{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:7LI6UMUXF3WFYMIG2H4YV46P7U","short_pith_number":"pith:7LI6UMUX","canonical_record":{"source":{"id":"1010.4680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-10-22T11:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"b452700570eeae830acb1c585dbbf1894941c442a01fd6aa11efbb1830f60140","abstract_canon_sha256":"db3aa97a98e4d15655bd310dc195c86e5bfce6c8032555a06fe6fa70d0f51841"},"schema_version":"1.0"},"canonical_sha256":"fad1ea32972eec5c3106d1f98af3cffd2208553f03ae4d8529310c09c5756b59","source":{"kind":"arxiv","id":"1010.4680","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4680","created_at":"2026-05-18T02:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4680v1","created_at":"2026-05-18T02:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4680","created_at":"2026-05-18T02:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"7LI6UMUXF3WF","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7LI6UMUXF3WFYMIG","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7LI6UMUX","created_at":"2026-05-18T12:26:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:7LI6UMUXF3WFYMIG2H4YV46P7U","target":"record","payload":{"canonical_record":{"source":{"id":"1010.4680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-10-22T11:39:08Z","cross_cats_sorted":[],"title_canon_sha256":"b452700570eeae830acb1c585dbbf1894941c442a01fd6aa11efbb1830f60140","abstract_canon_sha256":"db3aa97a98e4d15655bd310dc195c86e5bfce6c8032555a06fe6fa70d0f51841"},"schema_version":"1.0"},"canonical_sha256":"fad1ea32972eec5c3106d1f98af3cffd2208553f03ae4d8529310c09c5756b59","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:59.618937Z","signature_b64":"w5v+bPF/nSAIFIwcMPtruTk+qkxji8fg2Qlk+Fd8aUtjNlNk59k1Vpg5YQt7X8FLByD34NvcEh6MGz+lDgEPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fad1ea32972eec5c3106d1f98af3cffd2208553f03ae4d8529310c09c5756b59","last_reissued_at":"2026-05-18T02:04:59.618249Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:59.618249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.4680","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":"2026-05-18T02:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hREiS4QRPb62qTs3FCz2rS03av5/59EPtadh9POf8A+CwdWFbEg8mjDt12cNWhZDSJUpfokdcwQCpoJ7njBVBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:55:01.356745Z"},"content_sha256":"7606991f41596771f5b1655b06d2167c37db0041964d4b7dcb71a3f73109bd45","schema_version":"1.0","event_id":"sha256:7606991f41596771f5b1655b06d2167c37db0041964d4b7dcb71a3f73109bd45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:7LI6UMUXF3WFYMIG2H4YV46P7U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mesoscopic theory for inhomogeneous mixtures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.soft","authors_text":"A. Ciach","submitted_at":"2010-10-22T11:39:08Z","abstract_excerpt":"Mesoscopic density functional theory for inhomogeneous mixtures of sperical particles is developed in terms of mesoscopic volume fractions by a systematic coarse-graining procedure starting form microscopic theory. Approximate expressions for the correlation functions and for the grand potential are obtained for weak ordering on mesoscopic length scales. Stability analysis of the disordered phase is performed in mean-field approximation (MF) and beyond. MF shows existence of either a spinodal or a $\\lambda$-surface on the volume-fractions - temperature phase diagram. Separation into homogeneou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4680","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":""},"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":"2026-05-18T02:04:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mVK9ifTjqi5CDnSKnwkNoQ2XpWxPGsux/VBAzDGWC7310opx3Ht5IuIB4x8zMGnbloC/344hBfnKlf2JEYfUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T08:55:01.357553Z"},"content_sha256":"ad01dfb1408f0012be457f14a13a0752b3cabb58805d3fdee8ed722d167d3109","schema_version":"1.0","event_id":"sha256:ad01dfb1408f0012be457f14a13a0752b3cabb58805d3fdee8ed722d167d3109"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7LI6UMUXF3WFYMIG2H4YV46P7U/bundle.json","state_url":"https://pith.science/pith/7LI6UMUXF3WFYMIG2H4YV46P7U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7LI6UMUXF3WFYMIG2H4YV46P7U/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":"2026-05-31T08:55:01Z","links":{"resolver":"https://pith.science/pith/7LI6UMUXF3WFYMIG2H4YV46P7U","bundle":"https://pith.science/pith/7LI6UMUXF3WFYMIG2H4YV46P7U/bundle.json","state":"https://pith.science/pith/7LI6UMUXF3WFYMIG2H4YV46P7U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7LI6UMUXF3WFYMIG2H4YV46P7U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:7LI6UMUXF3WFYMIG2H4YV46P7U","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":"db3aa97a98e4d15655bd310dc195c86e5bfce6c8032555a06fe6fa70d0f51841","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-10-22T11:39:08Z","title_canon_sha256":"b452700570eeae830acb1c585dbbf1894941c442a01fd6aa11efbb1830f60140"},"schema_version":"1.0","source":{"id":"1010.4680","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4680","created_at":"2026-05-18T02:04:59Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4680v1","created_at":"2026-05-18T02:04:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4680","created_at":"2026-05-18T02:04:59Z"},{"alias_kind":"pith_short_12","alias_value":"7LI6UMUXF3WF","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"7LI6UMUXF3WFYMIG","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"7LI6UMUX","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:ad01dfb1408f0012be457f14a13a0752b3cabb58805d3fdee8ed722d167d3109","target":"graph","created_at":"2026-05-18T02:04:59Z","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":"Mesoscopic density functional theory for inhomogeneous mixtures of sperical particles is developed in terms of mesoscopic volume fractions by a systematic coarse-graining procedure starting form microscopic theory. Approximate expressions for the correlation functions and for the grand potential are obtained for weak ordering on mesoscopic length scales. Stability analysis of the disordered phase is performed in mean-field approximation (MF) and beyond. MF shows existence of either a spinodal or a $\\lambda$-surface on the volume-fractions - temperature phase diagram. Separation into homogeneou","authors_text":"A. Ciach","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-10-22T11:39:08Z","title":"Mesoscopic theory for inhomogeneous mixtures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4680","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":"sha256:7606991f41596771f5b1655b06d2167c37db0041964d4b7dcb71a3f73109bd45","target":"record","created_at":"2026-05-18T02:04:59Z","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":"db3aa97a98e4d15655bd310dc195c86e5bfce6c8032555a06fe6fa70d0f51841","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-10-22T11:39:08Z","title_canon_sha256":"b452700570eeae830acb1c585dbbf1894941c442a01fd6aa11efbb1830f60140"},"schema_version":"1.0","source":{"id":"1010.4680","kind":"arxiv","version":1}},"canonical_sha256":"fad1ea32972eec5c3106d1f98af3cffd2208553f03ae4d8529310c09c5756b59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fad1ea32972eec5c3106d1f98af3cffd2208553f03ae4d8529310c09c5756b59","first_computed_at":"2026-05-18T02:04:59.618249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:59.618249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w5v+bPF/nSAIFIwcMPtruTk+qkxji8fg2Qlk+Fd8aUtjNlNk59k1Vpg5YQt7X8FLByD34NvcEh6MGz+lDgEPDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:59.618937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4680","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7606991f41596771f5b1655b06d2167c37db0041964d4b7dcb71a3f73109bd45","sha256:ad01dfb1408f0012be457f14a13a0752b3cabb58805d3fdee8ed722d167d3109"],"state_sha256":"98677e8a522f81a33faf2a949aebd39ff94b8673261f2337b3908286e325d36d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fK7+9sR7VXGDJTVH+ZGZ5e0hPWh7pr6YZxqqdg67cn+iHOHnlBPxwOWpEVdFxC/HQhA2H9EgOfO21m/9zrg3Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T08:55:01.362576Z","bundle_sha256":"98af867b67567b54858432e9a2098ff3e8f43e60c2df75569f6ff8e81b77822d"}}