{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:EFWAQZXG3GY7ZS5YDZG7AI74DT","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":"f7ad0681c361f3f2cccae63adbb0fb194a69ea45af625ea284ab6782c7c5f571","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-04-19T00:05:44Z","title_canon_sha256":"5ffceec77b5eea3d0e39ed159b524fa0439c7feaaf99d2348972070c68857433"},"schema_version":"1.0","source":{"id":"2204.08591","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2204.08591","created_at":"2026-07-05T06:19:34Z"},{"alias_kind":"arxiv_version","alias_value":"2204.08591v2","created_at":"2026-07-05T06:19:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2204.08591","created_at":"2026-07-05T06:19:34Z"},{"alias_kind":"pith_short_12","alias_value":"EFWAQZXG3GY7","created_at":"2026-07-05T06:19:34Z"},{"alias_kind":"pith_short_16","alias_value":"EFWAQZXG3GY7ZS5Y","created_at":"2026-07-05T06:19:34Z"},{"alias_kind":"pith_short_8","alias_value":"EFWAQZXG","created_at":"2026-07-05T06:19:34Z"}],"graph_snapshots":[{"event_id":"sha256:6170feb2ac0045ebb801302f465a8dedeff07cf6d150c74fcc23c659a4bcea72","target":"graph","created_at":"2026-07-05T06:19:34Z","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/2204.08591/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $M$ be a fixed compact oriented embedded submanifold of a manifold $\\overline{M}$. Consider the volume $\\mathcal{V} (\\overline{g}) = \\int_M \\mathsf{vol}_{(M, g)}$ as a functional of the ambient metric $\\overline{g}$ on $\\overline{M}$, where $g = \\overline{g}|_M$. We show that $\\overline{g}$ is a critical point of $\\mathcal{V}$ with respect to a special class of variations of $\\overline{g}$, obtained by varying a calibration $\\mu$ on $\\overline{M}$ in a particular way, if and only if $M$ is calibrated by $\\mu$. We do not assume that the calibration is closed. We prove this for almost comple","authors_text":"Da Rong Cheng, Jesse Madnick, Spiro Karigiannis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-04-19T00:05:44Z","title":"A variational characterization of calibrated submanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.08591","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":"sha256:3adf2e37699de12a73d298df144053a04629432903013181459f5b91a6e142b5","target":"record","created_at":"2026-07-05T06:19:34Z","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":"f7ad0681c361f3f2cccae63adbb0fb194a69ea45af625ea284ab6782c7c5f571","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-04-19T00:05:44Z","title_canon_sha256":"5ffceec77b5eea3d0e39ed159b524fa0439c7feaaf99d2348972070c68857433"},"schema_version":"1.0","source":{"id":"2204.08591","kind":"arxiv","version":2}},"canonical_sha256":"216c0866e6d9b1fccbb81e4df023fc1cf7adcab53ed380f8a0f63634aab0f737","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"216c0866e6d9b1fccbb81e4df023fc1cf7adcab53ed380f8a0f63634aab0f737","first_computed_at":"2026-07-05T06:19:34.343485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:19:34.343485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7PW7ENG8z9lIHzVrkdu4yfaDNNrRZ/b0Mv4UBCvPMmMFYjj51Bs/rEizN/U6AMFXnt7lhYrgdKPz/he9cZHuCg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:19:34.343889Z","signed_message":"canonical_sha256_bytes"},"source_id":"2204.08591","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3adf2e37699de12a73d298df144053a04629432903013181459f5b91a6e142b5","sha256:6170feb2ac0045ebb801302f465a8dedeff07cf6d150c74fcc23c659a4bcea72"],"state_sha256":"a4f6c28755f0b5a8ffe86dec9124317b727f49c7a92a827a428afae0815d54ee"}