{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OLYLVLQBYGAKRRAYJ3B2SGVXFB","short_pith_number":"pith:OLYLVLQB","schema_version":"1.0","canonical_sha256":"72f0baae01c180a8c4184ec3a91ab72844cc5e0bd7f2ed6153b998f8d3162a56","source":{"kind":"arxiv","id":"1204.1234","version":1},"attestation_state":"computed","paper":{"title":"Free energy of a copolymer in a micro-emulsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frank den Hollander, Nicolas P\\'etr\\'elis","submitted_at":"2012-04-05T14:12:12Z","abstract_excerpt":"In this paper we consider a two-dimensional model of a copolymer consisting of a random concatenation of hydrophilic and hydrophobic monomers, immersed in a micro-emulsion of random droplets of oil and water. The copolymer interacts with the micro-emulsion through an interaction Hamiltonian that favors matches and disfavors mismatches between the monomers and the solvents, in such a way that the interaction with the oil is stronger than with the water.\n  The configurations of the copolymers are directed self-avoiding paths in which only steps up, down and right are allowed. The configurations "},"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":"1204.1234","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-04-05T14:12:12Z","cross_cats_sorted":[],"title_canon_sha256":"41615c0ee141a81eebd12d4fe3eb66953c0186ee7938adcbc49fc3f89c481aec","abstract_canon_sha256":"a6c1956a6e7e86c776fee0fa6524e0745b5803c4b59ac9d73f7b364bf3bcf464"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:27.152891Z","signature_b64":"Ue47FbohTllty+hIJXURBGem/KtGOo8WSlYMEHXAN0W1dF4hgXPbVV551W9Gsjdk5Vr5tbDA52Z2qTKqQnTaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72f0baae01c180a8c4184ec3a91ab72844cc5e0bd7f2ed6153b998f8d3162a56","last_reissued_at":"2026-05-18T03:58:27.151945Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:27.151945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Free energy of a copolymer in a micro-emulsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Frank den Hollander, Nicolas P\\'etr\\'elis","submitted_at":"2012-04-05T14:12:12Z","abstract_excerpt":"In this paper we consider a two-dimensional model of a copolymer consisting of a random concatenation of hydrophilic and hydrophobic monomers, immersed in a micro-emulsion of random droplets of oil and water. The copolymer interacts with the micro-emulsion through an interaction Hamiltonian that favors matches and disfavors mismatches between the monomers and the solvents, in such a way that the interaction with the oil is stronger than with the water.\n  The configurations of the copolymers are directed self-avoiding paths in which only steps up, down and right are allowed. The configurations "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1234","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":"1204.1234","created_at":"2026-05-18T03:58:27.152070+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.1234v1","created_at":"2026-05-18T03:58:27.152070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1234","created_at":"2026-05-18T03:58:27.152070+00:00"},{"alias_kind":"pith_short_12","alias_value":"OLYLVLQBYGAK","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OLYLVLQBYGAKRRAY","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OLYLVLQB","created_at":"2026-05-18T12:27:16.716162+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/OLYLVLQBYGAKRRAYJ3B2SGVXFB","json":"https://pith.science/pith/OLYLVLQBYGAKRRAYJ3B2SGVXFB.json","graph_json":"https://pith.science/api/pith-number/OLYLVLQBYGAKRRAYJ3B2SGVXFB/graph.json","events_json":"https://pith.science/api/pith-number/OLYLVLQBYGAKRRAYJ3B2SGVXFB/events.json","paper":"https://pith.science/paper/OLYLVLQB"},"agent_actions":{"view_html":"https://pith.science/pith/OLYLVLQBYGAKRRAYJ3B2SGVXFB","download_json":"https://pith.science/pith/OLYLVLQBYGAKRRAYJ3B2SGVXFB.json","view_paper":"https://pith.science/paper/OLYLVLQB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.1234&json=true","fetch_graph":"https://pith.science/api/pith-number/OLYLVLQBYGAKRRAYJ3B2SGVXFB/graph.json","fetch_events":"https://pith.science/api/pith-number/OLYLVLQBYGAKRRAYJ3B2SGVXFB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OLYLVLQBYGAKRRAYJ3B2SGVXFB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OLYLVLQBYGAKRRAYJ3B2SGVXFB/action/storage_attestation","attest_author":"https://pith.science/pith/OLYLVLQBYGAKRRAYJ3B2SGVXFB/action/author_attestation","sign_citation":"https://pith.science/pith/OLYLVLQBYGAKRRAYJ3B2SGVXFB/action/citation_signature","submit_replication":"https://pith.science/pith/OLYLVLQBYGAKRRAYJ3B2SGVXFB/action/replication_record"}},"created_at":"2026-05-18T03:58:27.152070+00:00","updated_at":"2026-05-18T03:58:27.152070+00:00"}