{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:PP2PNKCLQLJKSNBZFGPLX2HL4Q","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":"6d6fe455ce4232d5653bfc60e8990f79b1d0af2b759afc2c35dd6d1bda2d1080","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-08-07T07:57:31Z","title_canon_sha256":"595214ef94c4908ce3b8aff188478b8041e8e7147b39bad3990246cf5e9264ce"},"schema_version":"1.0","source":{"id":"2308.03378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.03378","created_at":"2026-07-05T06:38:16Z"},{"alias_kind":"arxiv_version","alias_value":"2308.03378v1","created_at":"2026-07-05T06:38:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.03378","created_at":"2026-07-05T06:38:16Z"},{"alias_kind":"pith_short_12","alias_value":"PP2PNKCLQLJK","created_at":"2026-07-05T06:38:16Z"},{"alias_kind":"pith_short_16","alias_value":"PP2PNKCLQLJKSNBZ","created_at":"2026-07-05T06:38:16Z"},{"alias_kind":"pith_short_8","alias_value":"PP2PNKCL","created_at":"2026-07-05T06:38:16Z"}],"graph_snapshots":[{"event_id":"sha256:37a74713d0b4f2200bd8ee583a0df66bd4a81074bd8ff4be95337768e27f0b60","target":"graph","created_at":"2026-07-05T06:38:16Z","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/2308.03378/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Friedrichs' systems (FS) are symmetric positive linear systems of first-order partial differential equations (PDEs), which provide a unified framework for describing various elliptic, parabolic and hyperbolic semi-linear PDEs such as the linearized Euler equations of gas dynamics, the equations of compressible linear elasticity and the Dirac-Klein-Gordon system. FS were studied to approximate PDEs of mixed elliptic and hyperbolic type in the same domain. For this and other reasons, the versatility of the discontinuous Galerkin method (DGM) represents the best approximation space for FS. We imp","authors_text":"Davide Torlo, Francesco Romor, Gianluigi Rozza","cross_cats":["cs.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-08-07T07:57:31Z","title":"Friedrichs' systems discretized with the Discontinuous Galerkin method: domain decomposable model order reduction and Graph Neural Networks approximating vanishing viscosity solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.03378","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:bef060fd17b2c66326a672c377d2dfd41a9379e9442399d48c9a2f608d6120b5","target":"record","created_at":"2026-07-05T06:38:16Z","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":"6d6fe455ce4232d5653bfc60e8990f79b1d0af2b759afc2c35dd6d1bda2d1080","cross_cats_sorted":["cs.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2023-08-07T07:57:31Z","title_canon_sha256":"595214ef94c4908ce3b8aff188478b8041e8e7147b39bad3990246cf5e9264ce"},"schema_version":"1.0","source":{"id":"2308.03378","kind":"arxiv","version":1}},"canonical_sha256":"7bf4f6a84b82d2a93439299ebbe8ebe42c89bceb8aeb81916be680af0475669e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7bf4f6a84b82d2a93439299ebbe8ebe42c89bceb8aeb81916be680af0475669e","first_computed_at":"2026-07-05T06:38:16.127774Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:38:16.127774Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8pNrM911oiccMaSYR3iTF/C0RuKcwo5vOjZsiBSiQFlYPHs5zNWdMYQGbCF0kYMQtXYrYWIA52n36oH4iDZ2Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T06:38:16.128253Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.03378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bef060fd17b2c66326a672c377d2dfd41a9379e9442399d48c9a2f608d6120b5","sha256:37a74713d0b4f2200bd8ee583a0df66bd4a81074bd8ff4be95337768e27f0b60"],"state_sha256":"860ec4585625afb409a3141f0848ec9b7e3f7e7ccf14b6095ff62a043dafe4fb"}