{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:7VEFAORHGO7TFVQV2PJK75UOB4","short_pith_number":"pith:7VEFAORH","canonical_record":{"source":{"id":"2110.09912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-19T12:19:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"5b9ac7f11021164c5fbb1d438d61ebc579421794bcd3bc429555e96a305cf452","abstract_canon_sha256":"bb5c5f7c708ea82f8327b8418ab44f152099dd3ce50716ae69e33fcd7b877c6d"},"schema_version":"1.0"},"canonical_sha256":"fd48503a2733bf32d615d3d2aff68e0f00982668d1961f69b4156aa24615bff7","source":{"kind":"arxiv","id":"2110.09912","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.09912","created_at":"2026-07-05T03:24:00Z"},{"alias_kind":"arxiv_version","alias_value":"2110.09912v1","created_at":"2026-07-05T03:24:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.09912","created_at":"2026-07-05T03:24:00Z"},{"alias_kind":"pith_short_12","alias_value":"7VEFAORHGO7T","created_at":"2026-07-05T03:24:00Z"},{"alias_kind":"pith_short_16","alias_value":"7VEFAORHGO7TFVQV","created_at":"2026-07-05T03:24:00Z"},{"alias_kind":"pith_short_8","alias_value":"7VEFAORH","created_at":"2026-07-05T03:24:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:7VEFAORHGO7TFVQV2PJK75UOB4","target":"record","payload":{"canonical_record":{"source":{"id":"2110.09912","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-19T12:19:40Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"5b9ac7f11021164c5fbb1d438d61ebc579421794bcd3bc429555e96a305cf452","abstract_canon_sha256":"bb5c5f7c708ea82f8327b8418ab44f152099dd3ce50716ae69e33fcd7b877c6d"},"schema_version":"1.0"},"canonical_sha256":"fd48503a2733bf32d615d3d2aff68e0f00982668d1961f69b4156aa24615bff7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:24:00.796443Z","signature_b64":"uWPCfKSwTuxKF/7EQgxMdtKlfr/phqremQkCsCyMR5RWF04XyMi3SuNjAxt3UU2czRBRpuknU73KyRaF0asnCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd48503a2733bf32d615d3d2aff68e0f00982668d1961f69b4156aa24615bff7","last_reissued_at":"2026-07-05T03:24:00.796036Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:24:00.796036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2110.09912","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":"2026-07-05T03:24:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BXAglkAiBeWcEdnXIBtL9/xfxQdCsvO79B6X1mV0t+6IwqY1A6ddPjqcn1S4wxCCR4PQ4F3CGeNz4fvQGaG8Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T14:10:34.966103Z"},"content_sha256":"58a6ad359d60e723c4d120faa110aa894d36c4440a7441a18dff97f7babf5859","schema_version":"1.0","event_id":"sha256:58a6ad359d60e723c4d120faa110aa894d36c4440a7441a18dff97f7babf5859"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:7VEFAORHGO7TFVQV2PJK75UOB4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal control using flux potentials: A way to construct bound-preserving finite element schemes for conservation laws","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Dmitri Kuzmin, Falko Ruppenthal","submitted_at":"2021-10-19T12:19:40Z","abstract_excerpt":"To ensure preservation of local or global bounds for numerical solutions of conservation laws, we constrain a baseline finite element discretization using optimization-based (OB) flux correction. The main novelty of the proposed methodology lies in the use of flux potentials as control variables and targets of inequality-constrained optimization problems for numerical fluxes. In contrast to optimal control via general source terms, the discrete conservation property of flux-corrected finite element approximations is guaranteed without the need to impose additional equality constraints. Since t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.09912","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2110.09912/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T03:24:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7nfGrxRVeJajLOdG07a4iWw4i76zzyNevNsLZYYHtEboJq/G8TPLsE1609WcnIOQ+X5O+JfJLUD6+f5JRLcKBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-31T14:10:34.966400Z"},"content_sha256":"54e2ad9e1d14b4f20b6c7aaaae31f593787c2b86a2287a2a54d284a4df63cc7e","schema_version":"1.0","event_id":"sha256:54e2ad9e1d14b4f20b6c7aaaae31f593787c2b86a2287a2a54d284a4df63cc7e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7VEFAORHGO7TFVQV2PJK75UOB4/bundle.json","state_url":"https://pith.science/pith/7VEFAORHGO7TFVQV2PJK75UOB4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7VEFAORHGO7TFVQV2PJK75UOB4/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":"2026-07-31T14:10:34Z","links":{"resolver":"https://pith.science/pith/7VEFAORHGO7TFVQV2PJK75UOB4","bundle":"https://pith.science/pith/7VEFAORHGO7TFVQV2PJK75UOB4/bundle.json","state":"https://pith.science/pith/7VEFAORHGO7TFVQV2PJK75UOB4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7VEFAORHGO7TFVQV2PJK75UOB4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:7VEFAORHGO7TFVQV2PJK75UOB4","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":"bb5c5f7c708ea82f8327b8418ab44f152099dd3ce50716ae69e33fcd7b877c6d","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-19T12:19:40Z","title_canon_sha256":"5b9ac7f11021164c5fbb1d438d61ebc579421794bcd3bc429555e96a305cf452"},"schema_version":"1.0","source":{"id":"2110.09912","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2110.09912","created_at":"2026-07-05T03:24:00Z"},{"alias_kind":"arxiv_version","alias_value":"2110.09912v1","created_at":"2026-07-05T03:24:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2110.09912","created_at":"2026-07-05T03:24:00Z"},{"alias_kind":"pith_short_12","alias_value":"7VEFAORHGO7T","created_at":"2026-07-05T03:24:00Z"},{"alias_kind":"pith_short_16","alias_value":"7VEFAORHGO7TFVQV","created_at":"2026-07-05T03:24:00Z"},{"alias_kind":"pith_short_8","alias_value":"7VEFAORH","created_at":"2026-07-05T03:24:00Z"}],"graph_snapshots":[{"event_id":"sha256:54e2ad9e1d14b4f20b6c7aaaae31f593787c2b86a2287a2a54d284a4df63cc7e","target":"graph","created_at":"2026-07-05T03:24:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2110.09912/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"To ensure preservation of local or global bounds for numerical solutions of conservation laws, we constrain a baseline finite element discretization using optimization-based (OB) flux correction. The main novelty of the proposed methodology lies in the use of flux potentials as control variables and targets of inequality-constrained optimization problems for numerical fluxes. In contrast to optimal control via general source terms, the discrete conservation property of flux-corrected finite element approximations is guaranteed without the need to impose additional equality constraints. Since t","authors_text":"Dmitri Kuzmin, Falko Ruppenthal","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-19T12:19:40Z","title":"Optimal control using flux potentials: A way to construct bound-preserving finite element schemes for conservation laws"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.09912","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":"sha256:58a6ad359d60e723c4d120faa110aa894d36c4440a7441a18dff97f7babf5859","target":"record","created_at":"2026-07-05T03:24:00Z","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":"bb5c5f7c708ea82f8327b8418ab44f152099dd3ce50716ae69e33fcd7b877c6d","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2021-10-19T12:19:40Z","title_canon_sha256":"5b9ac7f11021164c5fbb1d438d61ebc579421794bcd3bc429555e96a305cf452"},"schema_version":"1.0","source":{"id":"2110.09912","kind":"arxiv","version":1}},"canonical_sha256":"fd48503a2733bf32d615d3d2aff68e0f00982668d1961f69b4156aa24615bff7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd48503a2733bf32d615d3d2aff68e0f00982668d1961f69b4156aa24615bff7","first_computed_at":"2026-07-05T03:24:00.796036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:24:00.796036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uWPCfKSwTuxKF/7EQgxMdtKlfr/phqremQkCsCyMR5RWF04XyMi3SuNjAxt3UU2czRBRpuknU73KyRaF0asnCw==","signature_status":"signed_v1","signed_at":"2026-07-05T03:24:00.796443Z","signed_message":"canonical_sha256_bytes"},"source_id":"2110.09912","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58a6ad359d60e723c4d120faa110aa894d36c4440a7441a18dff97f7babf5859","sha256:54e2ad9e1d14b4f20b6c7aaaae31f593787c2b86a2287a2a54d284a4df63cc7e"],"state_sha256":"cb84eb3c267dab8130f7c08249fbfc1193f0c27b6946c3fc451846ab88d2fe52"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5o28lEI0wH0n5fvoVbX3BpP4IJZD7px9PHWL+TkLhxhejrKVDuATMgEFmU2S87yPLtjZbdWLrU6BPm3ebZNKCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-31T14:10:34.969612Z","bundle_sha256":"e3e7cb9d0fa36849d75acdd8828fc387827926a22a418955176c58822a7d3cc4"}}