{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:D6ZEDPMP3MITD5XGFJYNC2YGTF","short_pith_number":"pith:D6ZEDPMP","schema_version":"1.0","canonical_sha256":"1fb241bd8fdb1131f6e62a70d16b0699445677a5bc8bc6b376e3538d423196d2","source":{"kind":"arxiv","id":"1901.10844","version":1},"attestation_state":"computed","paper":{"title":"Self-Consistent Field Theory of Inhomogeneous Polymeric Systems: A Variational Derivation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.soft","authors_text":"An-Chang Shi","submitted_at":"2019-01-30T14:23:47Z","abstract_excerpt":"The self-consistent field theory (SCFT) is a powerful framework for the study of the phase behavior and structural properties of many-body systems. In particular, polymeric SCFT has been successfully applied to inhomogeneous polymeric systems such as polymer blends and block copolymer melts. The polymeric SCFT is commonly derived using field-theoretical techniques. Here we provide an alternative derivation of the SCFT equations and SCFT free energy functional using a variational principle. Numerical methods of solving the SCFT equations and applications of the SCFT are also briefly introduced."},"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":"1901.10844","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2019-01-30T14:23:47Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"b9bd5b29e283463b83b4786edc8f49bb8c4b67c1932841f8396d4b3a4b6d55d4","abstract_canon_sha256":"a1166f73a8798f3a2d391fce93e128110ef619804173c4a93dda46ed2bc1c9be"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:05.889396Z","signature_b64":"gY/O//ADHnBQtDNpVuPVucBbeI5779cRtkwDFerLdXnwCWeOWZbHHRbaYdTqpzh0nwlVxcPTP6QmhWr4Y+w2BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1fb241bd8fdb1131f6e62a70d16b0699445677a5bc8bc6b376e3538d423196d2","last_reissued_at":"2026-05-17T23:55:05.888934Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:05.888934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-Consistent Field Theory of Inhomogeneous Polymeric Systems: A Variational Derivation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.soft","authors_text":"An-Chang Shi","submitted_at":"2019-01-30T14:23:47Z","abstract_excerpt":"The self-consistent field theory (SCFT) is a powerful framework for the study of the phase behavior and structural properties of many-body systems. In particular, polymeric SCFT has been successfully applied to inhomogeneous polymeric systems such as polymer blends and block copolymer melts. The polymeric SCFT is commonly derived using field-theoretical techniques. Here we provide an alternative derivation of the SCFT equations and SCFT free energy functional using a variational principle. Numerical methods of solving the SCFT equations and applications of the SCFT are also briefly introduced."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10844","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1901.10844","created_at":"2026-05-17T23:55:05.888992+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.10844v1","created_at":"2026-05-17T23:55:05.888992+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10844","created_at":"2026-05-17T23:55:05.888992+00:00"},{"alias_kind":"pith_short_12","alias_value":"D6ZEDPMP3MIT","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_16","alias_value":"D6ZEDPMP3MITD5XG","created_at":"2026-05-18T12:33:15.570797+00:00"},{"alias_kind":"pith_short_8","alias_value":"D6ZEDPMP","created_at":"2026-05-18T12:33:15.570797+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/D6ZEDPMP3MITD5XGFJYNC2YGTF","json":"https://pith.science/pith/D6ZEDPMP3MITD5XGFJYNC2YGTF.json","graph_json":"https://pith.science/api/pith-number/D6ZEDPMP3MITD5XGFJYNC2YGTF/graph.json","events_json":"https://pith.science/api/pith-number/D6ZEDPMP3MITD5XGFJYNC2YGTF/events.json","paper":"https://pith.science/paper/D6ZEDPMP"},"agent_actions":{"view_html":"https://pith.science/pith/D6ZEDPMP3MITD5XGFJYNC2YGTF","download_json":"https://pith.science/pith/D6ZEDPMP3MITD5XGFJYNC2YGTF.json","view_paper":"https://pith.science/paper/D6ZEDPMP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.10844&json=true","fetch_graph":"https://pith.science/api/pith-number/D6ZEDPMP3MITD5XGFJYNC2YGTF/graph.json","fetch_events":"https://pith.science/api/pith-number/D6ZEDPMP3MITD5XGFJYNC2YGTF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/D6ZEDPMP3MITD5XGFJYNC2YGTF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/D6ZEDPMP3MITD5XGFJYNC2YGTF/action/storage_attestation","attest_author":"https://pith.science/pith/D6ZEDPMP3MITD5XGFJYNC2YGTF/action/author_attestation","sign_citation":"https://pith.science/pith/D6ZEDPMP3MITD5XGFJYNC2YGTF/action/citation_signature","submit_replication":"https://pith.science/pith/D6ZEDPMP3MITD5XGFJYNC2YGTF/action/replication_record"}},"created_at":"2026-05-17T23:55:05.888992+00:00","updated_at":"2026-05-17T23:55:05.888992+00:00"}