{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CAT7MHAENLXXJNELIJ7F222KZ5","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":"b67986df60b21337810f75d8390566c51cb3cb04f3061d84f5a50adef012a6a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-11T08:42:54Z","title_canon_sha256":"790e776a3037bb8be64355b2fa76bca4268c77c5f5c44088e52f9cbb3dfcc6e5"},"schema_version":"1.0","source":{"id":"1901.03510","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.03510","created_at":"2026-05-17T23:56:31Z"},{"alias_kind":"arxiv_version","alias_value":"1901.03510v1","created_at":"2026-05-17T23:56:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.03510","created_at":"2026-05-17T23:56:31Z"},{"alias_kind":"pith_short_12","alias_value":"CAT7MHAENLXX","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"CAT7MHAENLXXJNEL","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"CAT7MHAE","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:03fbea095ca8a544bbe2b34a588b9b3b851d50650eedec0604f7a0b40c36adf2","target":"graph","created_at":"2026-05-17T23:56:31Z","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":"Combining the results of a recent paper by Fleckinger-Hernandez-deTh{\\'e}lin [14] for a non cooperative $2\\times2$ system with the method of PhD Thesis of MH Lecureux we compute the sign of the solutions of a $n\\times n$ non-cooperative systems when the parameter varies near the lowest principal eigenvalue of the system.","authors_text":"B\\'en\\'edicte Alziary (IMT), Jacqueline Fleckinger (IMT)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-11T08:42:54Z","title":"Sign of the solution to a non-cooperative system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.03510","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":"sha256:4026b7205093006d2f9164db6cbb071f6df2afd3dfa6562cdd1bdf6a7480b8fe","target":"record","created_at":"2026-05-17T23:56:31Z","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":"b67986df60b21337810f75d8390566c51cb3cb04f3061d84f5a50adef012a6a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-11T08:42:54Z","title_canon_sha256":"790e776a3037bb8be64355b2fa76bca4268c77c5f5c44088e52f9cbb3dfcc6e5"},"schema_version":"1.0","source":{"id":"1901.03510","kind":"arxiv","version":1}},"canonical_sha256":"1027f61c046aef74b48b427e5d6b4acf424f750ea5933944c3586e1aa1b5fcf9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1027f61c046aef74b48b427e5d6b4acf424f750ea5933944c3586e1aa1b5fcf9","first_computed_at":"2026-05-17T23:56:31.059613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:31.059613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xdr9KCsviI801BEvuLIAmpMiawaeXWIHe9SqIHTyikIgLlXbe/Fkkm8iXtEGEU4ebsGj2LPlIEu0Ji/2uJ8yDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:31.060043Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.03510","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4026b7205093006d2f9164db6cbb071f6df2afd3dfa6562cdd1bdf6a7480b8fe","sha256:03fbea095ca8a544bbe2b34a588b9b3b851d50650eedec0604f7a0b40c36adf2"],"state_sha256":"76bc3aa2f0923ed200e743a062ab9576b934daa7539cf54d8b7470d108c75f32"}