{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:344K7GYVBKPGWGQQKLBYBVF5G7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0ad886c47a229bdd2b90d0d8b1f94905561425759379967655e2d5c3ed096edc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-22T17:32:54Z","title_canon_sha256":"fb09a70d6d78394efb670425cee766b23a86b4ccbe58ff113f0c134121d66ee3"},"schema_version":"1.0","source":{"id":"1509.06697","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06697","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06697v2","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06697","created_at":"2026-05-18T01:12:34Z"},{"alias_kind":"pith_short_12","alias_value":"344K7GYVBKPG","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"344K7GYVBKPGWGQQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"344K7GYV","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:291cac2e92ab88a08bcb35b8063db0ead9a290a6ef06b46ee304b75908503145","target":"graph","created_at":"2026-05-18T01:12:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The article is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second order elliptic problems by Chipot and Rougirel, where the force functions are considered on the cross section of domains, we prove the non-local counterpart of their result.\n  Furthermore, recently Yeressian established a weighted estimate for solutions of nonlocal Dirichlet problems which exhibit the asymptotic behavior. The case whens= 1=2 was also treated as an example ","authors_text":"Indranil Chowdhury, Prosenjit Roy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-22T17:32:54Z","title":"On the Asymptotic Analysis of Problems Involving Fractional Laplacian in Cylindrical Domains Tending to Infinity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06697","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:059dc3676d147b34572a6bbd9400c9bf0e74c6f51261ee0b9c80f8d20cbf2695","target":"record","created_at":"2026-05-18T01:12:34Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0ad886c47a229bdd2b90d0d8b1f94905561425759379967655e2d5c3ed096edc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-09-22T17:32:54Z","title_canon_sha256":"fb09a70d6d78394efb670425cee766b23a86b4ccbe58ff113f0c134121d66ee3"},"schema_version":"1.0","source":{"id":"1509.06697","kind":"arxiv","version":2}},"canonical_sha256":"df38af9b150a9e6b1a1052c380d4bd37d0fff43d0aadbe921ae6d2ffa385eeec","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df38af9b150a9e6b1a1052c380d4bd37d0fff43d0aadbe921ae6d2ffa385eeec","first_computed_at":"2026-05-18T01:12:34.835791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:34.835791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OnZrSoed6NW3BAbxVZ47uomDw4iDwdVzUEjoy64c6dsAiSIOgUbyxi2LlZHIItdhdwtNU1vuXmDACFF1OOHKDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:34.836202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06697","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:059dc3676d147b34572a6bbd9400c9bf0e74c6f51261ee0b9c80f8d20cbf2695","sha256:291cac2e92ab88a08bcb35b8063db0ead9a290a6ef06b46ee304b75908503145"],"state_sha256":"a75ce1c04b29250847fc0ae84a430b50b50adf4ee004dffd645fcb35e54a8451"}