{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:AWRV55RLXO6HKXKZXVGLAVX72G","short_pith_number":"pith:AWRV55RL","canonical_record":{"source":{"id":"1803.07579","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-20T18:09:32Z","cross_cats_sorted":[],"title_canon_sha256":"65a06bea6d4ed1ce771a5b5f88db9bd405a04cc1b56b58829e5a905028bbb59b","abstract_canon_sha256":"6ad2f6beb66d8fcfabee62d6c78c1d717e5da01231309c662cd7427835535e4e"},"schema_version":"1.0"},"canonical_sha256":"05a35ef62bbbbc755d59bd4cb056ffd1b8ac59e163ce0e84c54eedf213ab58c5","source":{"kind":"arxiv","id":"1803.07579","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07579","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07579v3","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07579","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"AWRV55RLXO6H","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AWRV55RLXO6HKXKZ","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AWRV55RL","created_at":"2026-05-18T12:32:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:AWRV55RLXO6HKXKZXVGLAVX72G","target":"record","payload":{"canonical_record":{"source":{"id":"1803.07579","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-20T18:09:32Z","cross_cats_sorted":[],"title_canon_sha256":"65a06bea6d4ed1ce771a5b5f88db9bd405a04cc1b56b58829e5a905028bbb59b","abstract_canon_sha256":"6ad2f6beb66d8fcfabee62d6c78c1d717e5da01231309c662cd7427835535e4e"},"schema_version":"1.0"},"canonical_sha256":"05a35ef62bbbbc755d59bd4cb056ffd1b8ac59e163ce0e84c54eedf213ab58c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:04.769627Z","signature_b64":"/WQIV0JQkQz6ZaQocmKMAY6izQNZOmlzTAqBvwZiP68AQpmod7tfLHUKp0U5GxNETcUh7O8wlSCKfDhFEKilCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05a35ef62bbbbc755d59bd4cb056ffd1b8ac59e163ce0e84c54eedf213ab58c5","last_reissued_at":"2026-05-18T00:15:04.769048Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:04.769048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.07579","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cUUw3VchbKgVz0MixI9DmzgtCGAuNvMHtNgtGhCj1BFecMKo84K89PEVooufQdTcM7zvWEaqHi7wEBJlVp/WCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:35:59.362378Z"},"content_sha256":"1eacfca1839b279cc07d33db8c67c6d57e15e38f746b92019b1e81489070f129","schema_version":"1.0","event_id":"sha256:1eacfca1839b279cc07d33db8c67c6d57e15e38f746b92019b1e81489070f129"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:AWRV55RLXO6HKXKZXVGLAVX72G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Schrodinger-Maxwell systems on compact Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Csaba Farkas","submitted_at":"2018-03-20T18:09:32Z","abstract_excerpt":"In this paper we are focusing to the following Schr\\\"odinger-Maxwell system $(\\mathcal{SM}_{\\Psi(\\lambda,\\cdot)}^{e})$:\n  \\[ \\begin{cases} -\\Delta_{g}u+\\beta(x)u+eu\\phi=\\Psi(\\lambda,x)f(u) & \\mathrm{in}\\ M -\\Delta_{g}\\phi+\\phi=qu^{2} & \\mathrm{\\mathrm{in}\\ M} \\end{cases} \\] where $(M,g)$ is a 3-dimensional compact Riemannian manifold without boundary, $e,q>0$ are positive numbers, $f:\\mathbb{R}\\to\\mathbb{R}$ is a continuous function, $\\beta\\in C^{\\infty}(M)$ and $\\Psi\\in C^{\\infty}(\\mathbb{R}_{+}\\times M)$ are positive functions. By various variational approaches, existence of multiple solutio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07579","kind":"arxiv","version":3},"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":"2026-05-18T00:15:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rNamkXG3EL2HIEPbVfZ34wZ6QK4RNXoNyBMt+oHp5WbkmDdG56lL2nzviqG8wvABnN7jQSIH+IO1O2eYC3yzBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T05:35:59.362727Z"},"content_sha256":"788c95c89997938f786cd774fd6665ebe89ce455dd5d6bf7347eae2add045a23","schema_version":"1.0","event_id":"sha256:788c95c89997938f786cd774fd6665ebe89ce455dd5d6bf7347eae2add045a23"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWRV55RLXO6HKXKZXVGLAVX72G/bundle.json","state_url":"https://pith.science/pith/AWRV55RLXO6HKXKZXVGLAVX72G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWRV55RLXO6HKXKZXVGLAVX72G/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":"2026-06-20T05:35:59Z","links":{"resolver":"https://pith.science/pith/AWRV55RLXO6HKXKZXVGLAVX72G","bundle":"https://pith.science/pith/AWRV55RLXO6HKXKZXVGLAVX72G/bundle.json","state":"https://pith.science/pith/AWRV55RLXO6HKXKZXVGLAVX72G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWRV55RLXO6HKXKZXVGLAVX72G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:AWRV55RLXO6HKXKZXVGLAVX72G","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":"6ad2f6beb66d8fcfabee62d6c78c1d717e5da01231309c662cd7427835535e4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-20T18:09:32Z","title_canon_sha256":"65a06bea6d4ed1ce771a5b5f88db9bd405a04cc1b56b58829e5a905028bbb59b"},"schema_version":"1.0","source":{"id":"1803.07579","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.07579","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"arxiv_version","alias_value":"1803.07579v3","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.07579","created_at":"2026-05-18T00:15:04Z"},{"alias_kind":"pith_short_12","alias_value":"AWRV55RLXO6H","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_16","alias_value":"AWRV55RLXO6HKXKZ","created_at":"2026-05-18T12:32:13Z"},{"alias_kind":"pith_short_8","alias_value":"AWRV55RL","created_at":"2026-05-18T12:32:13Z"}],"graph_snapshots":[{"event_id":"sha256:788c95c89997938f786cd774fd6665ebe89ce455dd5d6bf7347eae2add045a23","target":"graph","created_at":"2026-05-18T00:15:04Z","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":"In this paper we are focusing to the following Schr\\\"odinger-Maxwell system $(\\mathcal{SM}_{\\Psi(\\lambda,\\cdot)}^{e})$:\n  \\[ \\begin{cases} -\\Delta_{g}u+\\beta(x)u+eu\\phi=\\Psi(\\lambda,x)f(u) & \\mathrm{in}\\ M -\\Delta_{g}\\phi+\\phi=qu^{2} & \\mathrm{\\mathrm{in}\\ M} \\end{cases} \\] where $(M,g)$ is a 3-dimensional compact Riemannian manifold without boundary, $e,q>0$ are positive numbers, $f:\\mathbb{R}\\to\\mathbb{R}$ is a continuous function, $\\beta\\in C^{\\infty}(M)$ and $\\Psi\\in C^{\\infty}(\\mathbb{R}_{+}\\times M)$ are positive functions. By various variational approaches, existence of multiple solutio","authors_text":"Csaba Farkas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-20T18:09:32Z","title":"Schrodinger-Maxwell systems on compact Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07579","kind":"arxiv","version":3},"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":"sha256:1eacfca1839b279cc07d33db8c67c6d57e15e38f746b92019b1e81489070f129","target":"record","created_at":"2026-05-18T00:15:04Z","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":"6ad2f6beb66d8fcfabee62d6c78c1d717e5da01231309c662cd7427835535e4e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-20T18:09:32Z","title_canon_sha256":"65a06bea6d4ed1ce771a5b5f88db9bd405a04cc1b56b58829e5a905028bbb59b"},"schema_version":"1.0","source":{"id":"1803.07579","kind":"arxiv","version":3}},"canonical_sha256":"05a35ef62bbbbc755d59bd4cb056ffd1b8ac59e163ce0e84c54eedf213ab58c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05a35ef62bbbbc755d59bd4cb056ffd1b8ac59e163ce0e84c54eedf213ab58c5","first_computed_at":"2026-05-18T00:15:04.769048Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:04.769048Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/WQIV0JQkQz6ZaQocmKMAY6izQNZOmlzTAqBvwZiP68AQpmod7tfLHUKp0U5GxNETcUh7O8wlSCKfDhFEKilCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:04.769627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.07579","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1eacfca1839b279cc07d33db8c67c6d57e15e38f746b92019b1e81489070f129","sha256:788c95c89997938f786cd774fd6665ebe89ce455dd5d6bf7347eae2add045a23"],"state_sha256":"5d16df96680f9189cd06f06ce0cf907e6da46b32b0934c9957995bf19f4a9eeb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZW2WeKDlfGIdiDFbPmbEiE78rpWXxl7dUE0dg2+0nuioord7U35fEvIX6R55K7J84oIGyVERmUQpUpCejjPjBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T05:35:59.364644Z","bundle_sha256":"967cd36d4d9488eaa39067ceefe0cbb6efa649cc1b20f6f66237440e77c77954"}}