{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:YCDVMAXHAF7GHNWGUYSQQDWP3F","short_pith_number":"pith:YCDVMAXH","canonical_record":{"source":{"id":"1902.00848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-03T05:16:22Z","cross_cats_sorted":[],"title_canon_sha256":"584da4500d124314328961b4398967c8c686f43816d4f90ef9de48bca85ebb1e","abstract_canon_sha256":"a558c66521ba867d5dea9fc241d6bace06d3fdf3a300681539ae16f9dc5c0847"},"schema_version":"1.0"},"canonical_sha256":"c0875602e7017e63b6c6a625080ecfd95d859944171f23b2fbcae58b448fc5b6","source":{"kind":"arxiv","id":"1902.00848","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00848","created_at":"2026-05-17T23:54:51Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00848v1","created_at":"2026-05-17T23:54:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00848","created_at":"2026-05-17T23:54:51Z"},{"alias_kind":"pith_short_12","alias_value":"YCDVMAXHAF7G","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YCDVMAXHAF7GHNWG","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YCDVMAXH","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:YCDVMAXHAF7GHNWGUYSQQDWP3F","target":"record","payload":{"canonical_record":{"source":{"id":"1902.00848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-03T05:16:22Z","cross_cats_sorted":[],"title_canon_sha256":"584da4500d124314328961b4398967c8c686f43816d4f90ef9de48bca85ebb1e","abstract_canon_sha256":"a558c66521ba867d5dea9fc241d6bace06d3fdf3a300681539ae16f9dc5c0847"},"schema_version":"1.0"},"canonical_sha256":"c0875602e7017e63b6c6a625080ecfd95d859944171f23b2fbcae58b448fc5b6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:51.966883Z","signature_b64":"55osVFlCi2+HeV0q/NkqN6w9UouS7m9oOwVq/qU66974RpdRb09va2jBeAD+dWhriVQMG6GCks0MtUEkSuMtDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0875602e7017e63b6c6a625080ecfd95d859944171f23b2fbcae58b448fc5b6","last_reissued_at":"2026-05-17T23:54:51.966435Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:51.966435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.00848","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":"2026-05-17T23:54:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q8oYR9YV+KobUwIb5VdzlzoVTsPub/DrZyaakvz0EVSB1OeBcY+C3iEOWp4u1hn4u9mDb5co300u+vCTBQRaDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:36:24.703425Z"},"content_sha256":"4542e9844d39c06c86b2ffcb8a0c686c173c125f8930b5651f4ea3ccd92b1adc","schema_version":"1.0","event_id":"sha256:4542e9844d39c06c86b2ffcb8a0c686c173c125f8930b5651f4ea3ccd92b1adc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:YCDVMAXHAF7GHNWGUYSQQDWP3F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of a one-dimensional forager-exploiter model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Michael Winkler, Youshan Tao","submitted_at":"2019-02-03T05:16:22Z","abstract_excerpt":"\\begin{abstract} \\noindent % We consider the one-dimensional parabolic system\n  The system\n  \\bas\n  \\left\\{ \\begin{array}{l}\n  u_t= u_{xx} - \\chi_1 (uw_x)_x, \\\\[1mm]\n  v_t = v_{xx} - \\chi_2 (vu_x)_x, \\\\[1mm]\n  w_t = dw_{xx} - \\lambda (u+v)w - \\mu w + r,\n  \\end{array} \\right.\n  \\eas % that has been proposed as a model to describe social interactions within mixed forager-exploiter groups. is considered in a bounded real interval, with positive parameters $\\chi_1,\\chi_2,d,\\lambda$ and $\\mu$, and with $r \\ge 0$. Proposed to describe social interactions within mixed forager-exploiter groups, this m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00848","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":"2026-05-17T23:54:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OecKNk1eIAXCEpXnlE/M+vzUlrPLIVZQIS3I6Rmw7PPy5+bGIc/9tmgy5Z7Dd+9i6YStHF7qR8QsJJjMpc2nDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:36:24.703776Z"},"content_sha256":"8ce2e4e4fd067d5b5d14f7b5d19b3b862118588304cd4d77e788c2d32ea36581","schema_version":"1.0","event_id":"sha256:8ce2e4e4fd067d5b5d14f7b5d19b3b862118588304cd4d77e788c2d32ea36581"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCDVMAXHAF7GHNWGUYSQQDWP3F/bundle.json","state_url":"https://pith.science/pith/YCDVMAXHAF7GHNWGUYSQQDWP3F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCDVMAXHAF7GHNWGUYSQQDWP3F/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":"2026-06-02T20:36:24Z","links":{"resolver":"https://pith.science/pith/YCDVMAXHAF7GHNWGUYSQQDWP3F","bundle":"https://pith.science/pith/YCDVMAXHAF7GHNWGUYSQQDWP3F/bundle.json","state":"https://pith.science/pith/YCDVMAXHAF7GHNWGUYSQQDWP3F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCDVMAXHAF7GHNWGUYSQQDWP3F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YCDVMAXHAF7GHNWGUYSQQDWP3F","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":"a558c66521ba867d5dea9fc241d6bace06d3fdf3a300681539ae16f9dc5c0847","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-03T05:16:22Z","title_canon_sha256":"584da4500d124314328961b4398967c8c686f43816d4f90ef9de48bca85ebb1e"},"schema_version":"1.0","source":{"id":"1902.00848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.00848","created_at":"2026-05-17T23:54:51Z"},{"alias_kind":"arxiv_version","alias_value":"1902.00848v1","created_at":"2026-05-17T23:54:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.00848","created_at":"2026-05-17T23:54:51Z"},{"alias_kind":"pith_short_12","alias_value":"YCDVMAXHAF7G","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"YCDVMAXHAF7GHNWG","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"YCDVMAXH","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:8ce2e4e4fd067d5b5d14f7b5d19b3b862118588304cd4d77e788c2d32ea36581","target":"graph","created_at":"2026-05-17T23:54:51Z","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":"\\begin{abstract} \\noindent % We consider the one-dimensional parabolic system\n  The system\n  \\bas\n  \\left\\{ \\begin{array}{l}\n  u_t= u_{xx} - \\chi_1 (uw_x)_x, \\\\[1mm]\n  v_t = v_{xx} - \\chi_2 (vu_x)_x, \\\\[1mm]\n  w_t = dw_{xx} - \\lambda (u+v)w - \\mu w + r,\n  \\end{array} \\right.\n  \\eas % that has been proposed as a model to describe social interactions within mixed forager-exploiter groups. is considered in a bounded real interval, with positive parameters $\\chi_1,\\chi_2,d,\\lambda$ and $\\mu$, and with $r \\ge 0$. Proposed to describe social interactions within mixed forager-exploiter groups, this m","authors_text":"Michael Winkler, Youshan Tao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-03T05:16:22Z","title":"Analysis of a one-dimensional forager-exploiter model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.00848","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":"sha256:4542e9844d39c06c86b2ffcb8a0c686c173c125f8930b5651f4ea3ccd92b1adc","target":"record","created_at":"2026-05-17T23:54:51Z","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":"a558c66521ba867d5dea9fc241d6bace06d3fdf3a300681539ae16f9dc5c0847","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-02-03T05:16:22Z","title_canon_sha256":"584da4500d124314328961b4398967c8c686f43816d4f90ef9de48bca85ebb1e"},"schema_version":"1.0","source":{"id":"1902.00848","kind":"arxiv","version":1}},"canonical_sha256":"c0875602e7017e63b6c6a625080ecfd95d859944171f23b2fbcae58b448fc5b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0875602e7017e63b6c6a625080ecfd95d859944171f23b2fbcae58b448fc5b6","first_computed_at":"2026-05-17T23:54:51.966435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:51.966435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"55osVFlCi2+HeV0q/NkqN6w9UouS7m9oOwVq/qU66974RpdRb09va2jBeAD+dWhriVQMG6GCks0MtUEkSuMtDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:51.966883Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.00848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4542e9844d39c06c86b2ffcb8a0c686c173c125f8930b5651f4ea3ccd92b1adc","sha256:8ce2e4e4fd067d5b5d14f7b5d19b3b862118588304cd4d77e788c2d32ea36581"],"state_sha256":"ff1b70e2afb4b57a8e30fdd86253f16142e7a15ffdfa8b4e9feddbdc8d6d5863"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oLFau4VEdEpckl9078eVn/mdoETDyjXkK9ZM3zGuZrf98S+PQj4W0aAw7YwC/CfSoDQBnT5kptkXXUcro6E/Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:36:24.705837Z","bundle_sha256":"eef8178952b0fcf01ed577a2000bc0fa1d090cfbc8475a96bbb280c0ae80ddf6"}}