{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MZQZXSPGKY3UFXJXA6SC4VJAJZ","short_pith_number":"pith:MZQZXSPG","canonical_record":{"source":{"id":"1701.02619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-10T14:51:37Z","cross_cats_sorted":[],"title_canon_sha256":"b5a833f207e23f7bf7519e9d488666d47c6e428aff27f08469d298e51edb062b","abstract_canon_sha256":"4dca74f21e13f99bfd28eace2f6363b2406b6cd4719f482ba1d0c4b6adb9bd6c"},"schema_version":"1.0"},"canonical_sha256":"66619bc9e6563742dd3707a42e55204e5e33d7551b82aa1b4c49b447d79b224f","source":{"kind":"arxiv","id":"1701.02619","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02619","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02619v1","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02619","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"MZQZXSPGKY3U","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MZQZXSPGKY3UFXJX","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MZQZXSPG","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MZQZXSPGKY3UFXJXA6SC4VJAJZ","target":"record","payload":{"canonical_record":{"source":{"id":"1701.02619","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-10T14:51:37Z","cross_cats_sorted":[],"title_canon_sha256":"b5a833f207e23f7bf7519e9d488666d47c6e428aff27f08469d298e51edb062b","abstract_canon_sha256":"4dca74f21e13f99bfd28eace2f6363b2406b6cd4719f482ba1d0c4b6adb9bd6c"},"schema_version":"1.0"},"canonical_sha256":"66619bc9e6563742dd3707a42e55204e5e33d7551b82aa1b4c49b447d79b224f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:03.828711Z","signature_b64":"Ed15Irf3OG2rjOrZa257VR8lU7b8RH/6c1oEA8rVixQbcqe2nPdAUvfIqE8Dw31rGhQ/GkBkcLU/34dWewwZCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"66619bc9e6563742dd3707a42e55204e5e33d7551b82aa1b4c49b447d79b224f","last_reissued_at":"2026-05-18T00:53:03.828020Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:03.828020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.02619","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":"2026-05-18T00:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nwNILUUAjrgHcSHYAKGgAE0XDngvG2vFWnbjXJS0refyYsmVxpU18duOEGbD5k/H2vBBgKm+i2oGfOHO9gXEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T20:10:05.146692Z"},"content_sha256":"f43db60db7aafd23bd6ad3eb61dd08d2a4a013da6f58c2067cf3da706b3184a1","schema_version":"1.0","event_id":"sha256:f43db60db7aafd23bd6ad3eb61dd08d2a4a013da6f58c2067cf3da706b3184a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MZQZXSPGKY3UFXJXA6SC4VJAJZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stationary patterns of a diffusive predator-prey model with Crowley-Martin functional response","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jinzhu Yu, Junjie Wei, Shanshan Chen","submitted_at":"2017-01-10T14:51:37Z","abstract_excerpt":"A diffusive predator-prey system with predator interference and Neumann boundary conditions is considered in this paper. We derive some results on the existence and nonexistence of nonconstant stationary solutions. It is shown that there exist no nonconstant stationary solutions when the effect of the predator interference is strong or the conversion rate of the predator is large, and nonconstant stationary solutions emerge when the diffusion rate of the predator is large."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02619","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":"2026-05-18T00:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jOZqTUNV0x7EVVX9cBkyknKDwE/1RsuKuY5v5Njgagpyf/OWSNMfc5OSN3GKruQj3zpPLRtVs7Nc3uHOEA5OCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T20:10:05.147375Z"},"content_sha256":"152d3ca473b17b92d6ffe8497558d9403ff1b23e141a9cb587a6dc02632d63d0","schema_version":"1.0","event_id":"sha256:152d3ca473b17b92d6ffe8497558d9403ff1b23e141a9cb587a6dc02632d63d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MZQZXSPGKY3UFXJXA6SC4VJAJZ/bundle.json","state_url":"https://pith.science/pith/MZQZXSPGKY3UFXJXA6SC4VJAJZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MZQZXSPGKY3UFXJXA6SC4VJAJZ/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":"2026-05-19T20:10:05Z","links":{"resolver":"https://pith.science/pith/MZQZXSPGKY3UFXJXA6SC4VJAJZ","bundle":"https://pith.science/pith/MZQZXSPGKY3UFXJXA6SC4VJAJZ/bundle.json","state":"https://pith.science/pith/MZQZXSPGKY3UFXJXA6SC4VJAJZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MZQZXSPGKY3UFXJXA6SC4VJAJZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MZQZXSPGKY3UFXJXA6SC4VJAJZ","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":"4dca74f21e13f99bfd28eace2f6363b2406b6cd4719f482ba1d0c4b6adb9bd6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-10T14:51:37Z","title_canon_sha256":"b5a833f207e23f7bf7519e9d488666d47c6e428aff27f08469d298e51edb062b"},"schema_version":"1.0","source":{"id":"1701.02619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.02619","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"1701.02619v1","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.02619","created_at":"2026-05-18T00:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"MZQZXSPGKY3U","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MZQZXSPGKY3UFXJX","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MZQZXSPG","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:152d3ca473b17b92d6ffe8497558d9403ff1b23e141a9cb587a6dc02632d63d0","target":"graph","created_at":"2026-05-18T00:53:03Z","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":"A diffusive predator-prey system with predator interference and Neumann boundary conditions is considered in this paper. We derive some results on the existence and nonexistence of nonconstant stationary solutions. It is shown that there exist no nonconstant stationary solutions when the effect of the predator interference is strong or the conversion rate of the predator is large, and nonconstant stationary solutions emerge when the diffusion rate of the predator is large.","authors_text":"Jinzhu Yu, Junjie Wei, Shanshan Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-10T14:51:37Z","title":"Stationary patterns of a diffusive predator-prey model with Crowley-Martin functional response"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.02619","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:f43db60db7aafd23bd6ad3eb61dd08d2a4a013da6f58c2067cf3da706b3184a1","target":"record","created_at":"2026-05-18T00:53:03Z","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":"4dca74f21e13f99bfd28eace2f6363b2406b6cd4719f482ba1d0c4b6adb9bd6c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-10T14:51:37Z","title_canon_sha256":"b5a833f207e23f7bf7519e9d488666d47c6e428aff27f08469d298e51edb062b"},"schema_version":"1.0","source":{"id":"1701.02619","kind":"arxiv","version":1}},"canonical_sha256":"66619bc9e6563742dd3707a42e55204e5e33d7551b82aa1b4c49b447d79b224f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"66619bc9e6563742dd3707a42e55204e5e33d7551b82aa1b4c49b447d79b224f","first_computed_at":"2026-05-18T00:53:03.828020Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:03.828020Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ed15Irf3OG2rjOrZa257VR8lU7b8RH/6c1oEA8rVixQbcqe2nPdAUvfIqE8Dw31rGhQ/GkBkcLU/34dWewwZCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:03.828711Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.02619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f43db60db7aafd23bd6ad3eb61dd08d2a4a013da6f58c2067cf3da706b3184a1","sha256:152d3ca473b17b92d6ffe8497558d9403ff1b23e141a9cb587a6dc02632d63d0"],"state_sha256":"064ac960fcf10fb91a5dee5dd4ed7e89b2ae3badc8b8ac7cbe5669f522cd8e4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9OvGlXdI7bT7NcYJUiQyC6QeSl022MMu47rdxD07aZLAkINMtoy541iD0vLu6UBrGETze4rjwBvH5CZfGfqqAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T20:10:05.150630Z","bundle_sha256":"b96c746b15f85f73d195226d3e29f0db7bbb30f4e2d963d54c5731dbcabc870c"}}