{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VJ4WWCAB7N6QI56F45YYGPF5VC","short_pith_number":"pith:VJ4WWCAB","schema_version":"1.0","canonical_sha256":"aa796b0801fb7d0477c5e771833cbda8a5b19a15539dc18dad29335548858813","source":{"kind":"arxiv","id":"1612.02775","version":1},"attestation_state":"computed","paper":{"title":"Continuum limit and stochastic homogenization of discrete ferromagnetic thin films","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Braides, Marco Cicalese, Matthias Ruf","submitted_at":"2016-12-08T19:10:02Z","abstract_excerpt":"We study the discrete-to-continuum limit of ferromagnetic spin systems when the lattice spacing tends to zero. We assume that the atoms are part of a (maybe) non-periodic lattice close to a flat set in a lower dimensional space, typically a plate in three dimensions. Scaling the particle positions by a small parameter $\\varepsilon>0$ we perform a $\\Gamma$-convergence analysis of properly rescaled interfacial-type energies. We show that, up to subsequences, the energies converge to a surface integral defined on partitions of the flat space. In the second part of the paper we address the issue o"},"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":"1612.02775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-12-08T19:10:02Z","cross_cats_sorted":[],"title_canon_sha256":"5a0c48ce34931cd8a098a6c92ed1f374f391af89c84851a25a8d2a51369e6a6e","abstract_canon_sha256":"c782823ea486988003e175dd2b7dd510dc7dbea2e37c9056e310d9fe9b3589a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:56.899170Z","signature_b64":"HUx3itdZD6G1uQBdgOOYzjSoHnS/Gu1feixZY78L9PQ1rF3VxqHPpecVqr7UGQKc00DtoMje2el0XyPkcYGOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa796b0801fb7d0477c5e771833cbda8a5b19a15539dc18dad29335548858813","last_reissued_at":"2026-05-18T00:20:56.896225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:56.896225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Continuum limit and stochastic homogenization of discrete ferromagnetic thin films","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrea Braides, Marco Cicalese, Matthias Ruf","submitted_at":"2016-12-08T19:10:02Z","abstract_excerpt":"We study the discrete-to-continuum limit of ferromagnetic spin systems when the lattice spacing tends to zero. We assume that the atoms are part of a (maybe) non-periodic lattice close to a flat set in a lower dimensional space, typically a plate in three dimensions. Scaling the particle positions by a small parameter $\\varepsilon>0$ we perform a $\\Gamma$-convergence analysis of properly rescaled interfacial-type energies. We show that, up to subsequences, the energies converge to a surface integral defined on partitions of the flat space. In the second part of the paper we address the issue o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02775","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":"1612.02775","created_at":"2026-05-18T00:20:56.898632+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.02775v1","created_at":"2026-05-18T00:20:56.898632+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02775","created_at":"2026-05-18T00:20:56.898632+00:00"},{"alias_kind":"pith_short_12","alias_value":"VJ4WWCAB7N6Q","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VJ4WWCAB7N6QI56F","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VJ4WWCAB","created_at":"2026-05-18T12:30:48.956258+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/VJ4WWCAB7N6QI56F45YYGPF5VC","json":"https://pith.science/pith/VJ4WWCAB7N6QI56F45YYGPF5VC.json","graph_json":"https://pith.science/api/pith-number/VJ4WWCAB7N6QI56F45YYGPF5VC/graph.json","events_json":"https://pith.science/api/pith-number/VJ4WWCAB7N6QI56F45YYGPF5VC/events.json","paper":"https://pith.science/paper/VJ4WWCAB"},"agent_actions":{"view_html":"https://pith.science/pith/VJ4WWCAB7N6QI56F45YYGPF5VC","download_json":"https://pith.science/pith/VJ4WWCAB7N6QI56F45YYGPF5VC.json","view_paper":"https://pith.science/paper/VJ4WWCAB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.02775&json=true","fetch_graph":"https://pith.science/api/pith-number/VJ4WWCAB7N6QI56F45YYGPF5VC/graph.json","fetch_events":"https://pith.science/api/pith-number/VJ4WWCAB7N6QI56F45YYGPF5VC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VJ4WWCAB7N6QI56F45YYGPF5VC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VJ4WWCAB7N6QI56F45YYGPF5VC/action/storage_attestation","attest_author":"https://pith.science/pith/VJ4WWCAB7N6QI56F45YYGPF5VC/action/author_attestation","sign_citation":"https://pith.science/pith/VJ4WWCAB7N6QI56F45YYGPF5VC/action/citation_signature","submit_replication":"https://pith.science/pith/VJ4WWCAB7N6QI56F45YYGPF5VC/action/replication_record"}},"created_at":"2026-05-18T00:20:56.898632+00:00","updated_at":"2026-05-18T00:20:56.898632+00:00"}