{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:CMHEYR6DZXCOMOP4IAYLA2IT3M","short_pith_number":"pith:CMHEYR6D","schema_version":"1.0","canonical_sha256":"130e4c47c3cdc4e639fc4030b06913db2eeda7ac393315e2b3bfc46f022d719b","source":{"kind":"arxiv","id":"1112.2305","version":12},"attestation_state":"computed","paper":{"title":"On the $\\Gamma$-limit of singular perturbation problems with optimal profiles which are not one-dimensional. Part I: The upper bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arkady Poliakovsky","submitted_at":"2011-12-10T21:55:14Z","abstract_excerpt":"In Part I we construct the upper bound, in the spirit of $\\Gamma$- $\\limsup$, achieved by multidimensional profiles, for some general classes of singular perturbation problems, with or without the prescribed differential constraint, taking the form $$E_\\e(v):=\\int_\\Omega \\frac{1}{\\e}F\\Big(\\e^n\\nabla^n v,...,\\e\\nabla v,v\\Big)dx\\quad\\text{for} v:\\Omega\\subset\\R^N\\to\\R^k \\text{such that} A\\cdot\\nabla v=0,$$ where the function $F\\geq 0$ and $A:\\R^{k\\times N}\\to\\R^m$ is a prescribed linear operator (for example, $A:\\equiv 0$, $A\\cdot\\nabla v:=\\text{curl}v$ and $A\\cdot\\nabla v=\\text{div}\\,v$) which "},"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":"1112.2305","kind":"arxiv","version":12},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-10T21:55:14Z","cross_cats_sorted":[],"title_canon_sha256":"e442bd1f2f673c20af8e8f80e2c244e316e0b8ade23d7e134c3358884a09e7af","abstract_canon_sha256":"1a5edf13ad3ebc40e5cd6be8ba60aabf12270a0613c4bd0be3ce1381eb7fdfac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:37.986042Z","signature_b64":"EBukdDV/H+bXtQIrAT1WH/CH+MDJK86QR6iM6hsmQasy2QrRV5RkWYLHSxQ4oyi++3SgGMG+SLZLVu1SvbIIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"130e4c47c3cdc4e639fc4030b06913db2eeda7ac393315e2b3bfc46f022d719b","last_reissued_at":"2026-05-18T03:33:37.985334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:37.985334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the $\\Gamma$-limit of singular perturbation problems with optimal profiles which are not one-dimensional. Part I: The upper bound","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arkady Poliakovsky","submitted_at":"2011-12-10T21:55:14Z","abstract_excerpt":"In Part I we construct the upper bound, in the spirit of $\\Gamma$- $\\limsup$, achieved by multidimensional profiles, for some general classes of singular perturbation problems, with or without the prescribed differential constraint, taking the form $$E_\\e(v):=\\int_\\Omega \\frac{1}{\\e}F\\Big(\\e^n\\nabla^n v,...,\\e\\nabla v,v\\Big)dx\\quad\\text{for} v:\\Omega\\subset\\R^N\\to\\R^k \\text{such that} A\\cdot\\nabla v=0,$$ where the function $F\\geq 0$ and $A:\\R^{k\\times N}\\to\\R^m$ is a prescribed linear operator (for example, $A:\\equiv 0$, $A\\cdot\\nabla v:=\\text{curl}v$ and $A\\cdot\\nabla v=\\text{div}\\,v$) which "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.2305","kind":"arxiv","version":12},"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":"1112.2305","created_at":"2026-05-18T03:33:37.985442+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.2305v12","created_at":"2026-05-18T03:33:37.985442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.2305","created_at":"2026-05-18T03:33:37.985442+00:00"},{"alias_kind":"pith_short_12","alias_value":"CMHEYR6DZXCO","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"CMHEYR6DZXCOMOP4","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"CMHEYR6D","created_at":"2026-05-18T12:26:26.731475+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/CMHEYR6DZXCOMOP4IAYLA2IT3M","json":"https://pith.science/pith/CMHEYR6DZXCOMOP4IAYLA2IT3M.json","graph_json":"https://pith.science/api/pith-number/CMHEYR6DZXCOMOP4IAYLA2IT3M/graph.json","events_json":"https://pith.science/api/pith-number/CMHEYR6DZXCOMOP4IAYLA2IT3M/events.json","paper":"https://pith.science/paper/CMHEYR6D"},"agent_actions":{"view_html":"https://pith.science/pith/CMHEYR6DZXCOMOP4IAYLA2IT3M","download_json":"https://pith.science/pith/CMHEYR6DZXCOMOP4IAYLA2IT3M.json","view_paper":"https://pith.science/paper/CMHEYR6D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.2305&json=true","fetch_graph":"https://pith.science/api/pith-number/CMHEYR6DZXCOMOP4IAYLA2IT3M/graph.json","fetch_events":"https://pith.science/api/pith-number/CMHEYR6DZXCOMOP4IAYLA2IT3M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CMHEYR6DZXCOMOP4IAYLA2IT3M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CMHEYR6DZXCOMOP4IAYLA2IT3M/action/storage_attestation","attest_author":"https://pith.science/pith/CMHEYR6DZXCOMOP4IAYLA2IT3M/action/author_attestation","sign_citation":"https://pith.science/pith/CMHEYR6DZXCOMOP4IAYLA2IT3M/action/citation_signature","submit_replication":"https://pith.science/pith/CMHEYR6DZXCOMOP4IAYLA2IT3M/action/replication_record"}},"created_at":"2026-05-18T03:33:37.985442+00:00","updated_at":"2026-05-18T03:33:37.985442+00:00"}