{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:2H4XCQIDPWZSOBQOY7P75FN3DA","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":"9690b6d2d6c669e804ff212fc0e5688044da837cc341e1cd0b9a22f84f7d06c8","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-06-04T21:49:21Z","title_canon_sha256":"63a4a53b7b158fe9411fd788c5634f34b3deca9c076c8922728914b34ab05705"},"schema_version":"1.0","source":{"id":"2306.02490","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2306.02490","created_at":"2026-07-05T07:34:33Z"},{"alias_kind":"arxiv_version","alias_value":"2306.02490v3","created_at":"2026-07-05T07:34:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.02490","created_at":"2026-07-05T07:34:33Z"},{"alias_kind":"pith_short_12","alias_value":"2H4XCQIDPWZS","created_at":"2026-07-05T07:34:33Z"},{"alias_kind":"pith_short_16","alias_value":"2H4XCQIDPWZSOBQO","created_at":"2026-07-05T07:34:33Z"},{"alias_kind":"pith_short_8","alias_value":"2H4XCQID","created_at":"2026-07-05T07:34:33Z"}],"graph_snapshots":[{"event_id":"sha256:2c2f41e0d9651a3b8754188d301e0d0084fea3da6e6667f689230d98b6e9c4ea","target":"graph","created_at":"2026-07-05T07:34:33Z","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/2306.02490/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give new short proofs of Allard's regularity theorem for varifolds with bounded first variation and Brakke's regularity theorem for integral Brakke flows with bounded forcing. They are based on a decay of flatness, following from weighted versions of the respective monotonicity formulas, together with a characterization of non-homogeneous blow-ups using the viscosity approach introduced by Savin.","authors_text":"Carlo Gasparetto, Felix Schulze, Guido De Philippis","cross_cats":["math.DG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-06-04T21:49:21Z","title":"A short proof of Allard's and Brakke's regularity theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.02490","kind":"arxiv","version":3},"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":"sha256:983824d7eab584c944c39e2c5cacea4f9f6ceab65fb2b3bef797dc39e45fc644","target":"record","created_at":"2026-07-05T07:34:33Z","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":"9690b6d2d6c669e804ff212fc0e5688044da837cc341e1cd0b9a22f84f7d06c8","cross_cats_sorted":["math.DG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-06-04T21:49:21Z","title_canon_sha256":"63a4a53b7b158fe9411fd788c5634f34b3deca9c076c8922728914b34ab05705"},"schema_version":"1.0","source":{"id":"2306.02490","kind":"arxiv","version":3}},"canonical_sha256":"d1f97141037db327060ec7dffe95bb1807eea67b9d3661c73a15cceb51a346a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d1f97141037db327060ec7dffe95bb1807eea67b9d3661c73a15cceb51a346a3","first_computed_at":"2026-07-05T07:34:33.493770Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:34:33.493770Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zlQyj7Fwn2QAlpoLC/bOQsxIKT6jZNrXFQZuecvm4nbdl/FMMGMLadog3o2cOv4pEMaMwwicxzxFpSyFxKtCAg==","signature_status":"signed_v1","signed_at":"2026-07-05T07:34:33.494279Z","signed_message":"canonical_sha256_bytes"},"source_id":"2306.02490","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:983824d7eab584c944c39e2c5cacea4f9f6ceab65fb2b3bef797dc39e45fc644","sha256:2c2f41e0d9651a3b8754188d301e0d0084fea3da6e6667f689230d98b6e9c4ea"],"state_sha256":"10d004dbf2e2b3cd32d7fe8b44bbb6cb20823b499b13f43fac8660963e7a3a96"}