{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:IDYMTL24ABD454TREDPO7AEJCG","short_pith_number":"pith:IDYMTL24","canonical_record":{"source":{"id":"1905.05244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2019-05-13T19:04:03Z","cross_cats_sorted":["math.DS","nlin.AO"],"title_canon_sha256":"3f8a3ae8287683edf22619af747f4da598130d9a16795110f77de1899598dd4f","abstract_canon_sha256":"3eb111b7a6f37a423dc6a2066fa24b6d2c712d1bc1704ac00c2fe6c17104a0b5"},"schema_version":"1.0"},"canonical_sha256":"40f0c9af5c0047cef27120deef808911af19d68690dba7e1ecf633d04a0e1c0e","source":{"kind":"arxiv","id":"1905.05244","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05244","created_at":"2026-05-17T23:46:17Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05244v1","created_at":"2026-05-17T23:46:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05244","created_at":"2026-05-17T23:46:17Z"},{"alias_kind":"pith_short_12","alias_value":"IDYMTL24ABD4","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IDYMTL24ABD454TR","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IDYMTL24","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:IDYMTL24ABD454TREDPO7AEJCG","target":"record","payload":{"canonical_record":{"source":{"id":"1905.05244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2019-05-13T19:04:03Z","cross_cats_sorted":["math.DS","nlin.AO"],"title_canon_sha256":"3f8a3ae8287683edf22619af747f4da598130d9a16795110f77de1899598dd4f","abstract_canon_sha256":"3eb111b7a6f37a423dc6a2066fa24b6d2c712d1bc1704ac00c2fe6c17104a0b5"},"schema_version":"1.0"},"canonical_sha256":"40f0c9af5c0047cef27120deef808911af19d68690dba7e1ecf633d04a0e1c0e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:17.068420Z","signature_b64":"HgVN82xKLDhu5LKrjOPLuYpqnfbfuTlAupDniPbneVqggYkTOsyJiby0NwVokDRZIKLk18IRcc0bBFQwSXHrAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40f0c9af5c0047cef27120deef808911af19d68690dba7e1ecf633d04a0e1c0e","last_reissued_at":"2026-05-17T23:46:17.067796Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:17.067796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.05244","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":"2026-05-17T23:46:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yraeoZupv/XPm0ZkeQbbphIo7cd1BRZjy/lbyWR/bajWBbq0ym4i+3uZZEkaFvOu+6rIKrSvDhO2sa1yD916Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T14:40:53.470651Z"},"content_sha256":"231df9a72dc4a6aac526ff38d9a266473e061718fbb203b101432812ca9d2927","schema_version":"1.0","event_id":"sha256:231df9a72dc4a6aac526ff38d9a266473e061718fbb203b101432812ca9d2927"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:IDYMTL24ABD454TREDPO7AEJCG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Aphids, Ants and Ladybirds: a mathematical model predicting their population dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","nlin.AO"],"primary_cat":"q-bio.PE","authors_text":"Gianluca Gabbriellini","submitted_at":"2019-05-13T19:04:03Z","abstract_excerpt":"The interaction between aphids, ants and ladybirds has been investigated from an ecological point of view since many decades, while there are no attempts to describe it from a mathematical point of view. This paper introduces a new mathematical model to describe the within-season population dynamics in an ecological patch of a system composed by aphids, ants and ladybirds, through a set of four differential equations. The proposed model is based on the Kindlmann and Dixon set of differential equations, focused on the prediction of the aphids-ladybirds population densities, that share a prey-pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05244","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":"2026-05-17T23:46:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"psNFSZSiT+Cr/HTczBvAUBSADeCW8f++19INtKLyynEdg9knD1LRMLrW5VQLaPEVH1iBnfD07sJhYg0dIFXkAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T14:40:53.470989Z"},"content_sha256":"eb0681f1512068f8987bf39a048f9d63970daba8c911eff9b0f37e02f2d40146","schema_version":"1.0","event_id":"sha256:eb0681f1512068f8987bf39a048f9d63970daba8c911eff9b0f37e02f2d40146"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IDYMTL24ABD454TREDPO7AEJCG/bundle.json","state_url":"https://pith.science/pith/IDYMTL24ABD454TREDPO7AEJCG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IDYMTL24ABD454TREDPO7AEJCG/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":"2026-07-01T14:40:53Z","links":{"resolver":"https://pith.science/pith/IDYMTL24ABD454TREDPO7AEJCG","bundle":"https://pith.science/pith/IDYMTL24ABD454TREDPO7AEJCG/bundle.json","state":"https://pith.science/pith/IDYMTL24ABD454TREDPO7AEJCG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IDYMTL24ABD454TREDPO7AEJCG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:IDYMTL24ABD454TREDPO7AEJCG","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":"3eb111b7a6f37a423dc6a2066fa24b6d2c712d1bc1704ac00c2fe6c17104a0b5","cross_cats_sorted":["math.DS","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2019-05-13T19:04:03Z","title_canon_sha256":"3f8a3ae8287683edf22619af747f4da598130d9a16795110f77de1899598dd4f"},"schema_version":"1.0","source":{"id":"1905.05244","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.05244","created_at":"2026-05-17T23:46:17Z"},{"alias_kind":"arxiv_version","alias_value":"1905.05244v1","created_at":"2026-05-17T23:46:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.05244","created_at":"2026-05-17T23:46:17Z"},{"alias_kind":"pith_short_12","alias_value":"IDYMTL24ABD4","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"IDYMTL24ABD454TR","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"IDYMTL24","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:eb0681f1512068f8987bf39a048f9d63970daba8c911eff9b0f37e02f2d40146","target":"graph","created_at":"2026-05-17T23:46:17Z","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":"The interaction between aphids, ants and ladybirds has been investigated from an ecological point of view since many decades, while there are no attempts to describe it from a mathematical point of view. This paper introduces a new mathematical model to describe the within-season population dynamics in an ecological patch of a system composed by aphids, ants and ladybirds, through a set of four differential equations. The proposed model is based on the Kindlmann and Dixon set of differential equations, focused on the prediction of the aphids-ladybirds population densities, that share a prey-pr","authors_text":"Gianluca Gabbriellini","cross_cats":["math.DS","nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2019-05-13T19:04:03Z","title":"Aphids, Ants and Ladybirds: a mathematical model predicting their population dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.05244","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":"sha256:231df9a72dc4a6aac526ff38d9a266473e061718fbb203b101432812ca9d2927","target":"record","created_at":"2026-05-17T23:46:17Z","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":"3eb111b7a6f37a423dc6a2066fa24b6d2c712d1bc1704ac00c2fe6c17104a0b5","cross_cats_sorted":["math.DS","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2019-05-13T19:04:03Z","title_canon_sha256":"3f8a3ae8287683edf22619af747f4da598130d9a16795110f77de1899598dd4f"},"schema_version":"1.0","source":{"id":"1905.05244","kind":"arxiv","version":1}},"canonical_sha256":"40f0c9af5c0047cef27120deef808911af19d68690dba7e1ecf633d04a0e1c0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40f0c9af5c0047cef27120deef808911af19d68690dba7e1ecf633d04a0e1c0e","first_computed_at":"2026-05-17T23:46:17.067796Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:17.067796Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HgVN82xKLDhu5LKrjOPLuYpqnfbfuTlAupDniPbneVqggYkTOsyJiby0NwVokDRZIKLk18IRcc0bBFQwSXHrAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:17.068420Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.05244","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:231df9a72dc4a6aac526ff38d9a266473e061718fbb203b101432812ca9d2927","sha256:eb0681f1512068f8987bf39a048f9d63970daba8c911eff9b0f37e02f2d40146"],"state_sha256":"cac19942ccfd95bc92dec2f90fd487167d1d17eb2f1253f0dbc4a89412dd39c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QPesFoVhjAJBJSsuikYfwjDAmckEt7KCRerHnciDSWy8wDm73Y67zZjU2m73Vf/P6CY3M70tOOE7TJQRzzW4AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T14:40:53.472924Z","bundle_sha256":"458f7004d6f905e6f5af08883602c2e367dca12b62e30b08f5f51f5746ab5b02"}}