{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:GITWZRZGNDO3WFOHML3M23ZQNX","short_pith_number":"pith:GITWZRZG","schema_version":"1.0","canonical_sha256":"32276cc72668ddbb15c762f6cd6f306de86b950a9862e761c2f50ed3409f2f7a","source":{"kind":"arxiv","id":"1905.11162","version":1},"attestation_state":"computed","paper":{"title":"A necessary condition in a De Giorgi type conjecture for elliptic systems in infinite strips","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonin Monteil, Radu Ignat","submitted_at":"2019-05-27T12:22:19Z","abstract_excerpt":"Given a bounded Lipschitz domain $\\omega\\subset\\mathbb{R}^{d-1}$ and a lower semicontinuous function $W:\\mathbb{R}^N\\to\\mathbb{R}_+\\cup\\{+\\infty\\}$ that vanishes on a finite set and that is bounded from below by a positive constant at infinity, we show that every map $u:\\mathbb{R}\\times\\omega\\to\\mathbb{R}^N$ with \\[ \\int_{\\mathbb{R}\\times\\omega}\\big(\\lvert\\nabla u\\rvert^2+W(u)\\big)\\mathop{}\\mathopen{}\\mathrm{d} x_1\\mathop{}\\mathopen{}\\mathrm{d}x'<+\\infty\\] has a limit $u^\\pm\\in\\{W=0\\}$ as $x_1\\to\\pm\\infty$. The convergence holds in $L^2(\\omega)$ and almost everywhere in $\\omega$. We also prove"},"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":"1905.11162","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-05-27T12:22:19Z","cross_cats_sorted":[],"title_canon_sha256":"49746434bb75554d55e4d5ab8050330c404a53f66fdd0a8bb6cefc7c78317e24","abstract_canon_sha256":"9e5c2165d53402f7bae86fd65639f5b4a4084919cd5154779a9e091d843cd802"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:02.747980Z","signature_b64":"2NIsX3PqIAKUxQOuEPbQw5fNlO37nP6XFo4NxQNH/PyppU3+O7aIoRYAfMIxWlhPhYyKvWSKiKbaKDZ2VKVVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32276cc72668ddbb15c762f6cd6f306de86b950a9862e761c2f50ed3409f2f7a","last_reissued_at":"2026-05-17T23:45:02.747493Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:02.747493Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A necessary condition in a De Giorgi type conjecture for elliptic systems in infinite strips","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Antonin Monteil, Radu Ignat","submitted_at":"2019-05-27T12:22:19Z","abstract_excerpt":"Given a bounded Lipschitz domain $\\omega\\subset\\mathbb{R}^{d-1}$ and a lower semicontinuous function $W:\\mathbb{R}^N\\to\\mathbb{R}_+\\cup\\{+\\infty\\}$ that vanishes on a finite set and that is bounded from below by a positive constant at infinity, we show that every map $u:\\mathbb{R}\\times\\omega\\to\\mathbb{R}^N$ with \\[ \\int_{\\mathbb{R}\\times\\omega}\\big(\\lvert\\nabla u\\rvert^2+W(u)\\big)\\mathop{}\\mathopen{}\\mathrm{d} x_1\\mathop{}\\mathopen{}\\mathrm{d}x'<+\\infty\\] has a limit $u^\\pm\\in\\{W=0\\}$ as $x_1\\to\\pm\\infty$. The convergence holds in $L^2(\\omega)$ and almost everywhere in $\\omega$. We also prove"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11162","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":"1905.11162","created_at":"2026-05-17T23:45:02.747589+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.11162v1","created_at":"2026-05-17T23:45:02.747589+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.11162","created_at":"2026-05-17T23:45:02.747589+00:00"},{"alias_kind":"pith_short_12","alias_value":"GITWZRZGNDO3","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_16","alias_value":"GITWZRZGNDO3WFOH","created_at":"2026-05-18T12:33:18.533446+00:00"},{"alias_kind":"pith_short_8","alias_value":"GITWZRZG","created_at":"2026-05-18T12:33:18.533446+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/GITWZRZGNDO3WFOHML3M23ZQNX","json":"https://pith.science/pith/GITWZRZGNDO3WFOHML3M23ZQNX.json","graph_json":"https://pith.science/api/pith-number/GITWZRZGNDO3WFOHML3M23ZQNX/graph.json","events_json":"https://pith.science/api/pith-number/GITWZRZGNDO3WFOHML3M23ZQNX/events.json","paper":"https://pith.science/paper/GITWZRZG"},"agent_actions":{"view_html":"https://pith.science/pith/GITWZRZGNDO3WFOHML3M23ZQNX","download_json":"https://pith.science/pith/GITWZRZGNDO3WFOHML3M23ZQNX.json","view_paper":"https://pith.science/paper/GITWZRZG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.11162&json=true","fetch_graph":"https://pith.science/api/pith-number/GITWZRZGNDO3WFOHML3M23ZQNX/graph.json","fetch_events":"https://pith.science/api/pith-number/GITWZRZGNDO3WFOHML3M23ZQNX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GITWZRZGNDO3WFOHML3M23ZQNX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GITWZRZGNDO3WFOHML3M23ZQNX/action/storage_attestation","attest_author":"https://pith.science/pith/GITWZRZGNDO3WFOHML3M23ZQNX/action/author_attestation","sign_citation":"https://pith.science/pith/GITWZRZGNDO3WFOHML3M23ZQNX/action/citation_signature","submit_replication":"https://pith.science/pith/GITWZRZGNDO3WFOHML3M23ZQNX/action/replication_record"}},"created_at":"2026-05-17T23:45:02.747589+00:00","updated_at":"2026-05-17T23:45:02.747589+00:00"}