{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:V5NJJRITXHX3IDYYUSS4DQFEDI","short_pith_number":"pith:V5NJJRIT","canonical_record":{"source":{"id":"1105.2187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-11T13:48:07Z","cross_cats_sorted":[],"title_canon_sha256":"91b563a1c8a21d7cd1ea5d4c88091988fd3be70912b97149c010b7b88965e552","abstract_canon_sha256":"9c19f92db921e6029b0a827ec101ae7900580a927a9ab8ecb5282dfc855ea127"},"schema_version":"1.0"},"canonical_sha256":"af5a94c513b9efb40f18a4a5c1c0a41a0a4d7da6cb5122db2df2eddd84facca7","source":{"kind":"arxiv","id":"1105.2187","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2187","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2187v1","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2187","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"V5NJJRITXHX3","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V5NJJRITXHX3IDYY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V5NJJRIT","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:V5NJJRITXHX3IDYYUSS4DQFEDI","target":"record","payload":{"canonical_record":{"source":{"id":"1105.2187","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-11T13:48:07Z","cross_cats_sorted":[],"title_canon_sha256":"91b563a1c8a21d7cd1ea5d4c88091988fd3be70912b97149c010b7b88965e552","abstract_canon_sha256":"9c19f92db921e6029b0a827ec101ae7900580a927a9ab8ecb5282dfc855ea127"},"schema_version":"1.0"},"canonical_sha256":"af5a94c513b9efb40f18a4a5c1c0a41a0a4d7da6cb5122db2df2eddd84facca7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:21.339609Z","signature_b64":"cQ/Yqikt4ktRlNsKnNs+o26JGyTymx277l7rSCV1ZHvPWjetZRBGaPvnf1CBDn/ao4mh0qRbBwE9sDuyN8MFDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af5a94c513b9efb40f18a4a5c1c0a41a0a4d7da6cb5122db2df2eddd84facca7","last_reissued_at":"2026-05-18T04:22:21.338934Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:21.338934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.2187","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uj2NNFEuBod3jSaMMCoK+a1EVKT5yb1NWQnRwHsYx9sNVckjSX50AdFnkk5oqNSQMZCLGQHK/XyLnKQ/ndAPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:06:29.947140Z"},"content_sha256":"6ae1b0d3a255fb226c05f89b9220200ffeabd7e8ef202563a891f3fc2e3231b0","schema_version":"1.0","event_id":"sha256:6ae1b0d3a255fb226c05f89b9220200ffeabd7e8ef202563a891f3fc2e3231b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:V5NJJRITXHX3IDYYUSS4DQFEDI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Existence of sign-changing solutions for the nonlinear $p$-Laplacian boundary value problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Wei-Cheng Lian, Wei-Chuan Wang, Y.H. Cheng","submitted_at":"2011-05-11T13:48:07Z","abstract_excerpt":"We study the nonlinear one-dimensional $p$-Laplacian equation $$ -(y'^{(p-1)})'+(p-1)q(x)y^{(p-1)}=(p-1)w(x)f(y) on (0,1),$$ with linear separated boundary conditions. We give sufficient conditions for the existence of solutions with prescribed nodal properties concerning the behavior of $f(s)/s^{(p-1)}$ when $s$ are at infinity and zero. These results are more general and complementary for previous known ones for the case $p=2$ and $q$ is nonnegative."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2187","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:22:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DNiRUUTXVcar+YE0r3eAH1iQu15Z7UYFzbojg2K1BoO6x6aqryEg7hXs3n1eUYlRux1kX6OSeUByAt6uN5rbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:06:29.947503Z"},"content_sha256":"04f5b5141c6f8e66442c0a54f4c20b780960f5d13bc17e29e511d9487fd85a14","schema_version":"1.0","event_id":"sha256:04f5b5141c6f8e66442c0a54f4c20b780960f5d13bc17e29e511d9487fd85a14"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V5NJJRITXHX3IDYYUSS4DQFEDI/bundle.json","state_url":"https://pith.science/pith/V5NJJRITXHX3IDYYUSS4DQFEDI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V5NJJRITXHX3IDYYUSS4DQFEDI/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T02:06:29Z","links":{"resolver":"https://pith.science/pith/V5NJJRITXHX3IDYYUSS4DQFEDI","bundle":"https://pith.science/pith/V5NJJRITXHX3IDYYUSS4DQFEDI/bundle.json","state":"https://pith.science/pith/V5NJJRITXHX3IDYYUSS4DQFEDI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V5NJJRITXHX3IDYYUSS4DQFEDI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:V5NJJRITXHX3IDYYUSS4DQFEDI","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":"9c19f92db921e6029b0a827ec101ae7900580a927a9ab8ecb5282dfc855ea127","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-11T13:48:07Z","title_canon_sha256":"91b563a1c8a21d7cd1ea5d4c88091988fd3be70912b97149c010b7b88965e552"},"schema_version":"1.0","source":{"id":"1105.2187","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2187","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2187v1","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2187","created_at":"2026-05-18T04:22:21Z"},{"alias_kind":"pith_short_12","alias_value":"V5NJJRITXHX3","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"V5NJJRITXHX3IDYY","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"V5NJJRIT","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:04f5b5141c6f8e66442c0a54f4c20b780960f5d13bc17e29e511d9487fd85a14","target":"graph","created_at":"2026-05-18T04:22:21Z","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":"We study the nonlinear one-dimensional $p$-Laplacian equation $$ -(y'^{(p-1)})'+(p-1)q(x)y^{(p-1)}=(p-1)w(x)f(y) on (0,1),$$ with linear separated boundary conditions. We give sufficient conditions for the existence of solutions with prescribed nodal properties concerning the behavior of $f(s)/s^{(p-1)}$ when $s$ are at infinity and zero. These results are more general and complementary for previous known ones for the case $p=2$ and $q$ is nonnegative.","authors_text":"Wei-Cheng Lian, Wei-Chuan Wang, Y.H. Cheng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-11T13:48:07Z","title":"Existence of sign-changing solutions for the nonlinear $p$-Laplacian boundary value problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2187","kind":"arxiv","version":1},"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":"sha256:6ae1b0d3a255fb226c05f89b9220200ffeabd7e8ef202563a891f3fc2e3231b0","target":"record","created_at":"2026-05-18T04:22:21Z","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":"9c19f92db921e6029b0a827ec101ae7900580a927a9ab8ecb5282dfc855ea127","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-05-11T13:48:07Z","title_canon_sha256":"91b563a1c8a21d7cd1ea5d4c88091988fd3be70912b97149c010b7b88965e552"},"schema_version":"1.0","source":{"id":"1105.2187","kind":"arxiv","version":1}},"canonical_sha256":"af5a94c513b9efb40f18a4a5c1c0a41a0a4d7da6cb5122db2df2eddd84facca7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af5a94c513b9efb40f18a4a5c1c0a41a0a4d7da6cb5122db2df2eddd84facca7","first_computed_at":"2026-05-18T04:22:21.338934Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:21.338934Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cQ/Yqikt4ktRlNsKnNs+o26JGyTymx277l7rSCV1ZHvPWjetZRBGaPvnf1CBDn/ao4mh0qRbBwE9sDuyN8MFDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:21.339609Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2187","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ae1b0d3a255fb226c05f89b9220200ffeabd7e8ef202563a891f3fc2e3231b0","sha256:04f5b5141c6f8e66442c0a54f4c20b780960f5d13bc17e29e511d9487fd85a14"],"state_sha256":"b431a74c330cd142d92e7c97d820c870a8b7c275d8b8f683801e1b921cc567e3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gKUI+k7Dylo7s1d2Un1Xqw18U3nndAHjD/06ZK0OOgAmsK1XvgCsf893yYyF8YLp/lsqt7MPEmVYIjR66LZLBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:06:29.949576Z","bundle_sha256":"5d92cf52b9d7470bffd9b4125d74d6b5118a9bab2c150d376cace485bf617ee5"}}