{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:NVHTZLLXZFZS5CJ4XSONVBCIMU","short_pith_number":"pith:NVHTZLLX","canonical_record":{"source":{"id":"1903.10051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-24T20:02:03Z","cross_cats_sorted":[],"title_canon_sha256":"ff2a397b480f59f54015ada3af934094a5bdbda61c2a3285f2753d98f491b9c8","abstract_canon_sha256":"42360161460ce04bd01a3e60c6df3acdc975b5fdaf1d850f114a65a5766c693c"},"schema_version":"1.0"},"canonical_sha256":"6d4f3cad77c9732e893cbc9cda8448650eb0ee7b66a2edf34ab56aad75c7136a","source":{"kind":"arxiv","id":"1903.10051","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10051","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10051v1","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10051","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"pith_short_12","alias_value":"NVHTZLLXZFZS","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NVHTZLLXZFZS5CJ4","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NVHTZLLX","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:NVHTZLLXZFZS5CJ4XSONVBCIMU","target":"record","payload":{"canonical_record":{"source":{"id":"1903.10051","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-24T20:02:03Z","cross_cats_sorted":[],"title_canon_sha256":"ff2a397b480f59f54015ada3af934094a5bdbda61c2a3285f2753d98f491b9c8","abstract_canon_sha256":"42360161460ce04bd01a3e60c6df3acdc975b5fdaf1d850f114a65a5766c693c"},"schema_version":"1.0"},"canonical_sha256":"6d4f3cad77c9732e893cbc9cda8448650eb0ee7b66a2edf34ab56aad75c7136a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:34.659221Z","signature_b64":"FvHyvLphAFMx5mHjnTysjjykdVbRRa7Hdw6aas93adkmilASRJ4qL1lt2E8vi2R16qW+oCyP8SJVViKKJBx3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d4f3cad77c9732e893cbc9cda8448650eb0ee7b66a2edf34ab56aad75c7136a","last_reissued_at":"2026-05-17T23:50:34.658328Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:34.658328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.10051","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":"2026-05-17T23:50:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pqsaqVUejBQaP1MBSgrepPk1FgLod/gFJPeKR0QXT/+CEiOLeIjj82XwnT885rt+PclcStOlRiPwiOJ2w5hdDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:29:48.698309Z"},"content_sha256":"31408fdc72fdc48f4ded809e52f8bda64847ebb7ba8f6ff5b245d312febb69cf","schema_version":"1.0","event_id":"sha256:31408fdc72fdc48f4ded809e52f8bda64847ebb7ba8f6ff5b245d312febb69cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:NVHTZLLXZFZS5CJ4XSONVBCIMU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Anotida Madzvamuse, Nikos. I. Kavallaris, Raquel Barreira","submitted_at":"2019-03-24T20:02:03Z","abstract_excerpt":"The main purpose of the current paper is to contribute towards the comprehension of the dynamics of the shadow system of a singular Gierer-Meinhardt model on an isotropically evolving domain. In the case where the inhibitor's response to the activator's growth is rather weak, then the shadow system of the Gierer-Meinhardt model is reduced to a single though non-local equation whose dynamics is thoroughly investigated throughout the manuscript. The main focus is on the derivation of blow-up results for this non-local equation, which can be interpreted as instability patterns of the shadow syste"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10051","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":"2026-05-17T23:50:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FXTFV5skYCmzI8QDH+HfgAbLyi1GVFp51rfkvIimMrVYypQlcMxmf2rNjt0gh3mK8zr8NLt2Vu4HbO4SF1yeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:29:48.698668Z"},"content_sha256":"80d51ea85211d91e3c96ef4dbd628fd24fc2baebe153b54816afcb35ca331c97","schema_version":"1.0","event_id":"sha256:80d51ea85211d91e3c96ef4dbd628fd24fc2baebe153b54816afcb35ca331c97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NVHTZLLXZFZS5CJ4XSONVBCIMU/bundle.json","state_url":"https://pith.science/pith/NVHTZLLXZFZS5CJ4XSONVBCIMU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NVHTZLLXZFZS5CJ4XSONVBCIMU/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":"2026-06-21T23:29:48Z","links":{"resolver":"https://pith.science/pith/NVHTZLLXZFZS5CJ4XSONVBCIMU","bundle":"https://pith.science/pith/NVHTZLLXZFZS5CJ4XSONVBCIMU/bundle.json","state":"https://pith.science/pith/NVHTZLLXZFZS5CJ4XSONVBCIMU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NVHTZLLXZFZS5CJ4XSONVBCIMU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NVHTZLLXZFZS5CJ4XSONVBCIMU","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":"42360161460ce04bd01a3e60c6df3acdc975b5fdaf1d850f114a65a5766c693c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-24T20:02:03Z","title_canon_sha256":"ff2a397b480f59f54015ada3af934094a5bdbda61c2a3285f2753d98f491b9c8"},"schema_version":"1.0","source":{"id":"1903.10051","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.10051","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"arxiv_version","alias_value":"1903.10051v1","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.10051","created_at":"2026-05-17T23:50:34Z"},{"alias_kind":"pith_short_12","alias_value":"NVHTZLLXZFZS","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"NVHTZLLXZFZS5CJ4","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"NVHTZLLX","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:80d51ea85211d91e3c96ef4dbd628fd24fc2baebe153b54816afcb35ca331c97","target":"graph","created_at":"2026-05-17T23:50:34Z","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":"The main purpose of the current paper is to contribute towards the comprehension of the dynamics of the shadow system of a singular Gierer-Meinhardt model on an isotropically evolving domain. In the case where the inhibitor's response to the activator's growth is rather weak, then the shadow system of the Gierer-Meinhardt model is reduced to a single though non-local equation whose dynamics is thoroughly investigated throughout the manuscript. The main focus is on the derivation of blow-up results for this non-local equation, which can be interpreted as instability patterns of the shadow syste","authors_text":"Anotida Madzvamuse, Nikos. I. Kavallaris, Raquel Barreira","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-24T20:02:03Z","title":"Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.10051","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":"sha256:31408fdc72fdc48f4ded809e52f8bda64847ebb7ba8f6ff5b245d312febb69cf","target":"record","created_at":"2026-05-17T23:50:34Z","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":"42360161460ce04bd01a3e60c6df3acdc975b5fdaf1d850f114a65a5766c693c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-24T20:02:03Z","title_canon_sha256":"ff2a397b480f59f54015ada3af934094a5bdbda61c2a3285f2753d98f491b9c8"},"schema_version":"1.0","source":{"id":"1903.10051","kind":"arxiv","version":1}},"canonical_sha256":"6d4f3cad77c9732e893cbc9cda8448650eb0ee7b66a2edf34ab56aad75c7136a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d4f3cad77c9732e893cbc9cda8448650eb0ee7b66a2edf34ab56aad75c7136a","first_computed_at":"2026-05-17T23:50:34.658328Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:34.658328Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FvHyvLphAFMx5mHjnTysjjykdVbRRa7Hdw6aas93adkmilASRJ4qL1lt2E8vi2R16qW+oCyP8SJVViKKJBx3Cw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:34.659221Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.10051","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31408fdc72fdc48f4ded809e52f8bda64847ebb7ba8f6ff5b245d312febb69cf","sha256:80d51ea85211d91e3c96ef4dbd628fd24fc2baebe153b54816afcb35ca331c97"],"state_sha256":"88222da0fb4d78901bcd13d61d406628fec5651e55b1bfa70465d9fe09805a8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PgejQPKE+PJNpZItT4hRJ9dL2VeXADvTa6wMM8fkoPrGKmqloLZ59O69LUrGMnCF/CNIvSIVBMIlGuy0ssFEBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:29:48.700535Z","bundle_sha256":"0b897241e207002b5663afd3aaf203bd152464aa13778ebd200c521121f46956"}}