{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PKSNLISOKKKYXIMQ33A34W73JM","short_pith_number":"pith:PKSNLISO","canonical_record":{"source":{"id":"1806.07193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-19T12:50:09Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"8d52e54e67a4166deaeb05cafd715d58900694fdb3699d16255a731b9f660d68","abstract_canon_sha256":"ab2a44180cebbc762a06f0b42a005a1565730f8ca06c1a21b5240a0980192d08"},"schema_version":"1.0"},"canonical_sha256":"7aa4d5a24e52958ba190dec1be5bfb4b032a3e108dc056ae36061ad7784ca70a","source":{"kind":"arxiv","id":"1806.07193","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07193","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07193v2","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07193","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"PKSNLISOKKKY","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PKSNLISOKKKYXIMQ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PKSNLISO","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PKSNLISOKKKYXIMQ33A34W73JM","target":"record","payload":{"canonical_record":{"source":{"id":"1806.07193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-19T12:50:09Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"8d52e54e67a4166deaeb05cafd715d58900694fdb3699d16255a731b9f660d68","abstract_canon_sha256":"ab2a44180cebbc762a06f0b42a005a1565730f8ca06c1a21b5240a0980192d08"},"schema_version":"1.0"},"canonical_sha256":"7aa4d5a24e52958ba190dec1be5bfb4b032a3e108dc056ae36061ad7784ca70a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:30.338935Z","signature_b64":"oyyB99mfwIoKiUUZuAPkaT4Y9DJJ/CqQ+JorkPPcAEx2T5wdDj9XnNAjw/2HTINGx4aPsoUzegbEFA/GWfOEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7aa4d5a24e52958ba190dec1be5bfb4b032a3e108dc056ae36061ad7784ca70a","last_reissued_at":"2026-05-17T23:46:30.338382Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:30.338382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.07193","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M70vBYlezcEaj3HNxoCQBm2uypTi2t9JXIa7PYgrAFahgtfUBOroBmJxPbed64Z0MykMGO1s7v5+t1LwZEJfBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:39:37.568382Z"},"content_sha256":"68d9915103fb06eaf5a642145b4720cc72b1309a2ea4b0c84e644ca373383922","schema_version":"1.0","event_id":"sha256:68d9915103fb06eaf5a642145b4720cc72b1309a2ea4b0c84e644ca373383922"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PKSNLISOKKKYXIMQ33A34W73JM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Meshfree Generalized Finite Difference Method for Surface PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"math.NA","authors_text":"Joerg Kuhnert, Pratik Suchde","submitted_at":"2018-06-19T12:50:09Z","abstract_excerpt":"In this paper, we propose a novel meshfree Generalized Finite Difference Method (GFDM) approach to discretize PDEs defined on manifolds. Derivative approximations for the same are done directly on the tangent space, in a manner that mimics the procedure followed in volume-based meshfree GFDMs. As a result, the proposed method not only does not require a mesh, it also does not require an explicit reconstruction of the manifold. In contrast to existing methods, it avoids the complexities of dealing with a manifold metric, while also avoiding the need to solve a PDE in the embedding space. A majo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07193","kind":"arxiv","version":2},"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":"2026-05-17T23:46:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cjojtEdYgfXh+roQeuq5BbdM3Jhud/wsG2dzHx2b/mk7IY0f4LK/yRA0Rzs8ogx4wBKrLWcjp5ec5oao5F6cAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:39:37.569242Z"},"content_sha256":"3fa659e4608adb60607e488bb261af3efdf8e1d6e2882f433d5c063fd32b5de9","schema_version":"1.0","event_id":"sha256:3fa659e4608adb60607e488bb261af3efdf8e1d6e2882f433d5c063fd32b5de9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PKSNLISOKKKYXIMQ33A34W73JM/bundle.json","state_url":"https://pith.science/pith/PKSNLISOKKKYXIMQ33A34W73JM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PKSNLISOKKKYXIMQ33A34W73JM/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":"2026-05-31T09:39:37Z","links":{"resolver":"https://pith.science/pith/PKSNLISOKKKYXIMQ33A34W73JM","bundle":"https://pith.science/pith/PKSNLISOKKKYXIMQ33A34W73JM/bundle.json","state":"https://pith.science/pith/PKSNLISOKKKYXIMQ33A34W73JM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PKSNLISOKKKYXIMQ33A34W73JM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PKSNLISOKKKYXIMQ33A34W73JM","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":"ab2a44180cebbc762a06f0b42a005a1565730f8ca06c1a21b5240a0980192d08","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-19T12:50:09Z","title_canon_sha256":"8d52e54e67a4166deaeb05cafd715d58900694fdb3699d16255a731b9f660d68"},"schema_version":"1.0","source":{"id":"1806.07193","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07193","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07193v2","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07193","created_at":"2026-05-17T23:46:30Z"},{"alias_kind":"pith_short_12","alias_value":"PKSNLISOKKKY","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"PKSNLISOKKKYXIMQ","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"PKSNLISO","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:3fa659e4608adb60607e488bb261af3efdf8e1d6e2882f433d5c063fd32b5de9","target":"graph","created_at":"2026-05-17T23:46:30Z","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":"In this paper, we propose a novel meshfree Generalized Finite Difference Method (GFDM) approach to discretize PDEs defined on manifolds. Derivative approximations for the same are done directly on the tangent space, in a manner that mimics the procedure followed in volume-based meshfree GFDMs. As a result, the proposed method not only does not require a mesh, it also does not require an explicit reconstruction of the manifold. In contrast to existing methods, it avoids the complexities of dealing with a manifold metric, while also avoiding the need to solve a PDE in the embedding space. A majo","authors_text":"Joerg Kuhnert, Pratik Suchde","cross_cats":["physics.comp-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-19T12:50:09Z","title":"A Meshfree Generalized Finite Difference Method for Surface PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07193","kind":"arxiv","version":2},"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":"sha256:68d9915103fb06eaf5a642145b4720cc72b1309a2ea4b0c84e644ca373383922","target":"record","created_at":"2026-05-17T23:46:30Z","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":"ab2a44180cebbc762a06f0b42a005a1565730f8ca06c1a21b5240a0980192d08","cross_cats_sorted":["physics.comp-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2018-06-19T12:50:09Z","title_canon_sha256":"8d52e54e67a4166deaeb05cafd715d58900694fdb3699d16255a731b9f660d68"},"schema_version":"1.0","source":{"id":"1806.07193","kind":"arxiv","version":2}},"canonical_sha256":"7aa4d5a24e52958ba190dec1be5bfb4b032a3e108dc056ae36061ad7784ca70a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7aa4d5a24e52958ba190dec1be5bfb4b032a3e108dc056ae36061ad7784ca70a","first_computed_at":"2026-05-17T23:46:30.338382Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:30.338382Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oyyB99mfwIoKiUUZuAPkaT4Y9DJJ/CqQ+JorkPPcAEx2T5wdDj9XnNAjw/2HTINGx4aPsoUzegbEFA/GWfOEDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:30.338935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07193","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68d9915103fb06eaf5a642145b4720cc72b1309a2ea4b0c84e644ca373383922","sha256:3fa659e4608adb60607e488bb261af3efdf8e1d6e2882f433d5c063fd32b5de9"],"state_sha256":"5ede950f59db3e72b8cc7d8dc5acdf546db2eaf722c04e73bc2ef7d5939b6f6f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1jYmB66Ly2AXFQKO1ZwtPm6cYn4HO4cboT62FrD4rYydO1DLH8wrtNbLwbsbqtlP42DrFBEA4JDOTfnG2spCDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:39:37.574002Z","bundle_sha256":"38fa6f7de30236ce67ab3c17dd1686063b81e3dc5c77a971aaee8b448d27188e"}}