{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:QHQ7O4GKUII5US62CRGNNQOONB","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":"9a775818ebbdb96b76636284d47a4a695886d366d04851c5b78e8c664b55a941","cross_cats_sorted":["q-bio.PE","q-fin.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-16T11:31:05Z","title_canon_sha256":"20f9191b6cfd3679f02ceb3ed2429cb42bad1407f8bcecd434a80e236970622f"},"schema_version":"1.0","source":{"id":"1302.3958","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.3958","created_at":"2026-05-18T03:33:24Z"},{"alias_kind":"arxiv_version","alias_value":"1302.3958v1","created_at":"2026-05-18T03:33:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.3958","created_at":"2026-05-18T03:33:24Z"},{"alias_kind":"pith_short_12","alias_value":"QHQ7O4GKUII5","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"QHQ7O4GKUII5US62","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"QHQ7O4GK","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:cf26c650517f99a5f37441f2ba718bbb82ecac4787c5996b6c5d10a30b019e05","target":"graph","created_at":"2026-05-18T03:33:24Z","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":"This paper deals with the stability properties of a closed market, where capital and labour force are acting like a predator-prey system in population-dynamics. The spatial movement of the capital and labour force are taken into account by cross-diffusion effect. First, we are showing two possible ways for modeling this system in only one country's market (applying a simple functional response and a Holling-type ratio-dependent response as well), examining the conditions of their stability properties. We extend the ratio-dependent model into two countries common market where two kind of cross-","authors_text":"Krisztina Kiss, Laszlo Balazsi","cross_cats":["q-bio.PE","q-fin.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-16T11:31:05Z","title":"Cross-diffusion Modeling in Macroeconomics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.3958","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":"sha256:15bb16c3d84f0e65f3ba4058e9e4a4be0c08b7da38562d993631b6cb7b74f06c","target":"record","created_at":"2026-05-18T03:33:24Z","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":"9a775818ebbdb96b76636284d47a4a695886d366d04851c5b78e8c664b55a941","cross_cats_sorted":["q-bio.PE","q-fin.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-02-16T11:31:05Z","title_canon_sha256":"20f9191b6cfd3679f02ceb3ed2429cb42bad1407f8bcecd434a80e236970622f"},"schema_version":"1.0","source":{"id":"1302.3958","kind":"arxiv","version":1}},"canonical_sha256":"81e1f770caa211da4bda144cd6c1ce68763a1926d8dbd42958e29c332a563fef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81e1f770caa211da4bda144cd6c1ce68763a1926d8dbd42958e29c332a563fef","first_computed_at":"2026-05-18T03:33:24.773872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:24.773872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aRDWO/QBvXcocyje3VI7HWBlXygVPt7nGaVyTpf7OYjhKmitWO5lthxOt2ZRhB8bqjz9kRqS3e5JlwZZdkxfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:24.774591Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.3958","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15bb16c3d84f0e65f3ba4058e9e4a4be0c08b7da38562d993631b6cb7b74f06c","sha256:cf26c650517f99a5f37441f2ba718bbb82ecac4787c5996b6c5d10a30b019e05"],"state_sha256":"f8612a60ff96bbceae734284a385fc7f68ef5aa0ebec6faba4fa6673ee654443"}