{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:BGCASPGOTNDOGGRFEM4KO6TLSY","short_pith_number":"pith:BGCASPGO","canonical_record":{"source":{"id":"2302.11815","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2023-02-23T06:58:44Z","cross_cats_sorted":[],"title_canon_sha256":"1d558d66b6d9803f9decfcfa03d24774d030f3bea0e731f5a24f8265cd897b22","abstract_canon_sha256":"d1461e4d75b73df31cd3cba34e326615619c5f0f4f4923e737c9853a6be6deea"},"schema_version":"1.0"},"canonical_sha256":"0984093cce9b46e31a252338a77a6b963721a4b06082e483aee3b776ae983bb6","source":{"kind":"arxiv","id":"2302.11815","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.11815","created_at":"2026-07-05T06:09:48Z"},{"alias_kind":"arxiv_version","alias_value":"2302.11815v3","created_at":"2026-07-05T06:09:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.11815","created_at":"2026-07-05T06:09:48Z"},{"alias_kind":"pith_short_12","alias_value":"BGCASPGOTNDO","created_at":"2026-07-05T06:09:48Z"},{"alias_kind":"pith_short_16","alias_value":"BGCASPGOTNDOGGRF","created_at":"2026-07-05T06:09:48Z"},{"alias_kind":"pith_short_8","alias_value":"BGCASPGO","created_at":"2026-07-05T06:09:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:BGCASPGOTNDOGGRFEM4KO6TLSY","target":"record","payload":{"canonical_record":{"source":{"id":"2302.11815","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2023-02-23T06:58:44Z","cross_cats_sorted":[],"title_canon_sha256":"1d558d66b6d9803f9decfcfa03d24774d030f3bea0e731f5a24f8265cd897b22","abstract_canon_sha256":"d1461e4d75b73df31cd3cba34e326615619c5f0f4f4923e737c9853a6be6deea"},"schema_version":"1.0"},"canonical_sha256":"0984093cce9b46e31a252338a77a6b963721a4b06082e483aee3b776ae983bb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:09:48.584247Z","signature_b64":"01uS+y4s5oYbf+nvNMtKHLmFhvHrvXvytToexd9vxKeLfOrYlJetDo+7htdDPpivXtEYUdDAdK+K5q7wpGOrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0984093cce9b46e31a252338a77a6b963721a4b06082e483aee3b776ae983bb6","last_reissued_at":"2026-07-05T06:09:48.583798Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:09:48.583798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.11815","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T06:09:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DWAe5XvXwlO5zjwMSbmzTFnhbOybs7+gGI/IK8PUN/YK5UE7Lo12bSJhvzlhzIgXEcwz9s3Dmnnew3KsoUQJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T06:46:10.788926Z"},"content_sha256":"2f2898e3d1b45c8f7432aed23affe80e2925eb38f651b1142caac3802e906acd","schema_version":"1.0","event_id":"sha256:2f2898e3d1b45c8f7432aed23affe80e2925eb38f651b1142caac3802e906acd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:BGCASPGOTNDOGGRFEM4KO6TLSY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Walk on Stars: A Grid-Free Monte Carlo Method for PDEs with Neumann Boundary Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GR","authors_text":"Bailey Miller, Ioannis Gkioulekas, Keenan Crane, Rohan Sawhney","submitted_at":"2023-02-23T06:58:44Z","abstract_excerpt":"Grid-free Monte Carlo methods based on the walk on spheres (WoS) algorithm solve fundamental partial differential equations (PDEs) like the Poisson equation without discretizing the problem domain or approximating functions in a finite basis. Such methods hence avoid aliasing in the solution, and evade the many challenges of mesh generation. Yet for problems with complex geometry, practical grid-free methods have been largely limited to basic Dirichlet boundary conditions. We introduce the walk on stars (WoSt) algorithm, which solves linear elliptic PDEs with arbitrary mixed Neumann and Dirich"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.11815","kind":"arxiv","version":3},"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/2302.11815/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":"2026-07-05T06:09:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Sw8aORr2VDqmWgeNnOosgHfEFmq6PN2mRDWhXli71UzCtL+L6JGA7b3uMEidnuKO/OynjQkGZ2qTvxj99yefBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T06:46:10.789403Z"},"content_sha256":"1f51cc31a38b754dca8be179b43ed5a5ee2f00fbb40358e1883dcba87c80262a","schema_version":"1.0","event_id":"sha256:1f51cc31a38b754dca8be179b43ed5a5ee2f00fbb40358e1883dcba87c80262a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BGCASPGOTNDOGGRFEM4KO6TLSY/bundle.json","state_url":"https://pith.science/pith/BGCASPGOTNDOGGRFEM4KO6TLSY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BGCASPGOTNDOGGRFEM4KO6TLSY/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":"2026-08-05T06:46:10Z","links":{"resolver":"https://pith.science/pith/BGCASPGOTNDOGGRFEM4KO6TLSY","bundle":"https://pith.science/pith/BGCASPGOTNDOGGRFEM4KO6TLSY/bundle.json","state":"https://pith.science/pith/BGCASPGOTNDOGGRFEM4KO6TLSY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BGCASPGOTNDOGGRFEM4KO6TLSY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:BGCASPGOTNDOGGRFEM4KO6TLSY","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":"d1461e4d75b73df31cd3cba34e326615619c5f0f4f4923e737c9853a6be6deea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2023-02-23T06:58:44Z","title_canon_sha256":"1d558d66b6d9803f9decfcfa03d24774d030f3bea0e731f5a24f8265cd897b22"},"schema_version":"1.0","source":{"id":"2302.11815","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.11815","created_at":"2026-07-05T06:09:48Z"},{"alias_kind":"arxiv_version","alias_value":"2302.11815v3","created_at":"2026-07-05T06:09:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.11815","created_at":"2026-07-05T06:09:48Z"},{"alias_kind":"pith_short_12","alias_value":"BGCASPGOTNDO","created_at":"2026-07-05T06:09:48Z"},{"alias_kind":"pith_short_16","alias_value":"BGCASPGOTNDOGGRF","created_at":"2026-07-05T06:09:48Z"},{"alias_kind":"pith_short_8","alias_value":"BGCASPGO","created_at":"2026-07-05T06:09:48Z"}],"graph_snapshots":[{"event_id":"sha256:1f51cc31a38b754dca8be179b43ed5a5ee2f00fbb40358e1883dcba87c80262a","target":"graph","created_at":"2026-07-05T06:09:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.11815/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Grid-free Monte Carlo methods based on the walk on spheres (WoS) algorithm solve fundamental partial differential equations (PDEs) like the Poisson equation without discretizing the problem domain or approximating functions in a finite basis. Such methods hence avoid aliasing in the solution, and evade the many challenges of mesh generation. Yet for problems with complex geometry, practical grid-free methods have been largely limited to basic Dirichlet boundary conditions. We introduce the walk on stars (WoSt) algorithm, which solves linear elliptic PDEs with arbitrary mixed Neumann and Dirich","authors_text":"Bailey Miller, Ioannis Gkioulekas, Keenan Crane, Rohan Sawhney","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2023-02-23T06:58:44Z","title":"Walk on Stars: A Grid-Free Monte Carlo Method for PDEs with Neumann Boundary Conditions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.11815","kind":"arxiv","version":3},"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":"sha256:2f2898e3d1b45c8f7432aed23affe80e2925eb38f651b1142caac3802e906acd","target":"record","created_at":"2026-07-05T06:09:48Z","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":"d1461e4d75b73df31cd3cba34e326615619c5f0f4f4923e737c9853a6be6deea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2023-02-23T06:58:44Z","title_canon_sha256":"1d558d66b6d9803f9decfcfa03d24774d030f3bea0e731f5a24f8265cd897b22"},"schema_version":"1.0","source":{"id":"2302.11815","kind":"arxiv","version":3}},"canonical_sha256":"0984093cce9b46e31a252338a77a6b963721a4b06082e483aee3b776ae983bb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0984093cce9b46e31a252338a77a6b963721a4b06082e483aee3b776ae983bb6","first_computed_at":"2026-07-05T06:09:48.583798Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:09:48.583798Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"01uS+y4s5oYbf+nvNMtKHLmFhvHrvXvytToexd9vxKeLfOrYlJetDo+7htdDPpivXtEYUdDAdK+K5q7wpGOrBA==","signature_status":"signed_v1","signed_at":"2026-07-05T06:09:48.584247Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.11815","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f2898e3d1b45c8f7432aed23affe80e2925eb38f651b1142caac3802e906acd","sha256:1f51cc31a38b754dca8be179b43ed5a5ee2f00fbb40358e1883dcba87c80262a"],"state_sha256":"952e73971b19900b0eef8f408339bd3867d1752a45b8043f28d76cffcaf9e3a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iZ+4115AusJ8SxR/qXYRqHShmAnzH3PBcuPtE2i0V3vCq8QH51JZsFu0cZZaotqxkHdjJYbI6XD+rNzr/rC7Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T06:46:10.792722Z","bundle_sha256":"4cc3c06ad633e5b7826cfd6bb118d1eb4be3ccbffbf0f6efa20503b19b2ad93a"}}