{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:QR3QEPJ7JIKZOK4A4LUP7V4CYM","short_pith_number":"pith:QR3QEPJ7","canonical_record":{"source":{"id":"1807.01118","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-03T12:31:40Z","cross_cats_sorted":[],"title_canon_sha256":"d058d8c5bfc493c955061697e70a53b7e11e06711880fab6d40e96e01b07c0de","abstract_canon_sha256":"280a107580c498731ff6242dbc0c2b6c958e19f0d173a2c4924f8c93f7478501"},"schema_version":"1.0"},"canonical_sha256":"8477023d3f4a15972b80e2e8ffd782c325b9d821b11076fabfbcf64be2320a7b","source":{"kind":"arxiv","id":"1807.01118","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01118","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01118v1","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01118","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"QR3QEPJ7JIKZ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QR3QEPJ7JIKZOK4A","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QR3QEPJ7","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:QR3QEPJ7JIKZOK4A4LUP7V4CYM","target":"record","payload":{"canonical_record":{"source":{"id":"1807.01118","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-03T12:31:40Z","cross_cats_sorted":[],"title_canon_sha256":"d058d8c5bfc493c955061697e70a53b7e11e06711880fab6d40e96e01b07c0de","abstract_canon_sha256":"280a107580c498731ff6242dbc0c2b6c958e19f0d173a2c4924f8c93f7478501"},"schema_version":"1.0"},"canonical_sha256":"8477023d3f4a15972b80e2e8ffd782c325b9d821b11076fabfbcf64be2320a7b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:11:45.275764Z","signature_b64":"6JmtTm6yYgAF8som4xwWUZLIJl9s9RArT0pt7iWqpO46PCcd76FqcOnpsy95kn00DSjnphqgzGUTEGGHw3mmDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8477023d3f4a15972b80e2e8ffd782c325b9d821b11076fabfbcf64be2320a7b","last_reissued_at":"2026-05-18T00:11:45.275071Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:11:45.275071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.01118","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":"2026-05-18T00:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qVWsAuYaE0j/iC7E6L24ej+oky+ptkcTu4JlbBDlcYUfZEXx47CFDfilQbpxaKe3cdNKWc1CyJO/OeK50q7SBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T18:39:57.401450Z"},"content_sha256":"113439c0fe52d0cd92ab7cc28b9e2aac0ecdf1187a0a6d039dbcbd355e263538","schema_version":"1.0","event_id":"sha256:113439c0fe52d0cd92ab7cc28b9e2aac0ecdf1187a0a6d039dbcbd355e263538"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:QR3QEPJ7JIKZOK4A4LUP7V4CYM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Unconditionally energy stable fully discrete schemes for a chemo-repulsion model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Diego Armando Rueda-G\\'omez, Francisco Guill\\'en-Gonz\\'alez, Mar\\'ia \\'Angeles Rodr\\'iguez-Bellido","submitted_at":"2018-07-03T12:31:40Z","abstract_excerpt":"This work is devoted to study unconditionally energy stable and mass-conservative numerical schemes for the following repulsive-productive chemotaxis model: Find $u \\geq 0$, the cell density, and $v \\geq 0$, the chemical concentration, such that $$ \\left\\{ \\begin{array} [c]{lll} \\partial_t u - \\Delta u - \\nabla\\cdot (u\\nabla v)=0 \\ \\ \\mbox{in}\\ \\Omega,\\ t>0,\\\\ \\partial_t v - \\Delta v + v = u \\ \\ \\mbox{in}\\ \\Omega,\\ t>0, \\end{array} \\right. $$ in a bounded domain $\\Omega\\subseteq \\mathbb{R}^d$, $d=2,3$. By using a regularization technique, we propose three fully discrete Finite Element (FE) app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01118","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":"2026-05-18T00:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KsUODRDTZurYR5hIEOlQdIMO4cOQF7+N4E3kLoVfu/2LjZCYoL11b3AmBxAiB4lCZ+T5ajJUXxGceXxujoTmAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T18:39:57.401803Z"},"content_sha256":"35ece0cde460cd0cb382792eba7cc5e6a5a17c38986f4cb06244d97c78f44a0d","schema_version":"1.0","event_id":"sha256:35ece0cde460cd0cb382792eba7cc5e6a5a17c38986f4cb06244d97c78f44a0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QR3QEPJ7JIKZOK4A4LUP7V4CYM/bundle.json","state_url":"https://pith.science/pith/QR3QEPJ7JIKZOK4A4LUP7V4CYM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QR3QEPJ7JIKZOK4A4LUP7V4CYM/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":"2026-06-30T18:39:57Z","links":{"resolver":"https://pith.science/pith/QR3QEPJ7JIKZOK4A4LUP7V4CYM","bundle":"https://pith.science/pith/QR3QEPJ7JIKZOK4A4LUP7V4CYM/bundle.json","state":"https://pith.science/pith/QR3QEPJ7JIKZOK4A4LUP7V4CYM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QR3QEPJ7JIKZOK4A4LUP7V4CYM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:QR3QEPJ7JIKZOK4A4LUP7V4CYM","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":"280a107580c498731ff6242dbc0c2b6c958e19f0d173a2c4924f8c93f7478501","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-03T12:31:40Z","title_canon_sha256":"d058d8c5bfc493c955061697e70a53b7e11e06711880fab6d40e96e01b07c0de"},"schema_version":"1.0","source":{"id":"1807.01118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01118","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01118v1","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01118","created_at":"2026-05-18T00:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"QR3QEPJ7JIKZ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"QR3QEPJ7JIKZOK4A","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"QR3QEPJ7","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:35ece0cde460cd0cb382792eba7cc5e6a5a17c38986f4cb06244d97c78f44a0d","target":"graph","created_at":"2026-05-18T00:11:45Z","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":"This work is devoted to study unconditionally energy stable and mass-conservative numerical schemes for the following repulsive-productive chemotaxis model: Find $u \\geq 0$, the cell density, and $v \\geq 0$, the chemical concentration, such that $$ \\left\\{ \\begin{array} [c]{lll} \\partial_t u - \\Delta u - \\nabla\\cdot (u\\nabla v)=0 \\ \\ \\mbox{in}\\ \\Omega,\\ t>0,\\\\ \\partial_t v - \\Delta v + v = u \\ \\ \\mbox{in}\\ \\Omega,\\ t>0, \\end{array} \\right. $$ in a bounded domain $\\Omega\\subseteq \\mathbb{R}^d$, $d=2,3$. By using a regularization technique, we propose three fully discrete Finite Element (FE) app","authors_text":"Diego Armando Rueda-G\\'omez, Francisco Guill\\'en-Gonz\\'alez, Mar\\'ia \\'Angeles Rodr\\'iguez-Bellido","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-03T12:31:40Z","title":"Unconditionally energy stable fully discrete schemes for a chemo-repulsion model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01118","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":"sha256:113439c0fe52d0cd92ab7cc28b9e2aac0ecdf1187a0a6d039dbcbd355e263538","target":"record","created_at":"2026-05-18T00:11:45Z","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":"280a107580c498731ff6242dbc0c2b6c958e19f0d173a2c4924f8c93f7478501","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-07-03T12:31:40Z","title_canon_sha256":"d058d8c5bfc493c955061697e70a53b7e11e06711880fab6d40e96e01b07c0de"},"schema_version":"1.0","source":{"id":"1807.01118","kind":"arxiv","version":1}},"canonical_sha256":"8477023d3f4a15972b80e2e8ffd782c325b9d821b11076fabfbcf64be2320a7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8477023d3f4a15972b80e2e8ffd782c325b9d821b11076fabfbcf64be2320a7b","first_computed_at":"2026-05-18T00:11:45.275071Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:11:45.275071Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6JmtTm6yYgAF8som4xwWUZLIJl9s9RArT0pt7iWqpO46PCcd76FqcOnpsy95kn00DSjnphqgzGUTEGGHw3mmDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:11:45.275764Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:113439c0fe52d0cd92ab7cc28b9e2aac0ecdf1187a0a6d039dbcbd355e263538","sha256:35ece0cde460cd0cb382792eba7cc5e6a5a17c38986f4cb06244d97c78f44a0d"],"state_sha256":"3dfdb7f5d8166566593bd734f90858bcd92c16d30f2974843e86df47c516a24d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bRKbMFYzcju9l3TnnMYvQGRkOq7PQ8JRy+P1ffbR8uNwMv/fweIPKXTw9A7oAyzcZhbzxAujbOS/29Gu/WSFAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T18:39:57.404205Z","bundle_sha256":"ff467f85893a94e48ebcf18ae06861de4fcfe85e437ccacf7201e4ddfc37a884"}}