{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:HF2GUQLKRVZQ75B4X7WHLWLU6C","short_pith_number":"pith:HF2GUQLK","schema_version":"1.0","canonical_sha256":"39746a416a8d730ff43cbfec75d974f0b875e353ee8611650cc1117df5a80e38","source":{"kind":"arxiv","id":"1711.11238","version":1},"attestation_state":"computed","paper":{"title":"Parametric critical point theorems and their applications to boundary value problems on the Sierpi\\'{n}ski Gasket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Marek Galewski, Mateusz Krukowski","submitted_at":"2017-11-30T05:34:36Z","abstract_excerpt":"In this note we consider the classical variational tools like: Ekelenad's Variational Principle, Mountain Pass Lemma and some of their corollaries subject to a parameter. Next, we investigate the behaviour of critical points obtained once a sequence of parameters is allowed to be convergent. Applications for the Dirichlet Boundary Value Problem on the Sierpi\\'{n}ski Gasket are given in presence of assumptions which lead to fulfillment of the mountain geometry."},"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":"1711.11238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-11-30T05:34:36Z","cross_cats_sorted":[],"title_canon_sha256":"feff8f8d7055e800a41f1fc162b652709018d236214f5945d88ffcc2c9fa466a","abstract_canon_sha256":"350db4516a2fa14b03bfd0175e92e68e2e3645994521e249535041d899a31e9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:12.111628Z","signature_b64":"qMhvrzahmrtLISXP0zvMj81wGvzR4G92ihM04QWVpfpkyDQDebi9Rb7YgE1eU4vFSGQWBn0VdErrx5TSpDpOCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39746a416a8d730ff43cbfec75d974f0b875e353ee8611650cc1117df5a80e38","last_reissued_at":"2026-05-18T00:29:12.110967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:12.110967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Parametric critical point theorems and their applications to boundary value problems on the Sierpi\\'{n}ski Gasket","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Marek Galewski, Mateusz Krukowski","submitted_at":"2017-11-30T05:34:36Z","abstract_excerpt":"In this note we consider the classical variational tools like: Ekelenad's Variational Principle, Mountain Pass Lemma and some of their corollaries subject to a parameter. Next, we investigate the behaviour of critical points obtained once a sequence of parameters is allowed to be convergent. Applications for the Dirichlet Boundary Value Problem on the Sierpi\\'{n}ski Gasket are given in presence of assumptions which lead to fulfillment of the mountain geometry."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.11238","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":"1711.11238","created_at":"2026-05-18T00:29:12.111071+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.11238v1","created_at":"2026-05-18T00:29:12.111071+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.11238","created_at":"2026-05-18T00:29:12.111071+00:00"},{"alias_kind":"pith_short_12","alias_value":"HF2GUQLKRVZQ","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"HF2GUQLKRVZQ75B4","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"HF2GUQLK","created_at":"2026-05-18T12:31:18.294218+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/HF2GUQLKRVZQ75B4X7WHLWLU6C","json":"https://pith.science/pith/HF2GUQLKRVZQ75B4X7WHLWLU6C.json","graph_json":"https://pith.science/api/pith-number/HF2GUQLKRVZQ75B4X7WHLWLU6C/graph.json","events_json":"https://pith.science/api/pith-number/HF2GUQLKRVZQ75B4X7WHLWLU6C/events.json","paper":"https://pith.science/paper/HF2GUQLK"},"agent_actions":{"view_html":"https://pith.science/pith/HF2GUQLKRVZQ75B4X7WHLWLU6C","download_json":"https://pith.science/pith/HF2GUQLKRVZQ75B4X7WHLWLU6C.json","view_paper":"https://pith.science/paper/HF2GUQLK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.11238&json=true","fetch_graph":"https://pith.science/api/pith-number/HF2GUQLKRVZQ75B4X7WHLWLU6C/graph.json","fetch_events":"https://pith.science/api/pith-number/HF2GUQLKRVZQ75B4X7WHLWLU6C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HF2GUQLKRVZQ75B4X7WHLWLU6C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HF2GUQLKRVZQ75B4X7WHLWLU6C/action/storage_attestation","attest_author":"https://pith.science/pith/HF2GUQLKRVZQ75B4X7WHLWLU6C/action/author_attestation","sign_citation":"https://pith.science/pith/HF2GUQLKRVZQ75B4X7WHLWLU6C/action/citation_signature","submit_replication":"https://pith.science/pith/HF2GUQLKRVZQ75B4X7WHLWLU6C/action/replication_record"}},"created_at":"2026-05-18T00:29:12.111071+00:00","updated_at":"2026-05-18T00:29:12.111071+00:00"}