{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WO6AQVVZ4MJ6CFRXCVLFHRWAV2","short_pith_number":"pith:WO6AQVVZ","canonical_record":{"source":{"id":"1502.07232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-25T16:29:24Z","cross_cats_sorted":[],"title_canon_sha256":"d24983f16594795db631d51fba3ebc3b33e1857e2f7578a9070e1703bdc1faaa","abstract_canon_sha256":"daa0778b76dc2403d7e16ca7badab66d6ad69c56cebd723a30bf5b16473e2e04"},"schema_version":"1.0"},"canonical_sha256":"b3bc0856b9e313e11637155653c6c0ae8187b88a11a212a7d099251a5a18e59a","source":{"kind":"arxiv","id":"1502.07232","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07232","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07232v2","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07232","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"pith_short_12","alias_value":"WO6AQVVZ4MJ6","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WO6AQVVZ4MJ6CFRX","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WO6AQVVZ","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WO6AQVVZ4MJ6CFRXCVLFHRWAV2","target":"record","payload":{"canonical_record":{"source":{"id":"1502.07232","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-25T16:29:24Z","cross_cats_sorted":[],"title_canon_sha256":"d24983f16594795db631d51fba3ebc3b33e1857e2f7578a9070e1703bdc1faaa","abstract_canon_sha256":"daa0778b76dc2403d7e16ca7badab66d6ad69c56cebd723a30bf5b16473e2e04"},"schema_version":"1.0"},"canonical_sha256":"b3bc0856b9e313e11637155653c6c0ae8187b88a11a212a7d099251a5a18e59a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:51.892790Z","signature_b64":"BMTeN73X1x4Jve6wchYkguE6P6R6ZV2K8S5lf+WIiRK87tNOVMaffo0ZQeo0LlCTLJ33jNJGI7G84Jd51z/mDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3bc0856b9e313e11637155653c6c0ae8187b88a11a212a7d099251a5a18e59a","last_reissued_at":"2026-05-18T01:33:51.892114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:51.892114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.07232","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":"2026-05-18T01:33:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uN5ffy+Garv1HZI7G8UvIaK/7JHvtYaQaLmU1Xx4Bv4GY+1/64QNVqA8JktZN7UfqRI8XAvlysuvEkzbXzZEAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:07:24.239882Z"},"content_sha256":"9ab5eb623499d5c2725695fbf12f1d4e21caa3516c47a2e0e542a848cfdc20a4","schema_version":"1.0","event_id":"sha256:9ab5eb623499d5c2725695fbf12f1d4e21caa3516c47a2e0e542a848cfdc20a4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WO6AQVVZ4MJ6CFRXCVLFHRWAV2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global solutions to the volume-preserving mean-curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christian Seis, Emanuele Spadaro, Luca Mugnai","submitted_at":"2015-02-25T16:29:24Z","abstract_excerpt":"In this paper, we construct global distributional solutions to the volume-preserving mean-curvature flow using a variant of the time-discrete gradient flow approach proposed independently by Almgren, Taylor and Wang (SIAM J. Control Optim. 31(2): 387- 438, 1993) and Luckhaus and Sturzenhecker (Calc. Var. Partial Differential Equations 3(2): 253-271, 1995)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07232","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":""},"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":"2026-05-18T01:33:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HYPCTJVegg2wUaCuGWku0413a84tLs0ftgqw8sYi51OvB7kHJtUXYiexWy7KAMQtIT5WYLXO5wLAe0LIjAZHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:07:24.240222Z"},"content_sha256":"32d93a65ab9fd67accbfff0dec14052a2e4989fe6302134ad0ea78034919aa6c","schema_version":"1.0","event_id":"sha256:32d93a65ab9fd67accbfff0dec14052a2e4989fe6302134ad0ea78034919aa6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WO6AQVVZ4MJ6CFRXCVLFHRWAV2/bundle.json","state_url":"https://pith.science/pith/WO6AQVVZ4MJ6CFRXCVLFHRWAV2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WO6AQVVZ4MJ6CFRXCVLFHRWAV2/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":"2026-06-24T18:07:24Z","links":{"resolver":"https://pith.science/pith/WO6AQVVZ4MJ6CFRXCVLFHRWAV2","bundle":"https://pith.science/pith/WO6AQVVZ4MJ6CFRXCVLFHRWAV2/bundle.json","state":"https://pith.science/pith/WO6AQVVZ4MJ6CFRXCVLFHRWAV2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WO6AQVVZ4MJ6CFRXCVLFHRWAV2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WO6AQVVZ4MJ6CFRXCVLFHRWAV2","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":"daa0778b76dc2403d7e16ca7badab66d6ad69c56cebd723a30bf5b16473e2e04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-25T16:29:24Z","title_canon_sha256":"d24983f16594795db631d51fba3ebc3b33e1857e2f7578a9070e1703bdc1faaa"},"schema_version":"1.0","source":{"id":"1502.07232","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.07232","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"arxiv_version","alias_value":"1502.07232v2","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.07232","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"pith_short_12","alias_value":"WO6AQVVZ4MJ6","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WO6AQVVZ4MJ6CFRX","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WO6AQVVZ","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:32d93a65ab9fd67accbfff0dec14052a2e4989fe6302134ad0ea78034919aa6c","target":"graph","created_at":"2026-05-18T01:33:51Z","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 construct global distributional solutions to the volume-preserving mean-curvature flow using a variant of the time-discrete gradient flow approach proposed independently by Almgren, Taylor and Wang (SIAM J. Control Optim. 31(2): 387- 438, 1993) and Luckhaus and Sturzenhecker (Calc. Var. Partial Differential Equations 3(2): 253-271, 1995).","authors_text":"Christian Seis, Emanuele Spadaro, Luca Mugnai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-25T16:29:24Z","title":"Global solutions to the volume-preserving mean-curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07232","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":"sha256:9ab5eb623499d5c2725695fbf12f1d4e21caa3516c47a2e0e542a848cfdc20a4","target":"record","created_at":"2026-05-18T01:33:51Z","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":"daa0778b76dc2403d7e16ca7badab66d6ad69c56cebd723a30bf5b16473e2e04","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-02-25T16:29:24Z","title_canon_sha256":"d24983f16594795db631d51fba3ebc3b33e1857e2f7578a9070e1703bdc1faaa"},"schema_version":"1.0","source":{"id":"1502.07232","kind":"arxiv","version":2}},"canonical_sha256":"b3bc0856b9e313e11637155653c6c0ae8187b88a11a212a7d099251a5a18e59a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3bc0856b9e313e11637155653c6c0ae8187b88a11a212a7d099251a5a18e59a","first_computed_at":"2026-05-18T01:33:51.892114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:51.892114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BMTeN73X1x4Jve6wchYkguE6P6R6ZV2K8S5lf+WIiRK87tNOVMaffo0ZQeo0LlCTLJ33jNJGI7G84Jd51z/mDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:51.892790Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.07232","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9ab5eb623499d5c2725695fbf12f1d4e21caa3516c47a2e0e542a848cfdc20a4","sha256:32d93a65ab9fd67accbfff0dec14052a2e4989fe6302134ad0ea78034919aa6c"],"state_sha256":"21780001c9206c2b39118add7ed5a4d987b404ad9b0a444cc61ac7c88edeaa36"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"61Y06YRj5QIJ1y4W4V/c58+XmPDDbt3eSAIXosb6BZ2EnHTErU7gUwY20J7MLnWm895aVWbV9M/GBh7uMBZ9BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:07:24.242125Z","bundle_sha256":"7790011bbec522145c7cc9ffeb36821212344accdf0144813c30a96897b7f4d1"}}