{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:CACCTEX2A7QVNH5FSFQRWAXJMH","short_pith_number":"pith:CACCTEX2","canonical_record":{"source":{"id":"1601.06142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-22T20:34:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4985084e4283e4af4435cc234c39a894790fe01471b7de20157ee8d023bce4df","abstract_canon_sha256":"03bde0ee4e5f405817cf238d0ee953bbae86addae47f107d4e264f5f1cf219d4"},"schema_version":"1.0"},"canonical_sha256":"10042992fa07e1569fa591611b02e961d5c0912185523ca2797ff8041f19869e","source":{"kind":"arxiv","id":"1601.06142","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06142","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06142v1","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06142","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"CACCTEX2A7QV","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CACCTEX2A7QVNH5F","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CACCTEX2","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:CACCTEX2A7QVNH5FSFQRWAXJMH","target":"record","payload":{"canonical_record":{"source":{"id":"1601.06142","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-22T20:34:22Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"4985084e4283e4af4435cc234c39a894790fe01471b7de20157ee8d023bce4df","abstract_canon_sha256":"03bde0ee4e5f405817cf238d0ee953bbae86addae47f107d4e264f5f1cf219d4"},"schema_version":"1.0"},"canonical_sha256":"10042992fa07e1569fa591611b02e961d5c0912185523ca2797ff8041f19869e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:09.147301Z","signature_b64":"nJgnlvvl8T9EYHjXKnXa+mpynKaU3dM0OUVmPEqJJ8okwsYbuprAtf5tZ2PUwj0iQCNe2T41wDw/hFv356IuAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10042992fa07e1569fa591611b02e961d5c0912185523ca2797ff8041f19869e","last_reissued_at":"2026-05-18T01:22:09.146694Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:09.146694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.06142","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":"2026-05-18T01:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gziiHuT15S2zY0F6VF9N1fX0wUOFn5ePO1wk+Q4489YuAyVxKTfmobrroZxmjGdOvU4M2OdLx1GmhTdgeq3TBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:14:28.377986Z"},"content_sha256":"af1604fbc9320e13a0209937187c029c7e7c6948226cedb08289ee6e3539cb35","schema_version":"1.0","event_id":"sha256:af1604fbc9320e13a0209937187c029c7e7c6948226cedb08289ee6e3539cb35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:CACCTEX2A7QVNH5FSFQRWAXJMH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A kernel-based discretisation method for first order partial differential equations of evolution type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.NA","authors_text":"Holger Wendland, Tobias Ramming","submitted_at":"2016-01-22T20:34:22Z","abstract_excerpt":"We derive a new discretisation method for first order PDEs of arbitrary spatial dimension, which is based upon a meshfree spatial approximation. This spatial approximation is similar to the SPH (smoothed particle hydrodynamics) technique and is a typical kernel-based method. It differs, however, significantly from the SPH method since it employs an Eulerian and not a Lagrangian approach. We prove stability and convergence for the resulting semi-discrete scheme under certain smoothness assumptions on the defining function of the PDE. The approximation order depends on the underlying kernel and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06142","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":"2026-05-18T01:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QGMCSpppoPY2d5iLDwWqblrYovh1Vb1bppLJWYGjFX+3drexVa7smW5kU3PkXJMCYTWPKiW0PBAkifKsdO/zBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:14:28.378835Z"},"content_sha256":"e71b1fb18e798c11e1cbda795e0233a4606b897d7bb849d8843237137d5c312b","schema_version":"1.0","event_id":"sha256:e71b1fb18e798c11e1cbda795e0233a4606b897d7bb849d8843237137d5c312b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CACCTEX2A7QVNH5FSFQRWAXJMH/bundle.json","state_url":"https://pith.science/pith/CACCTEX2A7QVNH5FSFQRWAXJMH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CACCTEX2A7QVNH5FSFQRWAXJMH/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":"2026-06-06T15:14:28Z","links":{"resolver":"https://pith.science/pith/CACCTEX2A7QVNH5FSFQRWAXJMH","bundle":"https://pith.science/pith/CACCTEX2A7QVNH5FSFQRWAXJMH/bundle.json","state":"https://pith.science/pith/CACCTEX2A7QVNH5FSFQRWAXJMH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CACCTEX2A7QVNH5FSFQRWAXJMH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:CACCTEX2A7QVNH5FSFQRWAXJMH","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":"03bde0ee4e5f405817cf238d0ee953bbae86addae47f107d4e264f5f1cf219d4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-22T20:34:22Z","title_canon_sha256":"4985084e4283e4af4435cc234c39a894790fe01471b7de20157ee8d023bce4df"},"schema_version":"1.0","source":{"id":"1601.06142","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.06142","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1601.06142v1","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.06142","created_at":"2026-05-18T01:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"CACCTEX2A7QV","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"CACCTEX2A7QVNH5F","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"CACCTEX2","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:e71b1fb18e798c11e1cbda795e0233a4606b897d7bb849d8843237137d5c312b","target":"graph","created_at":"2026-05-18T01:22:09Z","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 derive a new discretisation method for first order PDEs of arbitrary spatial dimension, which is based upon a meshfree spatial approximation. This spatial approximation is similar to the SPH (smoothed particle hydrodynamics) technique and is a typical kernel-based method. It differs, however, significantly from the SPH method since it employs an Eulerian and not a Lagrangian approach. We prove stability and convergence for the resulting semi-discrete scheme under certain smoothness assumptions on the defining function of the PDE. The approximation order depends on the underlying kernel and ","authors_text":"Holger Wendland, Tobias Ramming","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-22T20:34:22Z","title":"A kernel-based discretisation method for first order partial differential equations of evolution type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06142","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:af1604fbc9320e13a0209937187c029c7e7c6948226cedb08289ee6e3539cb35","target":"record","created_at":"2026-05-18T01:22:09Z","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":"03bde0ee4e5f405817cf238d0ee953bbae86addae47f107d4e264f5f1cf219d4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-01-22T20:34:22Z","title_canon_sha256":"4985084e4283e4af4435cc234c39a894790fe01471b7de20157ee8d023bce4df"},"schema_version":"1.0","source":{"id":"1601.06142","kind":"arxiv","version":1}},"canonical_sha256":"10042992fa07e1569fa591611b02e961d5c0912185523ca2797ff8041f19869e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10042992fa07e1569fa591611b02e961d5c0912185523ca2797ff8041f19869e","first_computed_at":"2026-05-18T01:22:09.146694Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:09.146694Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nJgnlvvl8T9EYHjXKnXa+mpynKaU3dM0OUVmPEqJJ8okwsYbuprAtf5tZ2PUwj0iQCNe2T41wDw/hFv356IuAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:09.147301Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.06142","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af1604fbc9320e13a0209937187c029c7e7c6948226cedb08289ee6e3539cb35","sha256:e71b1fb18e798c11e1cbda795e0233a4606b897d7bb849d8843237137d5c312b"],"state_sha256":"ebbf5b34f8dc15fb89d8d6748b61254c7bd62859fd9d96e028e71a8a194d0008"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AJuiUeDN2axXMwoavNZnaWLP6Kmgm7/drnjexAfO3SpY38YucNywOFrAc/x3B13m12tCQ2RpZPoDKTBWzD4+Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:14:28.382970Z","bundle_sha256":"4a8c912a256b9caf690e54179919f3ca1491d2d35aadc3c6882a9c7969e40e7f"}}