{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:M4XBOMTMDV6CMO7QWEWX6K2WTI","short_pith_number":"pith:M4XBOMTM","canonical_record":{"source":{"id":"1811.00057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-31T18:39:28Z","cross_cats_sorted":[],"title_canon_sha256":"0cc7dc427e72741175d2b8d0e4eeb148d54edfaafd71c93205c82b646caf66b7","abstract_canon_sha256":"530bffadaa186238022a82a1c0ad6f55f263dc3b6b36f080b0e656dea0aedc28"},"schema_version":"1.0"},"canonical_sha256":"672e17326c1d7c263bf0b12d7f2b569a1980e19bdbd49da9c2e967c73d4cf4b7","source":{"kind":"arxiv","id":"1811.00057","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.00057","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"arxiv_version","alias_value":"1811.00057v1","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00057","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"pith_short_12","alias_value":"M4XBOMTMDV6C","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"M4XBOMTMDV6CMO7Q","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"M4XBOMTM","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:M4XBOMTMDV6CMO7QWEWX6K2WTI","target":"record","payload":{"canonical_record":{"source":{"id":"1811.00057","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-31T18:39:28Z","cross_cats_sorted":[],"title_canon_sha256":"0cc7dc427e72741175d2b8d0e4eeb148d54edfaafd71c93205c82b646caf66b7","abstract_canon_sha256":"530bffadaa186238022a82a1c0ad6f55f263dc3b6b36f080b0e656dea0aedc28"},"schema_version":"1.0"},"canonical_sha256":"672e17326c1d7c263bf0b12d7f2b569a1980e19bdbd49da9c2e967c73d4cf4b7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:48.364771Z","signature_b64":"NclLc90E51WDqDe0Wfuz81xctTxNOTLCCP/iaYRAn6q93ZyeCwzwHSkCcFewLTfLwCvcFBwVjHUwiBFWDThZDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"672e17326c1d7c263bf0b12d7f2b569a1980e19bdbd49da9c2e967c73d4cf4b7","last_reissued_at":"2026-05-18T00:01:48.364240Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:48.364240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.00057","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":"2026-05-18T00:01:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nCOHjbs/wFzxt++wmxUZMIwQS5ztHNNQPOk17Fc9FmpDgYsh7TbXu5GaaPriu88vK4Nz/C9Sddb5fojXyP8oBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:20:18.589797Z"},"content_sha256":"1db4407a8cdfa54a1c39f400c8bbea7d5645021106ed3b0646b29a4a35f4577d","schema_version":"1.0","event_id":"sha256:1db4407a8cdfa54a1c39f400c8bbea7d5645021106ed3b0646b29a4a35f4577d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:M4XBOMTMDV6CMO7QWEWX6K2WTI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multidimensional staggered grid residual distribution scheme for Lagrangian hydrodynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"K. Lipnikov, N. Morgan, R. Abgrall, S. Tokareva","submitted_at":"2018-10-31T18:39:28Z","abstract_excerpt":"We present the second-order multidimensional Staggered Grid Hydrodynamics Residual Distribution (SGH RD) scheme for Lagrangian hydrodynamics. The SGH RD scheme is based on the staggered finite element discretizations as in [Dobrev et al., SISC, 2012]. However, the advantage of the residual formulation over classical FEM approaches consists in the natural mass matrix diagonalization which allows one to avoid the solution of the linear system with the global sparse mass matrix while retaining the desired order of accuracy. This is achieved by using Bernstein polynomials as finite element shape f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00057","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":"2026-05-18T00:01:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xmMKD3Pyvz5g+eUrfVatw/0RIc/Z1r4SWCDBfoveCAd4kAUajoTpXf4cr7rCeD9fuZ1bzzBjIhq8Qepc+5xiBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T19:20:18.590126Z"},"content_sha256":"4b24b5487ea05af1c4db389e0e9b3c444f13b173e97af08150505cf5d8d5d6ea","schema_version":"1.0","event_id":"sha256:4b24b5487ea05af1c4db389e0e9b3c444f13b173e97af08150505cf5d8d5d6ea"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M4XBOMTMDV6CMO7QWEWX6K2WTI/bundle.json","state_url":"https://pith.science/pith/M4XBOMTMDV6CMO7QWEWX6K2WTI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M4XBOMTMDV6CMO7QWEWX6K2WTI/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":"2026-06-10T19:20:18Z","links":{"resolver":"https://pith.science/pith/M4XBOMTMDV6CMO7QWEWX6K2WTI","bundle":"https://pith.science/pith/M4XBOMTMDV6CMO7QWEWX6K2WTI/bundle.json","state":"https://pith.science/pith/M4XBOMTMDV6CMO7QWEWX6K2WTI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M4XBOMTMDV6CMO7QWEWX6K2WTI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:M4XBOMTMDV6CMO7QWEWX6K2WTI","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":"530bffadaa186238022a82a1c0ad6f55f263dc3b6b36f080b0e656dea0aedc28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-31T18:39:28Z","title_canon_sha256":"0cc7dc427e72741175d2b8d0e4eeb148d54edfaafd71c93205c82b646caf66b7"},"schema_version":"1.0","source":{"id":"1811.00057","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.00057","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"arxiv_version","alias_value":"1811.00057v1","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.00057","created_at":"2026-05-18T00:01:48Z"},{"alias_kind":"pith_short_12","alias_value":"M4XBOMTMDV6C","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"M4XBOMTMDV6CMO7Q","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"M4XBOMTM","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:4b24b5487ea05af1c4db389e0e9b3c444f13b173e97af08150505cf5d8d5d6ea","target":"graph","created_at":"2026-05-18T00:01:48Z","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 present the second-order multidimensional Staggered Grid Hydrodynamics Residual Distribution (SGH RD) scheme for Lagrangian hydrodynamics. The SGH RD scheme is based on the staggered finite element discretizations as in [Dobrev et al., SISC, 2012]. However, the advantage of the residual formulation over classical FEM approaches consists in the natural mass matrix diagonalization which allows one to avoid the solution of the linear system with the global sparse mass matrix while retaining the desired order of accuracy. This is achieved by using Bernstein polynomials as finite element shape f","authors_text":"K. Lipnikov, N. Morgan, R. Abgrall, S. Tokareva","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-31T18:39:28Z","title":"Multidimensional staggered grid residual distribution scheme for Lagrangian hydrodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.00057","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":"sha256:1db4407a8cdfa54a1c39f400c8bbea7d5645021106ed3b0646b29a4a35f4577d","target":"record","created_at":"2026-05-18T00:01:48Z","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":"530bffadaa186238022a82a1c0ad6f55f263dc3b6b36f080b0e656dea0aedc28","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-10-31T18:39:28Z","title_canon_sha256":"0cc7dc427e72741175d2b8d0e4eeb148d54edfaafd71c93205c82b646caf66b7"},"schema_version":"1.0","source":{"id":"1811.00057","kind":"arxiv","version":1}},"canonical_sha256":"672e17326c1d7c263bf0b12d7f2b569a1980e19bdbd49da9c2e967c73d4cf4b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"672e17326c1d7c263bf0b12d7f2b569a1980e19bdbd49da9c2e967c73d4cf4b7","first_computed_at":"2026-05-18T00:01:48.364240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:48.364240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NclLc90E51WDqDe0Wfuz81xctTxNOTLCCP/iaYRAn6q93ZyeCwzwHSkCcFewLTfLwCvcFBwVjHUwiBFWDThZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:48.364771Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.00057","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1db4407a8cdfa54a1c39f400c8bbea7d5645021106ed3b0646b29a4a35f4577d","sha256:4b24b5487ea05af1c4db389e0e9b3c444f13b173e97af08150505cf5d8d5d6ea"],"state_sha256":"5aade2151dda5f5d3f0aff0562d5a6269e1138d39bd40e2aa949673a4249bd50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1yXv+7Qe4wK6xvGnUYhYtoN0xEq7w5gAHCogWXJYoPLCrlPaU6GDTcbN0g60CPXiRUw9o5D6N+U52uAWV6MDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T19:20:18.591985Z","bundle_sha256":"5a81d3614db60b0d7d82757661e41621efba6b77e704b767f7444fe5aadbe8c6"}}