{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:JZBKTUC7QXDRGF63U5P7OSS2VF","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":"bdf97c0f3a4496d7f4bf6db17906646419b4025c19d7767b02113060bd3a7150","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-04T07:43:19Z","title_canon_sha256":"d82bad50c949f14a3a4c60a4c351c07cbead610b96f50aee113dc325cb4024e1"},"schema_version":"1.0","source":{"id":"1904.02391","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.02391","created_at":"2026-05-17T23:39:39Z"},{"alias_kind":"arxiv_version","alias_value":"1904.02391v3","created_at":"2026-05-17T23:39:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.02391","created_at":"2026-05-17T23:39:39Z"},{"alias_kind":"pith_short_12","alias_value":"JZBKTUC7QXDR","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"JZBKTUC7QXDRGF63","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"JZBKTUC7","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:bd63c2c7e16eeaf36a54767e1922d1496ddfed1e078327541ff2a946be150ad1","target":"graph","created_at":"2026-05-17T23:39:39Z","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"},"paper":{"abstract_excerpt":"In this paper, we study the line bundle mean curvature flow defined by Jacob and Yau. The line bundle mean curvature flow is a kind of parabolic flows to obtain deformed Hermitian Yang-Mills metrics on a given K\\\"ahler manifold. The goal of this paper is to give an $\\varepsilon$-regularity theorem for the line bundle mean curvature flow. To establish the theorem, we provide a scale invariant monotone quantity. As a critical point of this quantity, we define self-shrinker solution of the line bundle mean curvature flow. The Liouville type theorem for self-shrinkers is also given. It plays an im","authors_text":"Hikaru Yamamoto, Xiaoli Han","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-04T07:43:19Z","title":"An $\\varepsilon$-regularity theorem for line bundle mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.02391","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":"sha256:781d1c7c04ef82ed8a40a82cfba5b536472beb5a416866f4692628c720a34d89","target":"record","created_at":"2026-05-17T23:39:39Z","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":"bdf97c0f3a4496d7f4bf6db17906646419b4025c19d7767b02113060bd3a7150","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-04-04T07:43:19Z","title_canon_sha256":"d82bad50c949f14a3a4c60a4c351c07cbead610b96f50aee113dc325cb4024e1"},"schema_version":"1.0","source":{"id":"1904.02391","kind":"arxiv","version":3}},"canonical_sha256":"4e42a9d05f85c71317dba75ff74a5aa9732e89b7c1c80b889dbb09be9d7fdc38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e42a9d05f85c71317dba75ff74a5aa9732e89b7c1c80b889dbb09be9d7fdc38","first_computed_at":"2026-05-17T23:39:39.644728Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:39.644728Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wYn7mHfZLyVpe+28OkQoLHcfvU/mEVTpgO8nIHjmSEhmSB6xwTBida2RMQOpGD8J7RU5ea/PCqI6EzA2fs6YBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:39.645299Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.02391","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:781d1c7c04ef82ed8a40a82cfba5b536472beb5a416866f4692628c720a34d89","sha256:bd63c2c7e16eeaf36a54767e1922d1496ddfed1e078327541ff2a946be150ad1"],"state_sha256":"bba092df7aa67eaa8aa128dd93dad6f493d3a51be0ba8b5ee00665e204c569ab"}