{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:MK3XLK2ZRXAOFT5XJACURYBZLV","short_pith_number":"pith:MK3XLK2Z","canonical_record":{"source":{"id":"1303.2237","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-09T16:53:30Z","cross_cats_sorted":[],"title_canon_sha256":"e3e0645dcaed673ecd31b1c8e0323898c5a564f45ea3ba2c6a26a117f0217a2f","abstract_canon_sha256":"9d161e4fcf495bf2f02cdd90c44979aad8ee302ba8c04c3b0722c4d6329d41bb"},"schema_version":"1.0"},"canonical_sha256":"62b775ab598dc0e2cfb7480548e0395d615ab480711353ddde3edacbf3e1c7da","source":{"kind":"arxiv","id":"1303.2237","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2237","created_at":"2026-05-18T03:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2237v1","created_at":"2026-05-18T03:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2237","created_at":"2026-05-18T03:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"MK3XLK2ZRXAO","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MK3XLK2ZRXAOFT5X","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MK3XLK2Z","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:MK3XLK2ZRXAOFT5XJACURYBZLV","target":"record","payload":{"canonical_record":{"source":{"id":"1303.2237","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-09T16:53:30Z","cross_cats_sorted":[],"title_canon_sha256":"e3e0645dcaed673ecd31b1c8e0323898c5a564f45ea3ba2c6a26a117f0217a2f","abstract_canon_sha256":"9d161e4fcf495bf2f02cdd90c44979aad8ee302ba8c04c3b0722c4d6329d41bb"},"schema_version":"1.0"},"canonical_sha256":"62b775ab598dc0e2cfb7480548e0395d615ab480711353ddde3edacbf3e1c7da","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:19.603213Z","signature_b64":"FN3YqjEGZIuOFqvjogG98xDS0/eZMik8zmLnO+iyNgQKEF/aJ75hadO0c+hurvpP3klig7K/SQrj9JXlWzG8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"62b775ab598dc0e2cfb7480548e0395d615ab480711353ddde3edacbf3e1c7da","last_reissued_at":"2026-05-18T03:31:19.602591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:19.602591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.2237","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":"2026-05-18T03:31:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AZeh64Iic7iLca5hQXFPX6QHd+EQMcGNrxowchHExD8FUHOPMUuI2t5aH4qslRGI908eVdzWzoaQI4oSNH0cDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:32:14.828708Z"},"content_sha256":"90a7e40b77547a1aada890d26755ba54000e96c73cff3255b655df605143f0be","schema_version":"1.0","event_id":"sha256:90a7e40b77547a1aada890d26755ba54000e96c73cff3255b655df605143f0be"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:MK3XLK2ZRXAOFT5XJACURYBZLV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sign-Preserving Property for Some Fourth-Order Elliptic Operators in One Dimension and Radial Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Christoph Walker (IFAM), Philippe Laurencot (IMT)","submitted_at":"2013-03-09T16:53:30Z","abstract_excerpt":"For a class of one-dimensional linear elliptic fourth-order equations with homogeneous Dirichlet boundary conditions it is shown that a non-positive and non-vanishing right-hand side gives rise to a negative solution. A similar result is obtained for the same class of equations for radially symmetric solutions in a ball or in an annulus. Several applications are given, including applications to nonlinear equations and eigenvalue problems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2237","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":"2026-05-18T03:31:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v2RIKs3gQoimTL8yBKqz9s8ONkssSURLvGLqHQWCZvyyhrglC0Vadqif8Om84YF9Qm2gP6PiBUkfjjjuT8mJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T03:32:14.829327Z"},"content_sha256":"f1d6fa6a1a4597048d076788091ef32392af34b4dab08bc7169382b7f47fe88e","schema_version":"1.0","event_id":"sha256:f1d6fa6a1a4597048d076788091ef32392af34b4dab08bc7169382b7f47fe88e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MK3XLK2ZRXAOFT5XJACURYBZLV/bundle.json","state_url":"https://pith.science/pith/MK3XLK2ZRXAOFT5XJACURYBZLV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MK3XLK2ZRXAOFT5XJACURYBZLV/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":"2026-06-05T03:32:14Z","links":{"resolver":"https://pith.science/pith/MK3XLK2ZRXAOFT5XJACURYBZLV","bundle":"https://pith.science/pith/MK3XLK2ZRXAOFT5XJACURYBZLV/bundle.json","state":"https://pith.science/pith/MK3XLK2ZRXAOFT5XJACURYBZLV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MK3XLK2ZRXAOFT5XJACURYBZLV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:MK3XLK2ZRXAOFT5XJACURYBZLV","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":"9d161e4fcf495bf2f02cdd90c44979aad8ee302ba8c04c3b0722c4d6329d41bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-09T16:53:30Z","title_canon_sha256":"e3e0645dcaed673ecd31b1c8e0323898c5a564f45ea3ba2c6a26a117f0217a2f"},"schema_version":"1.0","source":{"id":"1303.2237","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.2237","created_at":"2026-05-18T03:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"1303.2237v1","created_at":"2026-05-18T03:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.2237","created_at":"2026-05-18T03:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"MK3XLK2ZRXAO","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"MK3XLK2ZRXAOFT5X","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"MK3XLK2Z","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:f1d6fa6a1a4597048d076788091ef32392af34b4dab08bc7169382b7f47fe88e","target":"graph","created_at":"2026-05-18T03:31:19Z","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":"For a class of one-dimensional linear elliptic fourth-order equations with homogeneous Dirichlet boundary conditions it is shown that a non-positive and non-vanishing right-hand side gives rise to a negative solution. A similar result is obtained for the same class of equations for radially symmetric solutions in a ball or in an annulus. Several applications are given, including applications to nonlinear equations and eigenvalue problems.","authors_text":"Christoph Walker (IFAM), Philippe Laurencot (IMT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-09T16:53:30Z","title":"Sign-Preserving Property for Some Fourth-Order Elliptic Operators in One Dimension and Radial Symmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.2237","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":"sha256:90a7e40b77547a1aada890d26755ba54000e96c73cff3255b655df605143f0be","target":"record","created_at":"2026-05-18T03:31:19Z","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":"9d161e4fcf495bf2f02cdd90c44979aad8ee302ba8c04c3b0722c4d6329d41bb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-03-09T16:53:30Z","title_canon_sha256":"e3e0645dcaed673ecd31b1c8e0323898c5a564f45ea3ba2c6a26a117f0217a2f"},"schema_version":"1.0","source":{"id":"1303.2237","kind":"arxiv","version":1}},"canonical_sha256":"62b775ab598dc0e2cfb7480548e0395d615ab480711353ddde3edacbf3e1c7da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"62b775ab598dc0e2cfb7480548e0395d615ab480711353ddde3edacbf3e1c7da","first_computed_at":"2026-05-18T03:31:19.602591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:19.602591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FN3YqjEGZIuOFqvjogG98xDS0/eZMik8zmLnO+iyNgQKEF/aJ75hadO0c+hurvpP3klig7K/SQrj9JXlWzG8DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:19.603213Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.2237","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90a7e40b77547a1aada890d26755ba54000e96c73cff3255b655df605143f0be","sha256:f1d6fa6a1a4597048d076788091ef32392af34b4dab08bc7169382b7f47fe88e"],"state_sha256":"a745e9d403a11f9c861439ac2722a8dee3e1adb10bfb6ef42afa1b0b7f1e66db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"98zL+tGJV5yZ8UFo3m0Yr51JoX/GVR9GO4/svd0sUzQxp30M9Ed8liT90X2PKdw5MdYL1WDooLB5TGHrDzxaAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T03:32:14.832469Z","bundle_sha256":"2d2e59d60cec0e6a9dcf060f2850474d3ad49139de4138218e995d49ebb809f3"}}