{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:3CSKBKOHPGKWPRNDYO32OLMRC5","short_pith_number":"pith:3CSKBKOH","canonical_record":{"source":{"id":"1311.1748","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2013-11-07T17:07:55Z","cross_cats_sorted":[],"title_canon_sha256":"a46be4b8a3a92a37cb81e4832c380ced47a18da813d109e3e9b892637d2dc2fd","abstract_canon_sha256":"3010ef6c15e566ea7d14ea353e2ee1239d2f6c53ce80397141346389de02dfc3"},"schema_version":"1.0"},"canonical_sha256":"d8a4a0a9c7799567c5a3c3b7a72d911770707441f6418938f36d128116a99f36","source":{"kind":"arxiv","id":"1311.1748","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1748","created_at":"2026-05-18T02:58:34Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1748v4","created_at":"2026-05-18T02:58:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1748","created_at":"2026-05-18T02:58:34Z"},{"alias_kind":"pith_short_12","alias_value":"3CSKBKOHPGKW","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3CSKBKOHPGKWPRND","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3CSKBKOH","created_at":"2026-05-18T12:27:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:3CSKBKOHPGKWPRNDYO32OLMRC5","target":"record","payload":{"canonical_record":{"source":{"id":"1311.1748","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2013-11-07T17:07:55Z","cross_cats_sorted":[],"title_canon_sha256":"a46be4b8a3a92a37cb81e4832c380ced47a18da813d109e3e9b892637d2dc2fd","abstract_canon_sha256":"3010ef6c15e566ea7d14ea353e2ee1239d2f6c53ce80397141346389de02dfc3"},"schema_version":"1.0"},"canonical_sha256":"d8a4a0a9c7799567c5a3c3b7a72d911770707441f6418938f36d128116a99f36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:34.573107Z","signature_b64":"xjbvWo3hkMqQ/oZvWn45v5gEdNE+43Abn6e7JmiStbOu0jqsWGY2/BRPQtfiO7f7S10vLM7/FPl+xvQYsmyXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8a4a0a9c7799567c5a3c3b7a72d911770707441f6418938f36d128116a99f36","last_reissued_at":"2026-05-18T02:58:34.571675Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:34.571675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.1748","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:58:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jvBLyGSWcU0bkg5KGSJS6M1qtim3i3JEv3d/pe8QCJX8d06d+THWeutMGUypxkYsguP58psOdVGL+7a7bAr4Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T04:26:09.909133Z"},"content_sha256":"6fa96b765c042f97ee86b79fabf6e3685dc74cdd86f84b5d0ba96015a9228d0c","schema_version":"1.0","event_id":"sha256:6fa96b765c042f97ee86b79fabf6e3685dc74cdd86f84b5d0ba96015a9228d0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:3CSKBKOHPGKWPRNDYO32OLMRC5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cross-diffusion driven instability in a predator-prey system with cross-diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"Eleonora Tulumello, Marco Sammartino, Maria Carmela Lombardo","submitted_at":"2013-11-07T17:07:55Z","abstract_excerpt":"In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1748","kind":"arxiv","version":4},"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":"2026-05-18T02:58:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qvi3eVeOdXRAigcAkNKqHS9B3TcH/T8QkVBQUu4KHsrsWYh3Q9TggBy6CIGmA8CLR+V5Qr+t4kXR8QdQVi2/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T04:26:09.909495Z"},"content_sha256":"92aa8788a15a6218911bf31d43865da1de6e3cdb57a229866b345c38c5e5b7f2","schema_version":"1.0","event_id":"sha256:92aa8788a15a6218911bf31d43865da1de6e3cdb57a229866b345c38c5e5b7f2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3CSKBKOHPGKWPRNDYO32OLMRC5/bundle.json","state_url":"https://pith.science/pith/3CSKBKOHPGKWPRNDYO32OLMRC5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3CSKBKOHPGKWPRNDYO32OLMRC5/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":"2026-07-01T04:26:09Z","links":{"resolver":"https://pith.science/pith/3CSKBKOHPGKWPRNDYO32OLMRC5","bundle":"https://pith.science/pith/3CSKBKOHPGKWPRNDYO32OLMRC5/bundle.json","state":"https://pith.science/pith/3CSKBKOHPGKWPRNDYO32OLMRC5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3CSKBKOHPGKWPRNDYO32OLMRC5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3CSKBKOHPGKWPRNDYO32OLMRC5","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":"3010ef6c15e566ea7d14ea353e2ee1239d2f6c53ce80397141346389de02dfc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2013-11-07T17:07:55Z","title_canon_sha256":"a46be4b8a3a92a37cb81e4832c380ced47a18da813d109e3e9b892637d2dc2fd"},"schema_version":"1.0","source":{"id":"1311.1748","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.1748","created_at":"2026-05-18T02:58:34Z"},{"alias_kind":"arxiv_version","alias_value":"1311.1748v4","created_at":"2026-05-18T02:58:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.1748","created_at":"2026-05-18T02:58:34Z"},{"alias_kind":"pith_short_12","alias_value":"3CSKBKOHPGKW","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3CSKBKOHPGKWPRND","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3CSKBKOH","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:92aa8788a15a6218911bf31d43865da1de6e3cdb57a229866b345c38c5e5b7f2","target":"graph","created_at":"2026-05-18T02:58:34Z","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 work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be","authors_text":"Eleonora Tulumello, Marco Sammartino, Maria Carmela Lombardo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2013-11-07T17:07:55Z","title":"Cross-diffusion driven instability in a predator-prey system with cross-diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.1748","kind":"arxiv","version":4},"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":"sha256:6fa96b765c042f97ee86b79fabf6e3685dc74cdd86f84b5d0ba96015a9228d0c","target":"record","created_at":"2026-05-18T02:58:34Z","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":"3010ef6c15e566ea7d14ea353e2ee1239d2f6c53ce80397141346389de02dfc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.PS","submitted_at":"2013-11-07T17:07:55Z","title_canon_sha256":"a46be4b8a3a92a37cb81e4832c380ced47a18da813d109e3e9b892637d2dc2fd"},"schema_version":"1.0","source":{"id":"1311.1748","kind":"arxiv","version":4}},"canonical_sha256":"d8a4a0a9c7799567c5a3c3b7a72d911770707441f6418938f36d128116a99f36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8a4a0a9c7799567c5a3c3b7a72d911770707441f6418938f36d128116a99f36","first_computed_at":"2026-05-18T02:58:34.571675Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:34.571675Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xjbvWo3hkMqQ/oZvWn45v5gEdNE+43Abn6e7JmiStbOu0jqsWGY2/BRPQtfiO7f7S10vLM7/FPl+xvQYsmyXDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:34.573107Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.1748","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6fa96b765c042f97ee86b79fabf6e3685dc74cdd86f84b5d0ba96015a9228d0c","sha256:92aa8788a15a6218911bf31d43865da1de6e3cdb57a229866b345c38c5e5b7f2"],"state_sha256":"2c24c3e57ca846046e07c174a7be60d8199a1d92c392a01eb43f45f2da705e0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8yUeFid5qW7GbvG3yJFsKHrJ7/Z+k24K8EUDCfgAgboKsbiYoSIpYdhAFgGKkiqzz79RqKw3wvimhQLipgajCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T04:26:09.911418Z","bundle_sha256":"24e878c473339696771e2acb709799706b4e15ad36a4b2a02705041db258f7c4"}}