{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:64WIVRYUKD74VOPNXEHSZ7QLIG","short_pith_number":"pith:64WIVRYU","canonical_record":{"source":{"id":"1907.02312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-04T10:07:10Z","cross_cats_sorted":[],"title_canon_sha256":"e142180fdbd3e351cbeefb435513866e9af62540e4813311fe7f9375c0b78b01","abstract_canon_sha256":"ae3c8664c955f382022cab2a73c94525dceabf117be68f00d92a9c5a4fb5c862"},"schema_version":"1.0"},"canonical_sha256":"f72c8ac71450ffcab9edb90f2cfe0b41af0fbd197ce5bf5a4910c06ca3db41d8","source":{"kind":"arxiv","id":"1907.02312","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02312","created_at":"2026-05-17T23:41:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02312v1","created_at":"2026-05-17T23:41:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02312","created_at":"2026-05-17T23:41:29Z"},{"alias_kind":"pith_short_12","alias_value":"64WIVRYUKD74","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"64WIVRYUKD74VOPN","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"64WIVRYU","created_at":"2026-05-18T12:33:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:64WIVRYUKD74VOPNXEHSZ7QLIG","target":"record","payload":{"canonical_record":{"source":{"id":"1907.02312","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-04T10:07:10Z","cross_cats_sorted":[],"title_canon_sha256":"e142180fdbd3e351cbeefb435513866e9af62540e4813311fe7f9375c0b78b01","abstract_canon_sha256":"ae3c8664c955f382022cab2a73c94525dceabf117be68f00d92a9c5a4fb5c862"},"schema_version":"1.0"},"canonical_sha256":"f72c8ac71450ffcab9edb90f2cfe0b41af0fbd197ce5bf5a4910c06ca3db41d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:29.035847Z","signature_b64":"Zkq3om8yO0wjpsISYaVa6DnXP92XpNwYPnm/vJRhM+QWRUHEM9/f0aper10WoL/iWaUA9hNZAVOijvmkDIEPDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f72c8ac71450ffcab9edb90f2cfe0b41af0fbd197ce5bf5a4910c06ca3db41d8","last_reissued_at":"2026-05-17T23:41:29.035187Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:29.035187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.02312","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:41:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IxuTKhIintNQUAyI5oEF7/i8UexYWdViERUyHTSIg52hMuRjjBYZhhe7tw36MuvvLubF5woEUmqSVkecuVtJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:55:54.823974Z"},"content_sha256":"9a4e696d32e257c5955f99939d7759d760b73dec68980b051829966a2f10f6c3","schema_version":"1.0","event_id":"sha256:9a4e696d32e257c5955f99939d7759d760b73dec68980b051829966a2f10f6c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:64WIVRYUKD74VOPNXEHSZ7QLIG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global dynamics and spatio-temporal patterns of predator-prey systems with density-dependent motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hai-Yang Jin, Zhi-An Wang","submitted_at":"2019-07-04T10:07:10Z","abstract_excerpt":"In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator-prey systems with density-dependent preytaxis in a two-dimensional bounded domain with Neumann boundary conditions, where the coefficients of motility (diffusion) and mobility (preytaxis) of the predator are correlated through a prey density dependent motility function. We establish the existence of classical solutions with uniform-in time bound and the global stability of the spatially homogeneous prey-only steady states and coexistence steady states under certain conditions on paramet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02312","kind":"arxiv","version":1},"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":"2026-05-17T23:41:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1/zYjhdPEDsCYoOwcjtXNXglJSmfy2qfMoojSn1zih7PdeyjmiuevU0wUb7c0ChfmrYjmOw/c5u9FNMIJP7uDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:55:54.824330Z"},"content_sha256":"e0d8879b646816d674f547fb7daa5785330f87ad376674ddb2ed2a09253030d1","schema_version":"1.0","event_id":"sha256:e0d8879b646816d674f547fb7daa5785330f87ad376674ddb2ed2a09253030d1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64WIVRYUKD74VOPNXEHSZ7QLIG/bundle.json","state_url":"https://pith.science/pith/64WIVRYUKD74VOPNXEHSZ7QLIG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64WIVRYUKD74VOPNXEHSZ7QLIG/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":"2026-06-23T14:55:54Z","links":{"resolver":"https://pith.science/pith/64WIVRYUKD74VOPNXEHSZ7QLIG","bundle":"https://pith.science/pith/64WIVRYUKD74VOPNXEHSZ7QLIG/bundle.json","state":"https://pith.science/pith/64WIVRYUKD74VOPNXEHSZ7QLIG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64WIVRYUKD74VOPNXEHSZ7QLIG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:64WIVRYUKD74VOPNXEHSZ7QLIG","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":"ae3c8664c955f382022cab2a73c94525dceabf117be68f00d92a9c5a4fb5c862","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-04T10:07:10Z","title_canon_sha256":"e142180fdbd3e351cbeefb435513866e9af62540e4813311fe7f9375c0b78b01"},"schema_version":"1.0","source":{"id":"1907.02312","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.02312","created_at":"2026-05-17T23:41:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.02312v1","created_at":"2026-05-17T23:41:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02312","created_at":"2026-05-17T23:41:29Z"},{"alias_kind":"pith_short_12","alias_value":"64WIVRYUKD74","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_16","alias_value":"64WIVRYUKD74VOPN","created_at":"2026-05-18T12:33:10Z"},{"alias_kind":"pith_short_8","alias_value":"64WIVRYU","created_at":"2026-05-18T12:33:10Z"}],"graph_snapshots":[{"event_id":"sha256:e0d8879b646816d674f547fb7daa5785330f87ad376674ddb2ed2a09253030d1","target":"graph","created_at":"2026-05-17T23:41:29Z","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":"In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator-prey systems with density-dependent preytaxis in a two-dimensional bounded domain with Neumann boundary conditions, where the coefficients of motility (diffusion) and mobility (preytaxis) of the predator are correlated through a prey density dependent motility function. We establish the existence of classical solutions with uniform-in time bound and the global stability of the spatially homogeneous prey-only steady states and coexistence steady states under certain conditions on paramet","authors_text":"Hai-Yang Jin, Zhi-An Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-04T10:07:10Z","title":"Global dynamics and spatio-temporal patterns of predator-prey systems with density-dependent motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02312","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":"sha256:9a4e696d32e257c5955f99939d7759d760b73dec68980b051829966a2f10f6c3","target":"record","created_at":"2026-05-17T23:41:29Z","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":"ae3c8664c955f382022cab2a73c94525dceabf117be68f00d92a9c5a4fb5c862","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-04T10:07:10Z","title_canon_sha256":"e142180fdbd3e351cbeefb435513866e9af62540e4813311fe7f9375c0b78b01"},"schema_version":"1.0","source":{"id":"1907.02312","kind":"arxiv","version":1}},"canonical_sha256":"f72c8ac71450ffcab9edb90f2cfe0b41af0fbd197ce5bf5a4910c06ca3db41d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f72c8ac71450ffcab9edb90f2cfe0b41af0fbd197ce5bf5a4910c06ca3db41d8","first_computed_at":"2026-05-17T23:41:29.035187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:41:29.035187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zkq3om8yO0wjpsISYaVa6DnXP92XpNwYPnm/vJRhM+QWRUHEM9/f0aper10WoL/iWaUA9hNZAVOijvmkDIEPDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:41:29.035847Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.02312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a4e696d32e257c5955f99939d7759d760b73dec68980b051829966a2f10f6c3","sha256:e0d8879b646816d674f547fb7daa5785330f87ad376674ddb2ed2a09253030d1"],"state_sha256":"181ae04aec070fe674d39c86098e9ee678fb18f3e1b19d4eefce1cc219dfcede"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UTr1TO9aadFbExIj0RclL5XDrnx3yHL5rJ1iim1e3D/jmkAhZRsmvSELnYtDqxBsvMAaw0K/XgFzV/x0O/lXBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:55:54.826238Z","bundle_sha256":"554f56a72196866fb1aea6516049e5c69a36b88ccc847f55096013302446ea39"}}