id":"sha256:62234c0673c087cb2ff3f681d1c12506172145e60dcb20db3660012545b97a17","target":"graph","created_at":"2026-07-05T11:11:57Z","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/2505.23222/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we propose a new notion of Brakke inequality for volume preserving mean curvature flow. We show the existence of integral varifolds solving the flow globally-in-time in the corresponding Brakke sense using the phase field method. Morever, such varifolds are solutions to volume preserving mean curvature flow in the $L^2$-flow sense as well. We thus extend a previous result by one of the authors [25].","authors_text":"Andrea Chiesa, Keisuke Takasao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-29T08:08:15Z","title":"Brakke inequality and the existence of Brakke-flow for volume preserving mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.23222","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":"sha256:2367e4981177da229d595266e34c118def3bc551732285a03a9d380a839f6382","target":"record","created_at":"2026-07-05T11:11:57Z","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":"8295383c5aa7b7275cc9576798d5378916b307823a953d414de436b7a67f4bc8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.AP","submitted_at":"2025-05-29T08:08:15Z","title_canon_sha256":"d24af7614d922abb01c129e2cd538af9d8f182573f6a8904626cad99b61e9f21"},"schema_version":"1.0","source":{"id":"2505.23222","kind":"arxiv","version":1}},"canonical_sha256":"1d71d508a2bf5302262ab6002a9f357b951aa50f26fa9676e5758158ce0cbed7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1d71d508a2bf5302262ab6002a9f357b951aa50f26fa9676e5758158ce0cbed7","first_computed_at":"2026-07-05T11:11:57.795018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:57.795018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"171Fq8oOGrWuOh7QJ/i4ayyLtVoMdVQsqLtZ2fUBOBj9qDMWr7HqSnnjfgEAxATbzygLMA91Q5xI2dj/mRbBCw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:57.795541Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.23222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2367e4981177da229d595266e34c118def3bc551732285a03a9d380a839f6382","sha256:62234c0673c087cb2ff3f681d1c12506172145e60dcb20db3660012545b97a17"],"state_sha256":"b2d1bde0bb61596d250caf9b0ee0fca2dd2f56d75638e172caf0a3ffa976cd61"}