{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:E6TEE5U6CIEAQJLYR74FKUCI5T","short_pith_number":"pith:E6TEE5U6","canonical_record":{"source":{"id":"1308.6658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-30T06:17:15Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"bcf4681ec49bdbc66eae82445f175aa3ac0bf36123f9ab7ce5e3defdf807d125","abstract_canon_sha256":"1907669aedde023c3def273ff017a27ef0169b18cafa729f440dd5b0baacd4c2"},"schema_version":"1.0"},"canonical_sha256":"27a642769e12080825788ff8555048ecdca2d7d8216459e8194e2ccfec3b78eb","source":{"kind":"arxiv","id":"1308.6658","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6658","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6658v1","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6658","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"E6TEE5U6CIEA","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E6TEE5U6CIEAQJLY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E6TEE5U6","created_at":"2026-05-18T12:27:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:E6TEE5U6CIEAQJLYR74FKUCI5T","target":"record","payload":{"canonical_record":{"source":{"id":"1308.6658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-30T06:17:15Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"bcf4681ec49bdbc66eae82445f175aa3ac0bf36123f9ab7ce5e3defdf807d125","abstract_canon_sha256":"1907669aedde023c3def273ff017a27ef0169b18cafa729f440dd5b0baacd4c2"},"schema_version":"1.0"},"canonical_sha256":"27a642769e12080825788ff8555048ecdca2d7d8216459e8194e2ccfec3b78eb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:38.500645Z","signature_b64":"CeBv1LNlrwiLAVzGPqXlX9SXZTX+jA1NKpdhxQrChXJZHebrUhwsRm43NDcbVBgWLRoyoe49PRxqYREC2qPoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27a642769e12080825788ff8555048ecdca2d7d8216459e8194e2ccfec3b78eb","last_reissued_at":"2026-05-18T03:14:38.500151Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:38.500151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.6658","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":"2026-05-18T03:14:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xSpdmSep9MyrLhZGOx3PAyGV2g/yIshSMbmBCvCFXFWOf7i+eq73ypGdNLzH9+bUltjgudOUv4evD5w75uZkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:11:50.394407Z"},"content_sha256":"07fced5878e5bd56eaf80ac9b7f2c31eda635ba2e9177fff452cd9ee74e5d53b","schema_version":"1.0","event_id":"sha256:07fced5878e5bd56eaf80ac9b7f2c31eda635ba2e9177fff452cd9ee74e5d53b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:E6TEE5U6CIEAQJLYR74FKUCI5T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Degenerate parabolic equation with zero flux boundary condition and its approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.AP","authors_text":"Mohamed Karimou Gazibo (LM-Besan\\c{c}on)","submitted_at":"2013-08-30T06:17:15Z","abstract_excerpt":"We study a degenerate parabolic-hyperbolic equation with zero flux boundary condition. The aim of this paper is to prove convergence of numerical approximate solutions towards the unique entropy solution. We propose an implicit finite volume scheme on admissible mesh. We establish fundamental estimates and prove that the approximate solution converge towards an entropy-process solution. Contrarily to the case of Dirichlet conditions, in zero-flux problem unnatural boundary regularity of the flux is required to establish that entropy-process solution is the unique entropy solution. In the study"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6658","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":"2026-05-18T03:14:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ym+IisNXTF4b6kViyaCz5ui/vfAuX/w/4iQbp4keIlwbwzo/e45+0tBXFjiXEMdxktKj2S92FRfcOISdWgufCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T20:11:50.394750Z"},"content_sha256":"05aaf2b05e09e8206e9e5969db2ba405c40669771ae54e7989873d69a52e86b3","schema_version":"1.0","event_id":"sha256:05aaf2b05e09e8206e9e5969db2ba405c40669771ae54e7989873d69a52e86b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E6TEE5U6CIEAQJLYR74FKUCI5T/bundle.json","state_url":"https://pith.science/pith/E6TEE5U6CIEAQJLYR74FKUCI5T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E6TEE5U6CIEAQJLYR74FKUCI5T/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":"2026-06-25T20:11:50Z","links":{"resolver":"https://pith.science/pith/E6TEE5U6CIEAQJLYR74FKUCI5T","bundle":"https://pith.science/pith/E6TEE5U6CIEAQJLYR74FKUCI5T/bundle.json","state":"https://pith.science/pith/E6TEE5U6CIEAQJLYR74FKUCI5T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E6TEE5U6CIEAQJLYR74FKUCI5T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:E6TEE5U6CIEAQJLYR74FKUCI5T","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":"1907669aedde023c3def273ff017a27ef0169b18cafa729f440dd5b0baacd4c2","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-30T06:17:15Z","title_canon_sha256":"bcf4681ec49bdbc66eae82445f175aa3ac0bf36123f9ab7ce5e3defdf807d125"},"schema_version":"1.0","source":{"id":"1308.6658","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6658","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6658v1","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6658","created_at":"2026-05-18T03:14:38Z"},{"alias_kind":"pith_short_12","alias_value":"E6TEE5U6CIEA","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"E6TEE5U6CIEAQJLY","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"E6TEE5U6","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:05aaf2b05e09e8206e9e5969db2ba405c40669771ae54e7989873d69a52e86b3","target":"graph","created_at":"2026-05-18T03:14:38Z","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 a degenerate parabolic-hyperbolic equation with zero flux boundary condition. The aim of this paper is to prove convergence of numerical approximate solutions towards the unique entropy solution. We propose an implicit finite volume scheme on admissible mesh. We establish fundamental estimates and prove that the approximate solution converge towards an entropy-process solution. Contrarily to the case of Dirichlet conditions, in zero-flux problem unnatural boundary regularity of the flux is required to establish that entropy-process solution is the unique entropy solution. In the study","authors_text":"Mohamed Karimou Gazibo (LM-Besan\\c{c}on)","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-30T06:17:15Z","title":"Degenerate parabolic equation with zero flux boundary condition and its approximations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6658","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":"sha256:07fced5878e5bd56eaf80ac9b7f2c31eda635ba2e9177fff452cd9ee74e5d53b","target":"record","created_at":"2026-05-18T03:14:38Z","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":"1907669aedde023c3def273ff017a27ef0169b18cafa729f440dd5b0baacd4c2","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-08-30T06:17:15Z","title_canon_sha256":"bcf4681ec49bdbc66eae82445f175aa3ac0bf36123f9ab7ce5e3defdf807d125"},"schema_version":"1.0","source":{"id":"1308.6658","kind":"arxiv","version":1}},"canonical_sha256":"27a642769e12080825788ff8555048ecdca2d7d8216459e8194e2ccfec3b78eb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27a642769e12080825788ff8555048ecdca2d7d8216459e8194e2ccfec3b78eb","first_computed_at":"2026-05-18T03:14:38.500151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:38.500151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CeBv1LNlrwiLAVzGPqXlX9SXZTX+jA1NKpdhxQrChXJZHebrUhwsRm43NDcbVBgWLRoyoe49PRxqYREC2qPoDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:38.500645Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6658","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:07fced5878e5bd56eaf80ac9b7f2c31eda635ba2e9177fff452cd9ee74e5d53b","sha256:05aaf2b05e09e8206e9e5969db2ba405c40669771ae54e7989873d69a52e86b3"],"state_sha256":"de25fab6c488e373da8f831c7aa95afe0f4e624379dbccb9677bec3b35b8df03"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eW+e6diGKlX8iXYHIYnJZsgtWd6ae8hpyYTFj+JBK0Af6jHrne7HQjBLdlQbUk8HfY3dfzGR/YsMJjh/4PBkDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T20:11:50.396685Z","bundle_sha256":"3d4332906a5807b14d33c2eae621edc711091a4668e93e127b72982bce09cb54"}}