{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:3EKHOGSBYPOSVQ55GY4ISD5B44","short_pith_number":"pith:3EKHOGSB","canonical_record":{"source":{"id":"2108.01733","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-08-03T20:15:20Z","cross_cats_sorted":[],"title_canon_sha256":"6d561b8b702f0f768aeea620ffec4d86bb7334d8f596ad32f6dc6ca9ea50f38b","abstract_canon_sha256":"d530a6b0baebcb47944bfca5ebf265e49c57d4c6ca30fb1fbdd9473303e20fb9"},"schema_version":"1.0"},"canonical_sha256":"d914771a41c3dd2ac3bd3638890fa1e723ef2cd8aae7cca916dd929b8f438f7e","source":{"kind":"arxiv","id":"2108.01733","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.01733","created_at":"2026-07-05T03:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"2108.01733v2","created_at":"2026-07-05T03:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.01733","created_at":"2026-07-05T03:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"3EKHOGSBYPOS","created_at":"2026-07-05T03:17:33Z"},{"alias_kind":"pith_short_16","alias_value":"3EKHOGSBYPOSVQ55","created_at":"2026-07-05T03:17:33Z"},{"alias_kind":"pith_short_8","alias_value":"3EKHOGSB","created_at":"2026-07-05T03:17:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:3EKHOGSBYPOSVQ55GY4ISD5B44","target":"record","payload":{"canonical_record":{"source":{"id":"2108.01733","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-08-03T20:15:20Z","cross_cats_sorted":[],"title_canon_sha256":"6d561b8b702f0f768aeea620ffec4d86bb7334d8f596ad32f6dc6ca9ea50f38b","abstract_canon_sha256":"d530a6b0baebcb47944bfca5ebf265e49c57d4c6ca30fb1fbdd9473303e20fb9"},"schema_version":"1.0"},"canonical_sha256":"d914771a41c3dd2ac3bd3638890fa1e723ef2cd8aae7cca916dd929b8f438f7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:17:33.219351Z","signature_b64":"zanRQjvI+WYsZiU8+QH8dysCob9nYwHIVXywljfww2BTd1uEjovXuXfB+wqlZsss3v3Lsi7S0zhTRXxRgebQAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d914771a41c3dd2ac3bd3638890fa1e723ef2cd8aae7cca916dd929b8f438f7e","last_reissued_at":"2026-07-05T03:17:33.218900Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:17:33.218900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2108.01733","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:17:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/AN6UmDGjN/nTCcnutKaASSgMVDUH+1njrvpnAYW2bNTSvBiq50r0HE3DBTkZ8WmJpuAlw/vjkrKGypXISP3Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T09:05:37.319995Z"},"content_sha256":"d5e0a0ccd8b9b94d522ae23510960ac53e6fcbca6e955357baeb5424aec3d735","schema_version":"1.0","event_id":"sha256:d5e0a0ccd8b9b94d522ae23510960ac53e6fcbca6e955357baeb5424aec3d735"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:3EKHOGSBYPOSVQ55GY4ISD5B44","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Weak-strong uniqueness for the mean curvature flow of double bubbles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Sebastian Hensel, Tim Laux","submitted_at":"2021-08-03T20:15:20Z","abstract_excerpt":"We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478v2] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.01733","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.01733/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:17:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lAH13CaWB7DzjVZqE/57EkjmuWFCa9kHGD61qJQ94y7R5Y1J2HMLYWN6vamipz3+H8iAzxhh452t7DLLs7uRCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T09:05:37.320499Z"},"content_sha256":"016708907a889d6e17d2f7fbdac1049327aa965cf9133c8557c469f595a78c68","schema_version":"1.0","event_id":"sha256:016708907a889d6e17d2f7fbdac1049327aa965cf9133c8557c469f595a78c68"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3EKHOGSBYPOSVQ55GY4ISD5B44/bundle.json","state_url":"https://pith.science/pith/3EKHOGSBYPOSVQ55GY4ISD5B44/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3EKHOGSBYPOSVQ55GY4ISD5B44/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-06T09:05:37Z","links":{"resolver":"https://pith.science/pith/3EKHOGSBYPOSVQ55GY4ISD5B44","bundle":"https://pith.science/pith/3EKHOGSBYPOSVQ55GY4ISD5B44/bundle.json","state":"https://pith.science/pith/3EKHOGSBYPOSVQ55GY4ISD5B44/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3EKHOGSBYPOSVQ55GY4ISD5B44/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:3EKHOGSBYPOSVQ55GY4ISD5B44","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":"d530a6b0baebcb47944bfca5ebf265e49c57d4c6ca30fb1fbdd9473303e20fb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-08-03T20:15:20Z","title_canon_sha256":"6d561b8b702f0f768aeea620ffec4d86bb7334d8f596ad32f6dc6ca9ea50f38b"},"schema_version":"1.0","source":{"id":"2108.01733","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.01733","created_at":"2026-07-05T03:17:33Z"},{"alias_kind":"arxiv_version","alias_value":"2108.01733v2","created_at":"2026-07-05T03:17:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.01733","created_at":"2026-07-05T03:17:33Z"},{"alias_kind":"pith_short_12","alias_value":"3EKHOGSBYPOS","created_at":"2026-07-05T03:17:33Z"},{"alias_kind":"pith_short_16","alias_value":"3EKHOGSBYPOSVQ55","created_at":"2026-07-05T03:17:33Z"},{"alias_kind":"pith_short_8","alias_value":"3EKHOGSB","created_at":"2026-07-05T03:17:33Z"}],"graph_snapshots":[{"event_id":"sha256:016708907a889d6e17d2f7fbdac1049327aa965cf9133c8557c469f595a78c68","target":"graph","created_at":"2026-07-05T03:17:33Z","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/2108.01733/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We derive a weak-strong uniqueness principle for BV solutions to multiphase mean curvature flow of triple line clusters in three dimensions. Our proof is based on the explicit construction of a gradient-flow calibration in the sense of the recent work of Fischer et al. [arXiv:2003.05478v2] for any such cluster. This extends the two-dimensional construction to the three-dimensional case of surfaces meeting along triple junctions.","authors_text":"Sebastian Hensel, Tim Laux","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-08-03T20:15:20Z","title":"Weak-strong uniqueness for the mean curvature flow of double bubbles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.01733","kind":"arxiv","version":2},"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:d5e0a0ccd8b9b94d522ae23510960ac53e6fcbca6e955357baeb5424aec3d735","target":"record","created_at":"2026-07-05T03:17:33Z","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":"d530a6b0baebcb47944bfca5ebf265e49c57d4c6ca30fb1fbdd9473303e20fb9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-08-03T20:15:20Z","title_canon_sha256":"6d561b8b702f0f768aeea620ffec4d86bb7334d8f596ad32f6dc6ca9ea50f38b"},"schema_version":"1.0","source":{"id":"2108.01733","kind":"arxiv","version":2}},"canonical_sha256":"d914771a41c3dd2ac3bd3638890fa1e723ef2cd8aae7cca916dd929b8f438f7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d914771a41c3dd2ac3bd3638890fa1e723ef2cd8aae7cca916dd929b8f438f7e","first_computed_at":"2026-07-05T03:17:33.218900Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:17:33.218900Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zanRQjvI+WYsZiU8+QH8dysCob9nYwHIVXywljfww2BTd1uEjovXuXfB+wqlZsss3v3Lsi7S0zhTRXxRgebQAg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:17:33.219351Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.01733","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5e0a0ccd8b9b94d522ae23510960ac53e6fcbca6e955357baeb5424aec3d735","sha256:016708907a889d6e17d2f7fbdac1049327aa965cf9133c8557c469f595a78c68"],"state_sha256":"97cf6e38e855de4ebc726da2cddc18f61c929a53722c835e2fe0cee9fc48887e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k8GhlQgjkxdz/isNCvlORuUjfx12hPuOuVbYEYfQ6bfbWhg6KpnQ8EkipVtMxPCC9wqYOiyS5StsI/RSgdjRDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T09:05:37.325070Z","bundle_sha256":"c41a95fea73b6ee59489eb9ae2de2e4143520ab8ccdbd3a4485a504b3fe75388"}}