{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:A4KKBIXQCTMJWHLZWB5JSTTBOF","short_pith_number":"pith:A4KKBIXQ","canonical_record":{"source":{"id":"1407.0163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-01T09:50:39Z","cross_cats_sorted":[],"title_canon_sha256":"a16714c54ecf036f0d49bacd749b5372c246ed0528a5e4d939de5b3889a0fc1f","abstract_canon_sha256":"c2da1b70589438d99dd7e1bdcca584e8f0a8f780a9269f591da0b92f8ce476db"},"schema_version":"1.0"},"canonical_sha256":"0714a0a2f014d89b1d79b07a994e61716f4157ed62a42087bcf0ec058e910417","source":{"kind":"arxiv","id":"1407.0163","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0163","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0163v1","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0163","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"A4KKBIXQCTMJ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A4KKBIXQCTMJWHLZ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A4KKBIXQ","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:A4KKBIXQCTMJWHLZWB5JSTTBOF","target":"record","payload":{"canonical_record":{"source":{"id":"1407.0163","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-01T09:50:39Z","cross_cats_sorted":[],"title_canon_sha256":"a16714c54ecf036f0d49bacd749b5372c246ed0528a5e4d939de5b3889a0fc1f","abstract_canon_sha256":"c2da1b70589438d99dd7e1bdcca584e8f0a8f780a9269f591da0b92f8ce476db"},"schema_version":"1.0"},"canonical_sha256":"0714a0a2f014d89b1d79b07a994e61716f4157ed62a42087bcf0ec058e910417","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:34.998231Z","signature_b64":"UbJDWOoSbiCYH8efLK6qtrblHGcpwywjEHQeHoYA/+bXEe/H207JNKDIGyQuBp1vYlFZXt8foSAbd7naYBv2Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0714a0a2f014d89b1d79b07a994e61716f4157ed62a42087bcf0ec058e910417","last_reissued_at":"2026-05-18T02:48:34.997565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:34.997565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1407.0163","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":"2026-05-18T02:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cz/lruWHTJu1x9MjS/16h4kZev3OLGibol/GU5OugOmMyIBrv8Lwy8t1uAwYhMkvW8e046lejDKnCC18pvvmBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T19:48:55.193162Z"},"content_sha256":"7e4f364790d4a3c3a2c49322057b5345790bea8b86394b8b0af6100cc096f658","schema_version":"1.0","event_id":"sha256:7e4f364790d4a3c3a2c49322057b5345790bea8b86394b8b0af6100cc096f658"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:A4KKBIXQCTMJWHLZWB5JSTTBOF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bifurcation curves of a diffusive logistic equation with harvesting orthogonal to the first eigenfunction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mayte P\\'erez-Llanos, Pedro M. Gir\\~ao","submitted_at":"2014-07-01T09:50:39Z","abstract_excerpt":"We study the global bifurcation curves of a diffusive logistic equation, when harvesting is orthogonal to the first eigenfunction of the Laplacian, for values of the linear growth up to $\\lambda_2+\\delta$, examining in detail their behavior as the linear growth rate crosses the first two eigenvalues. We observe some new behavior with regard to earlier works concerning this equation. Namely, the bifurcation curves suffer a transformation at $\\lambda_1$, they are compact above $\\lambda_1$, there are precisely two families of degenerate solutions with Morse index equal to zero, and the whole set "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0163","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":"2026-05-18T02:48:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+zLnveMW0X6dDoFSYiXdGqPyFb8/aMUUwiQhjmTIn3pfFiBpX3U+O5wpiQehToIf1wpBX6ACoTRQFSkMCG44Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T19:48:55.193523Z"},"content_sha256":"eb87b5fc44e50c74d13201c135c463594a1421e3d72fe9245c2f369edb8078fc","schema_version":"1.0","event_id":"sha256:eb87b5fc44e50c74d13201c135c463594a1421e3d72fe9245c2f369edb8078fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A4KKBIXQCTMJWHLZWB5JSTTBOF/bundle.json","state_url":"https://pith.science/pith/A4KKBIXQCTMJWHLZWB5JSTTBOF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A4KKBIXQCTMJWHLZWB5JSTTBOF/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":"2026-07-03T19:48:55Z","links":{"resolver":"https://pith.science/pith/A4KKBIXQCTMJWHLZWB5JSTTBOF","bundle":"https://pith.science/pith/A4KKBIXQCTMJWHLZWB5JSTTBOF/bundle.json","state":"https://pith.science/pith/A4KKBIXQCTMJWHLZWB5JSTTBOF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A4KKBIXQCTMJWHLZWB5JSTTBOF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:A4KKBIXQCTMJWHLZWB5JSTTBOF","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":"c2da1b70589438d99dd7e1bdcca584e8f0a8f780a9269f591da0b92f8ce476db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-01T09:50:39Z","title_canon_sha256":"a16714c54ecf036f0d49bacd749b5372c246ed0528a5e4d939de5b3889a0fc1f"},"schema_version":"1.0","source":{"id":"1407.0163","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0163","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0163v1","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0163","created_at":"2026-05-18T02:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"A4KKBIXQCTMJ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"A4KKBIXQCTMJWHLZ","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"A4KKBIXQ","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:eb87b5fc44e50c74d13201c135c463594a1421e3d72fe9245c2f369edb8078fc","target":"graph","created_at":"2026-05-18T02:48:34Z","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":"We study the global bifurcation curves of a diffusive logistic equation, when harvesting is orthogonal to the first eigenfunction of the Laplacian, for values of the linear growth up to $\\lambda_2+\\delta$, examining in detail their behavior as the linear growth rate crosses the first two eigenvalues. We observe some new behavior with regard to earlier works concerning this equation. Namely, the bifurcation curves suffer a transformation at $\\lambda_1$, they are compact above $\\lambda_1$, there are precisely two families of degenerate solutions with Morse index equal to zero, and the whole set ","authors_text":"Mayte P\\'erez-Llanos, Pedro M. Gir\\~ao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-01T09:50:39Z","title":"Bifurcation curves of a diffusive logistic equation with harvesting orthogonal to the first eigenfunction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0163","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":"sha256:7e4f364790d4a3c3a2c49322057b5345790bea8b86394b8b0af6100cc096f658","target":"record","created_at":"2026-05-18T02:48:34Z","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":"c2da1b70589438d99dd7e1bdcca584e8f0a8f780a9269f591da0b92f8ce476db","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-07-01T09:50:39Z","title_canon_sha256":"a16714c54ecf036f0d49bacd749b5372c246ed0528a5e4d939de5b3889a0fc1f"},"schema_version":"1.0","source":{"id":"1407.0163","kind":"arxiv","version":1}},"canonical_sha256":"0714a0a2f014d89b1d79b07a994e61716f4157ed62a42087bcf0ec058e910417","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0714a0a2f014d89b1d79b07a994e61716f4157ed62a42087bcf0ec058e910417","first_computed_at":"2026-05-18T02:48:34.997565Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:34.997565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UbJDWOoSbiCYH8efLK6qtrblHGcpwywjEHQeHoYA/+bXEe/H207JNKDIGyQuBp1vYlFZXt8foSAbd7naYBv2Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:34.998231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0163","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e4f364790d4a3c3a2c49322057b5345790bea8b86394b8b0af6100cc096f658","sha256:eb87b5fc44e50c74d13201c135c463594a1421e3d72fe9245c2f369edb8078fc"],"state_sha256":"ce93dee43c48cc1e5eadb3b1e1ee8d868973ad152f8a6f562783c083b1aa4212"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O6pmlTLI/S1EpfmrlMBRCOv9+Ff+fw61RUhwx4w5MsYQWIM3cCZSg7YAawDDpmgawUAYKSiDpkh4a632hiRKDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T19:48:55.195707Z","bundle_sha256":"13f0e53266d9ee482dae1c844161a0d6d1e27d77d6dcb980a6d0880b0903e61d"}}