{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:X4OH7NJFKTC2JGFUXKP6ML5H24","short_pith_number":"pith:X4OH7NJF","canonical_record":{"source":{"id":"1903.04212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-11T10:58:33Z","cross_cats_sorted":[],"title_canon_sha256":"8868e072123689cb7f96258ba362da12562c7e428cdac81e96c034176514eb15","abstract_canon_sha256":"6b63acf7801218eaf9f91f20b4dd1947a7affdf0beee64e31e8d50c2cc6a6783"},"schema_version":"1.0"},"canonical_sha256":"bf1c7fb52554c5a498b4ba9fe62fa7d7078d902bf4bccb942d69c7823e41adfa","source":{"kind":"arxiv","id":"1903.04212","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04212","created_at":"2026-05-17T23:51:36Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04212v1","created_at":"2026-05-17T23:51:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04212","created_at":"2026-05-17T23:51:36Z"},{"alias_kind":"pith_short_12","alias_value":"X4OH7NJFKTC2","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"X4OH7NJFKTC2JGFU","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"X4OH7NJF","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:X4OH7NJFKTC2JGFUXKP6ML5H24","target":"record","payload":{"canonical_record":{"source":{"id":"1903.04212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-11T10:58:33Z","cross_cats_sorted":[],"title_canon_sha256":"8868e072123689cb7f96258ba362da12562c7e428cdac81e96c034176514eb15","abstract_canon_sha256":"6b63acf7801218eaf9f91f20b4dd1947a7affdf0beee64e31e8d50c2cc6a6783"},"schema_version":"1.0"},"canonical_sha256":"bf1c7fb52554c5a498b4ba9fe62fa7d7078d902bf4bccb942d69c7823e41adfa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:36.221422Z","signature_b64":"pE/FZCD8ZUYevfYgrEpPu1h6+8YJHIqQfNVMh6Kl90rWj2wbXnD/zYZXKuVwVJ12B+XIvNGBBdfwJ3EXkaFGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf1c7fb52554c5a498b4ba9fe62fa7d7078d902bf4bccb942d69c7823e41adfa","last_reissued_at":"2026-05-17T23:51:36.220715Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:36.220715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.04212","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":"2026-05-17T23:51:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aVDOhlyznXcHy4t9bHoyreMIRQkHNuTS84RUraiAJVj466FiLqQeWU6Lrw+z8VzgupTFdTSBuv/0h229C/iGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:33:57.544885Z"},"content_sha256":"726ea8f6db6668c142e07fca25cae5dc79e830dca4df959043ed43302220253c","schema_version":"1.0","event_id":"sha256:726ea8f6db6668c142e07fca25cae5dc79e830dca4df959043ed43302220253c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:X4OH7NJFKTC2JGFUXKP6ML5H24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A structure-preserving discontinuous Galerkin scheme for the Fischer-KPP equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Ansgar J\\\"ungel, Francesca Bonizzoni, Ilaria Perugia, Marcel Braukhoff","submitted_at":"2019-03-11T10:58:33Z","abstract_excerpt":"An implicit Euler discontinuous Galerkin scheme for the Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP) equation for population densities with no-flux boundary conditions is suggested and analyzed. Using an exponential variable transformation, the numerical scheme automatically preserves the positivity of the discrete solution. A discrete entropy inequality is derived, and the exponential time decay of the discrete density to the stable steady state in the L1 norm is proved if the initial entropy is smaller than the measure of the domain. The discrete solution is proved to converge in the L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04212","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":"2026-05-17T23:51:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8t+khVHPDKIEFlcCsyH9VpEbOPraMDjbGBi35eM6bBwl+46Nb9Z/fXmmu6PB6Sk2JCOa3Ar9lRqL1lqbkdy8BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:33:57.545248Z"},"content_sha256":"9d7d26ab38e6a5005ed13a3d770fc23441ced7869585d36e5c89a7b9e8af8584","schema_version":"1.0","event_id":"sha256:9d7d26ab38e6a5005ed13a3d770fc23441ced7869585d36e5c89a7b9e8af8584"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X4OH7NJFKTC2JGFUXKP6ML5H24/bundle.json","state_url":"https://pith.science/pith/X4OH7NJFKTC2JGFUXKP6ML5H24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X4OH7NJFKTC2JGFUXKP6ML5H24/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":"2026-06-02T17:33:57Z","links":{"resolver":"https://pith.science/pith/X4OH7NJFKTC2JGFUXKP6ML5H24","bundle":"https://pith.science/pith/X4OH7NJFKTC2JGFUXKP6ML5H24/bundle.json","state":"https://pith.science/pith/X4OH7NJFKTC2JGFUXKP6ML5H24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X4OH7NJFKTC2JGFUXKP6ML5H24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:X4OH7NJFKTC2JGFUXKP6ML5H24","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":"6b63acf7801218eaf9f91f20b4dd1947a7affdf0beee64e31e8d50c2cc6a6783","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-11T10:58:33Z","title_canon_sha256":"8868e072123689cb7f96258ba362da12562c7e428cdac81e96c034176514eb15"},"schema_version":"1.0","source":{"id":"1903.04212","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.04212","created_at":"2026-05-17T23:51:36Z"},{"alias_kind":"arxiv_version","alias_value":"1903.04212v1","created_at":"2026-05-17T23:51:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.04212","created_at":"2026-05-17T23:51:36Z"},{"alias_kind":"pith_short_12","alias_value":"X4OH7NJFKTC2","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"X4OH7NJFKTC2JGFU","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"X4OH7NJF","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:9d7d26ab38e6a5005ed13a3d770fc23441ced7869585d36e5c89a7b9e8af8584","target":"graph","created_at":"2026-05-17T23:51:36Z","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":"An implicit Euler discontinuous Galerkin scheme for the Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP) equation for population densities with no-flux boundary conditions is suggested and analyzed. Using an exponential variable transformation, the numerical scheme automatically preserves the positivity of the discrete solution. A discrete entropy inequality is derived, and the exponential time decay of the discrete density to the stable steady state in the L1 norm is proved if the initial entropy is smaller than the measure of the domain. The discrete solution is proved to converge in the L","authors_text":"Ansgar J\\\"ungel, Francesca Bonizzoni, Ilaria Perugia, Marcel Braukhoff","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-11T10:58:33Z","title":"A structure-preserving discontinuous Galerkin scheme for the Fischer-KPP equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.04212","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":"sha256:726ea8f6db6668c142e07fca25cae5dc79e830dca4df959043ed43302220253c","target":"record","created_at":"2026-05-17T23:51:36Z","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":"6b63acf7801218eaf9f91f20b4dd1947a7affdf0beee64e31e8d50c2cc6a6783","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2019-03-11T10:58:33Z","title_canon_sha256":"8868e072123689cb7f96258ba362da12562c7e428cdac81e96c034176514eb15"},"schema_version":"1.0","source":{"id":"1903.04212","kind":"arxiv","version":1}},"canonical_sha256":"bf1c7fb52554c5a498b4ba9fe62fa7d7078d902bf4bccb942d69c7823e41adfa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf1c7fb52554c5a498b4ba9fe62fa7d7078d902bf4bccb942d69c7823e41adfa","first_computed_at":"2026-05-17T23:51:36.220715Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:36.220715Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pE/FZCD8ZUYevfYgrEpPu1h6+8YJHIqQfNVMh6Kl90rWj2wbXnD/zYZXKuVwVJ12B+XIvNGBBdfwJ3EXkaFGBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:36.221422Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.04212","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:726ea8f6db6668c142e07fca25cae5dc79e830dca4df959043ed43302220253c","sha256:9d7d26ab38e6a5005ed13a3d770fc23441ced7869585d36e5c89a7b9e8af8584"],"state_sha256":"68966df03dcb24dd4663ac2c164b9039a0acabf85d6117e7fefc012bb3711aa5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e0DieDNf3c3Knmhbx+OP2eDVa5S3gnylth49AXbduvyqt/9H5JFJKSj/+pL1yvQXuMZXDttpjF3NTbe33HmTBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:33:57.547377Z","bundle_sha256":"e748c936d1dce22d2def8c33da4ee235b2924019ff22028f1b29825351ad757d"}}