{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:LGNCUKSGELMHO552RUI53H4SAN","short_pith_number":"pith:LGNCUKSG","canonical_record":{"source":{"id":"1907.11160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-18T17:35:29Z","cross_cats_sorted":[],"title_canon_sha256":"5afb9dfe4bcb8e8df832a22c4c90232c870bab0a431e61cd8e8d9d37d0cef99e","abstract_canon_sha256":"669a198be84fd82ba521d876d24147ba6e9e99b4143a381ec02393739c69829f"},"schema_version":"1.0"},"canonical_sha256":"599a2a2a4622d87777ba8d11dd9f9203564a3fcbc7f1054d075e59c34ef39f53","source":{"kind":"arxiv","id":"1907.11160","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11160","created_at":"2026-05-17T23:39:33Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11160v1","created_at":"2026-05-17T23:39:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11160","created_at":"2026-05-17T23:39:33Z"},{"alias_kind":"pith_short_12","alias_value":"LGNCUKSGELMH","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LGNCUKSGELMHO552","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LGNCUKSG","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:LGNCUKSGELMHO552RUI53H4SAN","target":"record","payload":{"canonical_record":{"source":{"id":"1907.11160","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-18T17:35:29Z","cross_cats_sorted":[],"title_canon_sha256":"5afb9dfe4bcb8e8df832a22c4c90232c870bab0a431e61cd8e8d9d37d0cef99e","abstract_canon_sha256":"669a198be84fd82ba521d876d24147ba6e9e99b4143a381ec02393739c69829f"},"schema_version":"1.0"},"canonical_sha256":"599a2a2a4622d87777ba8d11dd9f9203564a3fcbc7f1054d075e59c34ef39f53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:33.113245Z","signature_b64":"yMZ3dBW54qStdb5VwB3hht2KQsVHzPnrvDR2ghkUTTpZCwSIEvdCHMsbVJDcPkzTiSA+dj6QjFQIbXIBfC6HAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"599a2a2a4622d87777ba8d11dd9f9203564a3fcbc7f1054d075e59c34ef39f53","last_reissued_at":"2026-05-17T23:39:33.112566Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:33.112566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.11160","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":"2026-05-17T23:39:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EtccTkvWvoVjeoUjd6fKn1lRyXwn2VdUWTge0lAQp6wGH/8jh0Tq2nsuuW5EyXVdyBf/sAOeG0whTlwD1pVrBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:36:22.475560Z"},"content_sha256":"4556907a89f00cf87c2a2072a4090f594a5783acc3b0b1584d204aaa636209cc","schema_version":"1.0","event_id":"sha256:4556907a89f00cf87c2a2072a4090f594a5783acc3b0b1584d204aaa636209cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:LGNCUKSGELMHO552RUI53H4SAN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Controllability for a degenerate cascade system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Genni Fragnelli, Idriss Boutaayamou","submitted_at":"2019-07-18T17:35:29Z","abstract_excerpt":"In this paper we consider a cascade system in non divergence form which models the interaction between two different species, the first one can be seen as a predator and the other as a prey. Both of them depend on time, on age and on space. Moreover, the diffusion coefficients degenerate at the boundary of domain. We study, in particular, null controllability of the system via the observability inequality for the non homogeneous adjoint problem, which is deduced by Carleman estimates."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11160","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":"2026-05-17T23:39:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wbkytMYdg6OLUTrNZLxk/3f4+2Sy9wORYZ1ZncuNLRrMFRix7R2iQ/BEmWenzG3M968O9I7kC3uMiWDQYJ7wAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:36:22.476219Z"},"content_sha256":"fbadd773f52a71738b2900acd84ef165d5707dedc294a9a2b3b449345d6a7e86","schema_version":"1.0","event_id":"sha256:fbadd773f52a71738b2900acd84ef165d5707dedc294a9a2b3b449345d6a7e86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LGNCUKSGELMHO552RUI53H4SAN/bundle.json","state_url":"https://pith.science/pith/LGNCUKSGELMHO552RUI53H4SAN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LGNCUKSGELMHO552RUI53H4SAN/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":"2026-06-09T08:36:22Z","links":{"resolver":"https://pith.science/pith/LGNCUKSGELMHO552RUI53H4SAN","bundle":"https://pith.science/pith/LGNCUKSGELMHO552RUI53H4SAN/bundle.json","state":"https://pith.science/pith/LGNCUKSGELMHO552RUI53H4SAN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LGNCUKSGELMHO552RUI53H4SAN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:LGNCUKSGELMHO552RUI53H4SAN","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":"669a198be84fd82ba521d876d24147ba6e9e99b4143a381ec02393739c69829f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-18T17:35:29Z","title_canon_sha256":"5afb9dfe4bcb8e8df832a22c4c90232c870bab0a431e61cd8e8d9d37d0cef99e"},"schema_version":"1.0","source":{"id":"1907.11160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.11160","created_at":"2026-05-17T23:39:33Z"},{"alias_kind":"arxiv_version","alias_value":"1907.11160v1","created_at":"2026-05-17T23:39:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.11160","created_at":"2026-05-17T23:39:33Z"},{"alias_kind":"pith_short_12","alias_value":"LGNCUKSGELMH","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"LGNCUKSGELMHO552","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"LGNCUKSG","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:fbadd773f52a71738b2900acd84ef165d5707dedc294a9a2b3b449345d6a7e86","target":"graph","created_at":"2026-05-17T23:39:33Z","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 consider a cascade system in non divergence form which models the interaction between two different species, the first one can be seen as a predator and the other as a prey. Both of them depend on time, on age and on space. Moreover, the diffusion coefficients degenerate at the boundary of domain. We study, in particular, null controllability of the system via the observability inequality for the non homogeneous adjoint problem, which is deduced by Carleman estimates.","authors_text":"Genni Fragnelli, Idriss Boutaayamou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-18T17:35:29Z","title":"Controllability for a degenerate cascade system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.11160","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":"sha256:4556907a89f00cf87c2a2072a4090f594a5783acc3b0b1584d204aaa636209cc","target":"record","created_at":"2026-05-17T23:39:33Z","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":"669a198be84fd82ba521d876d24147ba6e9e99b4143a381ec02393739c69829f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-18T17:35:29Z","title_canon_sha256":"5afb9dfe4bcb8e8df832a22c4c90232c870bab0a431e61cd8e8d9d37d0cef99e"},"schema_version":"1.0","source":{"id":"1907.11160","kind":"arxiv","version":1}},"canonical_sha256":"599a2a2a4622d87777ba8d11dd9f9203564a3fcbc7f1054d075e59c34ef39f53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"599a2a2a4622d87777ba8d11dd9f9203564a3fcbc7f1054d075e59c34ef39f53","first_computed_at":"2026-05-17T23:39:33.112566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:39:33.112566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yMZ3dBW54qStdb5VwB3hht2KQsVHzPnrvDR2ghkUTTpZCwSIEvdCHMsbVJDcPkzTiSA+dj6QjFQIbXIBfC6HAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:39:33.113245Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.11160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4556907a89f00cf87c2a2072a4090f594a5783acc3b0b1584d204aaa636209cc","sha256:fbadd773f52a71738b2900acd84ef165d5707dedc294a9a2b3b449345d6a7e86"],"state_sha256":"73335d4cd174c492125fe26cdc2bc4e64866f2cd9414a21ce9ef06ced2cc2e6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VfDCl+6/DB+u6JILtwy0IN9fq9v0FIaYyrWyNNBCeT0itdox4nw5E/GRXSLNje2Nrk1VxXoSyBp088C5s/8zAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:36:22.480965Z","bundle_sha256":"9c6501e46a0618a27d0434b7a0e51439f5747974203b15d3eb4f5d602106aded"}}