{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UYDEARJX22UYHOYFFY5YW4LKGY","short_pith_number":"pith:UYDEARJX","schema_version":"1.0","canonical_sha256":"a606404537d6a983bb052e3b8b716a363e206542c5db5d95a9ff1897b3542101","source":{"kind":"arxiv","id":"1901.01809","version":1},"attestation_state":"computed","paper":{"title":"First critical field of highly anisotropic three-dimensional superconductors via a vortex density model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andres Contreras, Guanying Peng","submitted_at":"2019-01-07T14:00:07Z","abstract_excerpt":"We analyze a mean field model for $3$d anisotropic superconductors with a layered structure, in the presence of a strong magnetic field. The mean field model arises as the $Gamma$-limit of the Lawrence-Doniach energy in certain regimes. A reformulation of the problem based on convex duality allows us to characterize the first critical field $H_{c_1}$ of the layered superconductor, up to leading order. In previous work, Alama-Bronsard-Sandier \\cite{ABS} have derived the asymptotic value of $H_{c_1}$ for configurations satisfying periodic boundary conditions; in that setting describing minimizer"},"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":"1901.01809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-07T14:00:07Z","cross_cats_sorted":[],"title_canon_sha256":"bb30d029680cae7644dce97fcb770bfea803ee9ba1ba358946d71c9444cd1ca3","abstract_canon_sha256":"33c1347e6ee7df4833a985f840c3b7d247fea115266656715de3c46d81ec3055"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:51.213005Z","signature_b64":"5PDTQG/snfTs0eCA5hDIrDAPOabakTESzJco85ytE+r2aqB9xCrt4VwNqluIBdUpgHdkxVQOZIkHF5KmjfWcDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a606404537d6a983bb052e3b8b716a363e206542c5db5d95a9ff1897b3542101","last_reissued_at":"2026-05-17T23:56:51.212596Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:51.212596Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"First critical field of highly anisotropic three-dimensional superconductors via a vortex density model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andres Contreras, Guanying Peng","submitted_at":"2019-01-07T14:00:07Z","abstract_excerpt":"We analyze a mean field model for $3$d anisotropic superconductors with a layered structure, in the presence of a strong magnetic field. The mean field model arises as the $Gamma$-limit of the Lawrence-Doniach energy in certain regimes. A reformulation of the problem based on convex duality allows us to characterize the first critical field $H_{c_1}$ of the layered superconductor, up to leading order. In previous work, Alama-Bronsard-Sandier \\cite{ABS} have derived the asymptotic value of $H_{c_1}$ for configurations satisfying periodic boundary conditions; in that setting describing minimizer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01809","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":"1901.01809","created_at":"2026-05-17T23:56:51.212659+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.01809v1","created_at":"2026-05-17T23:56:51.212659+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.01809","created_at":"2026-05-17T23:56:51.212659+00:00"},{"alias_kind":"pith_short_12","alias_value":"UYDEARJX22UY","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"UYDEARJX22UYHOYF","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"UYDEARJX","created_at":"2026-05-18T12:33:30.264802+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/UYDEARJX22UYHOYFFY5YW4LKGY","json":"https://pith.science/pith/UYDEARJX22UYHOYFFY5YW4LKGY.json","graph_json":"https://pith.science/api/pith-number/UYDEARJX22UYHOYFFY5YW4LKGY/graph.json","events_json":"https://pith.science/api/pith-number/UYDEARJX22UYHOYFFY5YW4LKGY/events.json","paper":"https://pith.science/paper/UYDEARJX"},"agent_actions":{"view_html":"https://pith.science/pith/UYDEARJX22UYHOYFFY5YW4LKGY","download_json":"https://pith.science/pith/UYDEARJX22UYHOYFFY5YW4LKGY.json","view_paper":"https://pith.science/paper/UYDEARJX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.01809&json=true","fetch_graph":"https://pith.science/api/pith-number/UYDEARJX22UYHOYFFY5YW4LKGY/graph.json","fetch_events":"https://pith.science/api/pith-number/UYDEARJX22UYHOYFFY5YW4LKGY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UYDEARJX22UYHOYFFY5YW4LKGY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UYDEARJX22UYHOYFFY5YW4LKGY/action/storage_attestation","attest_author":"https://pith.science/pith/UYDEARJX22UYHOYFFY5YW4LKGY/action/author_attestation","sign_citation":"https://pith.science/pith/UYDEARJX22UYHOYFFY5YW4LKGY/action/citation_signature","submit_replication":"https://pith.science/pith/UYDEARJX22UYHOYFFY5YW4LKGY/action/replication_record"}},"created_at":"2026-05-17T23:56:51.212659+00:00","updated_at":"2026-05-17T23:56:51.212659+00:00"}