{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:YPAT6BKCEJPHJJMKUNHCQAEHVT","short_pith_number":"pith:YPAT6BKC","schema_version":"1.0","canonical_sha256":"c3c13f0542225e74a58aa34e280087acd57c4ba9bcb19aa2167c2ad6d285b556","source":{"kind":"arxiv","id":"1310.1317","version":1},"attestation_state":"computed","paper":{"title":"$p$-Laplace equations with singular weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Inbo Sim, Kanishka Perera","submitted_at":"2013-10-04T15:24:14Z","abstract_excerpt":"We study a class of $p$-Laplacian Dirichlet problems with weights that are possibly singular on the boundary of the domain, and obtain nontrivial solutions using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get an estimate of the critical groups."},"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":"1310.1317","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-04T15:24:14Z","cross_cats_sorted":[],"title_canon_sha256":"f0c3c7d27cb1f5f74f63169711c3094ac3f89f58c6f41dffc7baf8c243714681","abstract_canon_sha256":"9fbf0f6edac29818c48dec70bde630b4a4781705f58f6f50ac0444d5af972745"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:22.861902Z","signature_b64":"QVtsUsAu6rJ8HyIzxBisFuf4Xx+xXC61Tj+zS5z8g6RAbF0vdMDHBY9hZvLUfrx7TSvI7RRHKTvMsT130+xNAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3c13f0542225e74a58aa34e280087acd57c4ba9bcb19aa2167c2ad6d285b556","last_reissued_at":"2026-05-18T03:11:22.861277Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:22.861277Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$p$-Laplace equations with singular weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Inbo Sim, Kanishka Perera","submitted_at":"2013-10-04T15:24:14Z","abstract_excerpt":"We study a class of $p$-Laplacian Dirichlet problems with weights that are possibly singular on the boundary of the domain, and obtain nontrivial solutions using Morse theory. In the absence of a direct sum decomposition, we use a cohomological local splitting to get an estimate of the critical groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1317","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":"1310.1317","created_at":"2026-05-18T03:11:22.861401+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.1317v1","created_at":"2026-05-18T03:11:22.861401+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1317","created_at":"2026-05-18T03:11:22.861401+00:00"},{"alias_kind":"pith_short_12","alias_value":"YPAT6BKCEJPH","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"YPAT6BKCEJPHJJMK","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"YPAT6BKC","created_at":"2026-05-18T12:28:09.283467+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/YPAT6BKCEJPHJJMKUNHCQAEHVT","json":"https://pith.science/pith/YPAT6BKCEJPHJJMKUNHCQAEHVT.json","graph_json":"https://pith.science/api/pith-number/YPAT6BKCEJPHJJMKUNHCQAEHVT/graph.json","events_json":"https://pith.science/api/pith-number/YPAT6BKCEJPHJJMKUNHCQAEHVT/events.json","paper":"https://pith.science/paper/YPAT6BKC"},"agent_actions":{"view_html":"https://pith.science/pith/YPAT6BKCEJPHJJMKUNHCQAEHVT","download_json":"https://pith.science/pith/YPAT6BKCEJPHJJMKUNHCQAEHVT.json","view_paper":"https://pith.science/paper/YPAT6BKC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.1317&json=true","fetch_graph":"https://pith.science/api/pith-number/YPAT6BKCEJPHJJMKUNHCQAEHVT/graph.json","fetch_events":"https://pith.science/api/pith-number/YPAT6BKCEJPHJJMKUNHCQAEHVT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YPAT6BKCEJPHJJMKUNHCQAEHVT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YPAT6BKCEJPHJJMKUNHCQAEHVT/action/storage_attestation","attest_author":"https://pith.science/pith/YPAT6BKCEJPHJJMKUNHCQAEHVT/action/author_attestation","sign_citation":"https://pith.science/pith/YPAT6BKCEJPHJJMKUNHCQAEHVT/action/citation_signature","submit_replication":"https://pith.science/pith/YPAT6BKCEJPHJJMKUNHCQAEHVT/action/replication_record"}},"created_at":"2026-05-18T03:11:22.861401+00:00","updated_at":"2026-05-18T03:11:22.861401+00:00"}