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Assuming this holds true for a 1-parameter family of surfaces $\\Sigma_t$ evolving in an initial data set {with the dominant energy condition}, we compute an expression for the derivative of the Bartnik mass along these surfaces. An immediate consequence of this formula is that the Bartnik mass of $\\Sigma_t$ is monotone non-decreasing whenever $\\Sigma_t$ flows outward.\n  It is our pleasure to dedicat"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1902.02284","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2019-02-06T17:19:49Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"a7653c31b565c0fd51eff7f883a12f295fc5a9f34d41328690b16df48b826674","abstract_canon_sha256":"33bac1bb37f0b5c1488086e862ad2015e8d289125034e5b71ab1316d7e880577"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:44:21.687819Z","signature_b64":"pIGP/FzgzDebAgiWuyd6PNmfEV6zItylbgJ2q+7aZdMEBm6kX+Zpc4bXLrW8qb9zg8ScpADWpQxmN1SLpIDMCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e92d406e7e7a05193c9c8d6f97d957fc02cbdb5280e60c261aab708efc38b5b4","last_reissued_at":"2026-05-17T23:44:21.687148Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:44:21.687148Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the evolution of the spacetime Bartnik mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Pengzi Miao, Stephen McCormick","submitted_at":"2019-02-06T17:19:49Z","abstract_excerpt":"It is conjectured that the full (spacetime) Bartnik mass of a surface $\\Sigma$ is realised as the ADM mass of some stationary asymptotically flat manifold with boundary data prescribed by $\\Sigma$. 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