{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:DDYHO7M5MJPSTCUXHER4V65GEI","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":"c5501cc57a77d3f4194e68ac528dd23385c16cd353ba330d68d676253d9d10f2","cross_cats_sorted":["math.DG","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-07-26T16:55:56Z","title_canon_sha256":"28a747a0196f7f5428ca2c5b1667fc63eab82f468641db78d610d333ccbbc1fc"},"schema_version":"1.0","source":{"id":"2407.18868","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.18868","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"arxiv_version","alias_value":"2407.18868v1","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.18868","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"pith_short_12","alias_value":"DDYHO7M5MJPS","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"pith_short_16","alias_value":"DDYHO7M5MJPSTCUX","created_at":"2026-07-05T08:48:55Z"},{"alias_kind":"pith_short_8","alias_value":"DDYHO7M5","created_at":"2026-07-05T08:48:55Z"}],"graph_snapshots":[{"event_id":"sha256:f30080b6ce0bf137d5639b9fc3eeab2994fe3ad1035bf78ee377859df587eff6","target":"graph","created_at":"2026-07-05T08:48:55Z","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/2407.18868/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a diffused interface version of the volume-preserving mean curvature flow in the Euclidean space, and prove, in every dimension and under natural assumptions on the initial datum, exponential convergence towards single \"diffused balls\".","authors_text":"Daniel Restrepo, Francesco Maggi, Matteo Bonforte","cross_cats":["math.DG","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-07-26T16:55:56Z","title":"Asymptotic behavior of a diffused interface volume-preserving mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.18868","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:e3ba82b2d65cca22cd739a599f9eb7c23ab08b67769ff8c960ac2349a55767f9","target":"record","created_at":"2026-07-05T08:48:55Z","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":"c5501cc57a77d3f4194e68ac528dd23385c16cd353ba330d68d676253d9d10f2","cross_cats_sorted":["math.DG","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-07-26T16:55:56Z","title_canon_sha256":"28a747a0196f7f5428ca2c5b1667fc63eab82f468641db78d610d333ccbbc1fc"},"schema_version":"1.0","source":{"id":"2407.18868","kind":"arxiv","version":1}},"canonical_sha256":"18f0777d9d625f298a973923cafba62234b4e26c84c0ec0ba62a35aaa62a158a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18f0777d9d625f298a973923cafba62234b4e26c84c0ec0ba62a35aaa62a158a","first_computed_at":"2026-07-05T08:48:55.711250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:48:55.711250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/CVrsckKxKO+mGlBA3MkjPHIPbId2V4WbQO+hmxNhfqnqdXPOCaulVearTneB6SN2BFVdqFP2TMSGQbM2TvNAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:48:55.711631Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.18868","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3ba82b2d65cca22cd739a599f9eb7c23ab08b67769ff8c960ac2349a55767f9","sha256:f30080b6ce0bf137d5639b9fc3eeab2994fe3ad1035bf78ee377859df587eff6"],"state_sha256":"9656ec041ea45d9578ca94befb7e241958f21b8467ec2a0de6361a75598bff5f"}