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Writingσ V = √m2 and ","work_id":"547427e2-6f40-4345-9de4-df2711f15933","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Coexistence reference state and local notation Throughout this Appendix, temperatureTis fixed and the reference state is the planar liquid–vapor coexistence point (T,P0), where P0 =P sat(T),µ l(T,P0) ","work_id":"28d56ede-0ef2-4202-baa6-d74dfff4740f","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"These pressure derivatives provide the local expansion co- efficients used later when the chemical-potential equality is expanded directly in excess-pressure variables","work_id":"c874b85e-992d-48f6-b4e7-b85b47fad9db","year":null}],"snapshot_sha256":"56dd1131c9344f371935da69f7c293651aa6e1c2044898a29140b72fa6547f84"},"source":{"id":"2605.13244","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-14T18:35:35.223208Z","id":"39b0e43b-16da-4131-8867-c94cf02cfbc4","model_set":{"reader":"grok-4.3"},"one_line_summary":"The planar-limit Tolman length is derived as a bulk fluctuation observable from second and third moments of the volume distribution in the NPT ensemble, giving -0.7 Å for water at coexistence from SPC/E, TIP4P/2005 simulations and IAPWS-IF97 data.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The planar-limit Tolman length at liquid-vapor coexistence is a bulk fluctuation-response observable expressible through the liquid's isothermal compressibility and its pressure derivative.","strongest_claim":"At coexistence, the planar-limit value of the same Tolman length reduces to a combination of the liquid isothermal compressibility and its pressure derivative and can be recast as a bulk fluctuation-response observable of the homogeneous liquid in the isothermal-isobaric ensemble.","weakest_assumption":"For weakly compressible liquids the adopted asymmetric density-based formulation is the practically relevant one, with finite-curvature effects entering through vapor supersaturation under capillary equilibrium."}},"verdict_id":"39b0e43b-16da-4131-8867-c94cf02cfbc4"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:59e8e2a1cdae6b1751c764a9a564d2a476d3dfbea57ac5557fd7ae64cb098a00","target":"record","created_at":"2026-05-18T02:44:49Z","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":"c3145fa76da9bc48b33f34d59dcdc0e96647a4b835f59a3d7007d829a4e6191b","cross_cats_sorted":["cond-mat.stat-mech","physics.chem-ph"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cond-mat.soft","submitted_at":"2026-05-13T09:30:06Z","title_canon_sha256":"734e467b32a488d05d9e3325201f06f6b34e4d246a3558762c557001ee7c7db8"},"schema_version":"1.0","source":{"id":"2605.13244","kind":"arxiv","version":1}},"canonical_sha256":"ad0fb659b4799fa9b42535b0372c77f670f954e58d40ac3e986e1a8a2f015eb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad0fb659b4799fa9b42535b0372c77f670f954e58d40ac3e986e1a8a2f015eb4","first_computed_at":"2026-05-18T02:44:49.480019Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:49.480019Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MKmw5KLflSvQCG1mxuDtFXYIktVpgdR7PHn2WidX++Um556s9Bxr86o9RhilA94TFUeyOBZdaxrWzsQN83juBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:49.480505Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59e8e2a1cdae6b1751c764a9a564d2a476d3dfbea57ac5557fd7ae64cb098a00","sha256:a12b66e43374988b9f4ca24edf26fb5a29dd03f927f67de4581b47bbe09768ec","sha256:e9bc140ab1460ee31f43b3ed34d3deed7e28f62879dc3838bf9f3dee1030b32c"],"state_sha256":"8e93dd8f50793eb7a90a908932e91b9b3de9a9dfae7f38463b1eda89c45fef65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CJOlYd167z7vr6DRv+vuVlW9CBNTdsO0PLV1xkM2/M8rahPJrlna/XIHr6uYmgjdG7Y88KlssB/2x4yVXJPVCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T04:34:50.871806Z","bundle_sha256":"c64126efd9b5c26a1212328455fcca59dedf6a7bc7c061388c065a32b0d4f89c"}}