{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:34A7MZ5BXGHQKM7WIPZCOP2KMV","short_pith_number":"pith:34A7MZ5B","canonical_record":{"source":{"id":"1701.05575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-19T19:32:39Z","cross_cats_sorted":[],"title_canon_sha256":"0ef29e4722b3db39cb16dc1e0b3a6e5bcb15037e190fdefada93c9b0d162abba","abstract_canon_sha256":"a6bc3f36679090305bbe1d646e6c6d918e477956952e287015a14eb3effee1df"},"schema_version":"1.0"},"canonical_sha256":"df01f667a1b98f0533f643f2273f4a65517895c8ce4448f75bc77649dde675b6","source":{"kind":"arxiv","id":"1701.05575","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05575","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05575v2","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05575","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"pith_short_12","alias_value":"34A7MZ5BXGHQ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"34A7MZ5BXGHQKM7W","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"34A7MZ5B","created_at":"2026-05-18T12:30:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:34A7MZ5BXGHQKM7WIPZCOP2KMV","target":"record","payload":{"canonical_record":{"source":{"id":"1701.05575","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-19T19:32:39Z","cross_cats_sorted":[],"title_canon_sha256":"0ef29e4722b3db39cb16dc1e0b3a6e5bcb15037e190fdefada93c9b0d162abba","abstract_canon_sha256":"a6bc3f36679090305bbe1d646e6c6d918e477956952e287015a14eb3effee1df"},"schema_version":"1.0"},"canonical_sha256":"df01f667a1b98f0533f643f2273f4a65517895c8ce4448f75bc77649dde675b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:29.901003Z","signature_b64":"QKhEEdxlc9XC9oqiH+tK5mYaU2RlJWO4/fT6alUsA/5zrgdy7fZ6Je5Vgk9+R6VXBrgZ/Uzz6ch7vK4SUy9MBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"df01f667a1b98f0533f643f2273f4a65517895c8ce4448f75bc77649dde675b6","last_reissued_at":"2026-05-18T00:51:29.900600Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:29.900600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.05575","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tZs8M4TatYVJjKsXdp3rFAf21pRdBz3JG8OTiGmmcjbNPWIqqKjXDr51+1apjD7SpxBoJ1fLzCly0vAri4xZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:44:09.041286Z"},"content_sha256":"23e2c756023bb56ae0db84ad19944506a7ad49b67013a49554ee1d1286356b1e","schema_version":"1.0","event_id":"sha256:23e2c756023bb56ae0db84ad19944506a7ad49b67013a49554ee1d1286356b1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:34A7MZ5BXGHQKM7WIPZCOP2KMV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Results of Ambrosetti-Prodi type for non-selfadjoint elliptic operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andr\\'e Zaccur, Boyan Sirakov, Carlos Tomei","submitted_at":"2017-01-19T19:32:39Z","abstract_excerpt":"The well-known Ambrosetti-Prodi theorem considers perturbations of the Dirichlet Laplacian by a nonlinear function whose derivative jumps over the principal eigenvalue of the operator. Various extensions of this landmark result were obtained for self-adjoint operators, in particular by Berger and Podolak, who gave a geometrical description of the solution set. In this text we show that similar theorems are valid for non self-adjoint operators. In particular, we prove that the semilinear operator is a global fold. As a consequence, we obtain what appears to be the first exact multiplicity resul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05575","kind":"arxiv","version":2},"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":"2026-05-18T00:51:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3QvcC2LGIXKnSmRsPFk6zN9kypOjGFw4OTPEVDf3UJnHueItL1WEkIIGB2X0uTOoY2x+IGh22UcV3u8E/FTEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:44:09.042045Z"},"content_sha256":"e163080961a2e5dd53860fc472a18997550baf56aed17170c5e336ae7686194b","schema_version":"1.0","event_id":"sha256:e163080961a2e5dd53860fc472a18997550baf56aed17170c5e336ae7686194b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/34A7MZ5BXGHQKM7WIPZCOP2KMV/bundle.json","state_url":"https://pith.science/pith/34A7MZ5BXGHQKM7WIPZCOP2KMV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/34A7MZ5BXGHQKM7WIPZCOP2KMV/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":"2026-06-09T07:44:09Z","links":{"resolver":"https://pith.science/pith/34A7MZ5BXGHQKM7WIPZCOP2KMV","bundle":"https://pith.science/pith/34A7MZ5BXGHQKM7WIPZCOP2KMV/bundle.json","state":"https://pith.science/pith/34A7MZ5BXGHQKM7WIPZCOP2KMV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/34A7MZ5BXGHQKM7WIPZCOP2KMV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:34A7MZ5BXGHQKM7WIPZCOP2KMV","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":"a6bc3f36679090305bbe1d646e6c6d918e477956952e287015a14eb3effee1df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-19T19:32:39Z","title_canon_sha256":"0ef29e4722b3db39cb16dc1e0b3a6e5bcb15037e190fdefada93c9b0d162abba"},"schema_version":"1.0","source":{"id":"1701.05575","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.05575","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.05575v2","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.05575","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"pith_short_12","alias_value":"34A7MZ5BXGHQ","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"34A7MZ5BXGHQKM7W","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"34A7MZ5B","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:e163080961a2e5dd53860fc472a18997550baf56aed17170c5e336ae7686194b","target":"graph","created_at":"2026-05-18T00:51:29Z","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 well-known Ambrosetti-Prodi theorem considers perturbations of the Dirichlet Laplacian by a nonlinear function whose derivative jumps over the principal eigenvalue of the operator. Various extensions of this landmark result were obtained for self-adjoint operators, in particular by Berger and Podolak, who gave a geometrical description of the solution set. In this text we show that similar theorems are valid for non self-adjoint operators. In particular, we prove that the semilinear operator is a global fold. As a consequence, we obtain what appears to be the first exact multiplicity resul","authors_text":"Andr\\'e Zaccur, Boyan Sirakov, Carlos Tomei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-19T19:32:39Z","title":"Results of Ambrosetti-Prodi type for non-selfadjoint elliptic operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.05575","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":"sha256:23e2c756023bb56ae0db84ad19944506a7ad49b67013a49554ee1d1286356b1e","target":"record","created_at":"2026-05-18T00:51:29Z","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":"a6bc3f36679090305bbe1d646e6c6d918e477956952e287015a14eb3effee1df","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-01-19T19:32:39Z","title_canon_sha256":"0ef29e4722b3db39cb16dc1e0b3a6e5bcb15037e190fdefada93c9b0d162abba"},"schema_version":"1.0","source":{"id":"1701.05575","kind":"arxiv","version":2}},"canonical_sha256":"df01f667a1b98f0533f643f2273f4a65517895c8ce4448f75bc77649dde675b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df01f667a1b98f0533f643f2273f4a65517895c8ce4448f75bc77649dde675b6","first_computed_at":"2026-05-18T00:51:29.900600Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:29.900600Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QKhEEdxlc9XC9oqiH+tK5mYaU2RlJWO4/fT6alUsA/5zrgdy7fZ6Je5Vgk9+R6VXBrgZ/Uzz6ch7vK4SUy9MBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:29.901003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.05575","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:23e2c756023bb56ae0db84ad19944506a7ad49b67013a49554ee1d1286356b1e","sha256:e163080961a2e5dd53860fc472a18997550baf56aed17170c5e336ae7686194b"],"state_sha256":"a1e5cc1d764fa261656900fa535200c1e69fda6bc5965ad4813de593619ca7c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zwhYDxWSulvQcOnXcQZc+IXFAOtPBU9nd3NNyAAhWs4MDrZ/bwaHWLvwyPxPTUDX1OCf5PS45K3zqv/D7eGABA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:44:09.046005Z","bundle_sha256":"fb9ab656c35e001250ebf92181c4b5d2377297e324d47e7082dcaca660bfb558"}}