{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:5BLAXEHWZ37CQB5KMMDPOUINBR","short_pith_number":"pith:5BLAXEHW","canonical_record":{"source":{"id":"2412.19063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-26T05:18:05Z","cross_cats_sorted":[],"title_canon_sha256":"fc5acdac7f1788cc3adfcc7d06cc485a58fbe2800f1086f7ba548c010bef9728","abstract_canon_sha256":"84962f3aaed3176de56f49aa5b6bdbfb3ac4ff88437a12704ac0f6f437668247"},"schema_version":"1.0"},"canonical_sha256":"e8560b90f6cefe2807aa6306f7510d0c7d0f0e679f15f63fd19fad9bfe99c0e1","source":{"kind":"arxiv","id":"2412.19063","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.19063","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"2412.19063v1","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19063","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"5BLAXEHWZ37C","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"pith_short_16","alias_value":"5BLAXEHWZ37CQB5K","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"pith_short_8","alias_value":"5BLAXEHW","created_at":"2026-07-05T09:54:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:5BLAXEHWZ37CQB5KMMDPOUINBR","target":"record","payload":{"canonical_record":{"source":{"id":"2412.19063","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-26T05:18:05Z","cross_cats_sorted":[],"title_canon_sha256":"fc5acdac7f1788cc3adfcc7d06cc485a58fbe2800f1086f7ba548c010bef9728","abstract_canon_sha256":"84962f3aaed3176de56f49aa5b6bdbfb3ac4ff88437a12704ac0f6f437668247"},"schema_version":"1.0"},"canonical_sha256":"e8560b90f6cefe2807aa6306f7510d0c7d0f0e679f15f63fd19fad9bfe99c0e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:54:15.547207Z","signature_b64":"YQGlb+fKFx6XEjAzAunv+yp0t7cAkuTZnD2OK/Bs3t+tG50NypAwgXJhoi5u+CgLjN6voGDqIPOp66vkESYmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8560b90f6cefe2807aa6306f7510d0c7d0f0e679f15f63fd19fad9bfe99c0e1","last_reissued_at":"2026-07-05T09:54:15.546821Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:54:15.546821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.19063","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SYfPRbdRxQkphADpjqQ8iDIKFiOtJeyFDdH9i1wDGY/GT/jE7ngDacJ1pzAWvk3JhKRosFV427cnAqJ7rXnYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:18:40.107995Z"},"content_sha256":"13ad09e194675521cb8e71f5c48feabb980f91a4f401a9a5cd3b6d33f4d6618d","schema_version":"1.0","event_id":"sha256:13ad09e194675521cb8e71f5c48feabb980f91a4f401a9a5cd3b6d33f4d6618d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:5BLAXEHWZ37CQB5KMMDPOUINBR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Wulff inequality for minimal submanifolds in Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Wenkui Du, Yuchao Yi, Ziyi Zhao","submitted_at":"2024-12-26T05:18:05Z","abstract_excerpt":"In this paper, we prove a Wulff inequality for $n$-dimensional minimal submanifolds with boundary in $\\mathbb{R}^{n+m}$, where we associate a nonnegative anisotropic weight $\\Phi: S^{n+m-1}\\to \\mathbb{R}^{+}$ to the boundary of minimal submanifolds. The Wulff inequality constant depends only on $m$ and $n$, and is independent of the weights. The inequality is sharp if $m=1, 2$ and $\\Phi$ is the support function of ellipsoids or certain type of centrally symmetric long convex bodies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19063","kind":"arxiv","version":1},"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/2412.19063/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":"2026-07-05T09:54:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/+SpA6IIQHUtUkbC3zSXX3k0t18zEvCtX4rkI/PAaEbXn9aTlyjv9aTTdTo+UGRw5Uu5UUiSpkXtaHJoyW3rCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:18:40.108382Z"},"content_sha256":"ffac784bec5dd370176371cc2c8efe72edc53fc13da564a68d7de5eb9b5325f7","schema_version":"1.0","event_id":"sha256:ffac784bec5dd370176371cc2c8efe72edc53fc13da564a68d7de5eb9b5325f7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5BLAXEHWZ37CQB5KMMDPOUINBR/bundle.json","state_url":"https://pith.science/pith/5BLAXEHWZ37CQB5KMMDPOUINBR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5BLAXEHWZ37CQB5KMMDPOUINBR/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":"2026-07-06T20:18:40Z","links":{"resolver":"https://pith.science/pith/5BLAXEHWZ37CQB5KMMDPOUINBR","bundle":"https://pith.science/pith/5BLAXEHWZ37CQB5KMMDPOUINBR/bundle.json","state":"https://pith.science/pith/5BLAXEHWZ37CQB5KMMDPOUINBR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5BLAXEHWZ37CQB5KMMDPOUINBR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:5BLAXEHWZ37CQB5KMMDPOUINBR","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":"84962f3aaed3176de56f49aa5b6bdbfb3ac4ff88437a12704ac0f6f437668247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-26T05:18:05Z","title_canon_sha256":"fc5acdac7f1788cc3adfcc7d06cc485a58fbe2800f1086f7ba548c010bef9728"},"schema_version":"1.0","source":{"id":"2412.19063","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.19063","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"arxiv_version","alias_value":"2412.19063v1","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.19063","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"pith_short_12","alias_value":"5BLAXEHWZ37C","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"pith_short_16","alias_value":"5BLAXEHWZ37CQB5K","created_at":"2026-07-05T09:54:15Z"},{"alias_kind":"pith_short_8","alias_value":"5BLAXEHW","created_at":"2026-07-05T09:54:15Z"}],"graph_snapshots":[{"event_id":"sha256:ffac784bec5dd370176371cc2c8efe72edc53fc13da564a68d7de5eb9b5325f7","target":"graph","created_at":"2026-07-05T09:54:15Z","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/2412.19063/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove a Wulff inequality for $n$-dimensional minimal submanifolds with boundary in $\\mathbb{R}^{n+m}$, where we associate a nonnegative anisotropic weight $\\Phi: S^{n+m-1}\\to \\mathbb{R}^{+}$ to the boundary of minimal submanifolds. The Wulff inequality constant depends only on $m$ and $n$, and is independent of the weights. The inequality is sharp if $m=1, 2$ and $\\Phi$ is the support function of ellipsoids or certain type of centrally symmetric long convex bodies.","authors_text":"Wenkui Du, Yuchao Yi, Ziyi Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-26T05:18:05Z","title":"Wulff inequality for minimal submanifolds in Euclidean space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19063","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":"sha256:13ad09e194675521cb8e71f5c48feabb980f91a4f401a9a5cd3b6d33f4d6618d","target":"record","created_at":"2026-07-05T09:54:15Z","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":"84962f3aaed3176de56f49aa5b6bdbfb3ac4ff88437a12704ac0f6f437668247","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-12-26T05:18:05Z","title_canon_sha256":"fc5acdac7f1788cc3adfcc7d06cc485a58fbe2800f1086f7ba548c010bef9728"},"schema_version":"1.0","source":{"id":"2412.19063","kind":"arxiv","version":1}},"canonical_sha256":"e8560b90f6cefe2807aa6306f7510d0c7d0f0e679f15f63fd19fad9bfe99c0e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8560b90f6cefe2807aa6306f7510d0c7d0f0e679f15f63fd19fad9bfe99c0e1","first_computed_at":"2026-07-05T09:54:15.546821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:54:15.546821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YQGlb+fKFx6XEjAzAunv+yp0t7cAkuTZnD2OK/Bs3t+tG50NypAwgXJhoi5u+CgLjN6voGDqIPOp66vkESYmCw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:54:15.547207Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.19063","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13ad09e194675521cb8e71f5c48feabb980f91a4f401a9a5cd3b6d33f4d6618d","sha256:ffac784bec5dd370176371cc2c8efe72edc53fc13da564a68d7de5eb9b5325f7"],"state_sha256":"0521d71e63de97659a0fe94db51541173bc883b06c1c69fc461d39af69f220e4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OycDGnYm4HsigxTegs/FTHiH6YVadTB0X1Xug05xaqzT1zov473ADclR4y0yK0ZdZVTnWGofvuM3o7ulGEf5AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T20:18:40.110363Z","bundle_sha256":"16ab65c1f2100148c15b97a735e4e4c5a9ff897ee5921a940ece77a2959cb78c"}}