{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5EOSKBM2XFSWPHJ5F4NQBP6JHB","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":"78ae8f8bf2cc9dc8dbea99cc9044258a4659608d4365a2d228961f87547b55d1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-06T16:41:52Z","title_canon_sha256":"347cdea904c613cabbe42c9e9eeb6524570993d11e5ff2df5d46f15a4d936c2e"},"schema_version":"1.0","source":{"id":"1110.1315","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.1315","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"1110.1315v2","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1315","created_at":"2026-05-18T04:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"5EOSKBM2XFSW","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5EOSKBM2XFSWPHJ5","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5EOSKBM2","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:f76958ff45f3f50c0a6102eb2520f86cd5ce666c1ce590aff39697a0d7ae004a","target":"graph","created_at":"2026-05-18T04:02:01Z","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":"In this paper we consider a two-dimensional copolymer consisting of a random concatenation of hydrophobic and hydrophilic monomers near a linear interface separating oil and water acting as solvents. The configurations of the copolymer are directed paths that can move above and below the interface. The interaction\n  Hamiltonian, which rewards matches and penalizes mismatches of the monomers and the solvents, depends on two parameters: the interaction strength $\\beta\\geq 0$ and the interaction bias $h \\geq 0$. The quenched excess free energy per monomer $(\\beta,h) \\mapsto g^\\mathrm{que} (\\beta,","authors_text":"A.A. Opoku, E. Bolthausen, F. den Hollander","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-06T16:41:52Z","title":"A copolymer near a selective interface: variational characterization of the free energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1315","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":"sha256:42d4ce3f7b01272555dcfb8a9351415a7d510b2015a75575d7ce7eec47f3c41b","target":"record","created_at":"2026-05-18T04:02:01Z","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":"78ae8f8bf2cc9dc8dbea99cc9044258a4659608d4365a2d228961f87547b55d1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-06T16:41:52Z","title_canon_sha256":"347cdea904c613cabbe42c9e9eeb6524570993d11e5ff2df5d46f15a4d936c2e"},"schema_version":"1.0","source":{"id":"1110.1315","kind":"arxiv","version":2}},"canonical_sha256":"e91d25059ab965679d3d2f1b00bfc93853c1e1e38979689d13c3980daab2a2f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e91d25059ab965679d3d2f1b00bfc93853c1e1e38979689d13c3980daab2a2f3","first_computed_at":"2026-05-18T04:02:01.751695Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:01.751695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zWBEVFztZEZFnjGXYz5wSqA09hZaxrRolZ67sFQlFmwBRElj2nRwIblWsZju4hZxhyvQM5frCDWLkC4mY1taDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:01.752873Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.1315","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:42d4ce3f7b01272555dcfb8a9351415a7d510b2015a75575d7ce7eec47f3c41b","sha256:f76958ff45f3f50c0a6102eb2520f86cd5ce666c1ce590aff39697a0d7ae004a"],"state_sha256":"d39ede4987fa1dcf1ff8b91c408fef55ffc0e8c37b00ac82cf2b911f39bbc9d8"}