{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:YSCDYF2UPMSS4UOTZFKXVX3IO6","short_pith_number":"pith:YSCDYF2U","canonical_record":{"source":{"id":"1906.10734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2019-06-25T19:30:00Z","cross_cats_sorted":["astro-ph.CO","astro-ph.GA"],"title_canon_sha256":"6b071d08373166d774f193a96e4a8d22ef4a663182ac24a12d23238816f33f81","abstract_canon_sha256":"74af17046e7fb9e9e2692ab2da004ef49db6e7a2bd3b537108a03151bf8e8fb2"},"schema_version":"1.0"},"canonical_sha256":"c4843c17547b252e51d3c9557adf68778d15fbe288159981b79fb2ef9231857d","source":{"kind":"arxiv","id":"1906.10734","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10734","created_at":"2026-07-04T23:50:20Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10734v1","created_at":"2026-07-04T23:50:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10734","created_at":"2026-07-04T23:50:20Z"},{"alias_kind":"pith_short_12","alias_value":"YSCDYF2UPMSS","created_at":"2026-07-04T23:50:20Z"},{"alias_kind":"pith_short_16","alias_value":"YSCDYF2UPMSS4UOT","created_at":"2026-07-04T23:50:20Z"},{"alias_kind":"pith_short_8","alias_value":"YSCDYF2U","created_at":"2026-07-04T23:50:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:YSCDYF2UPMSS4UOTZFKXVX3IO6","target":"record","payload":{"canonical_record":{"source":{"id":"1906.10734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2019-06-25T19:30:00Z","cross_cats_sorted":["astro-ph.CO","astro-ph.GA"],"title_canon_sha256":"6b071d08373166d774f193a96e4a8d22ef4a663182ac24a12d23238816f33f81","abstract_canon_sha256":"74af17046e7fb9e9e2692ab2da004ef49db6e7a2bd3b537108a03151bf8e8fb2"},"schema_version":"1.0"},"canonical_sha256":"c4843c17547b252e51d3c9557adf68778d15fbe288159981b79fb2ef9231857d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:50:20.479394Z","signature_b64":"g7rIHUD8tc1Jl0F5poPsGbjF20UiBCq3xnKDQCW7lpj/wvdGfB9vnh7vTDtDVvplDKUkqAvgKxT5XT0MBNM/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4843c17547b252e51d3c9557adf68778d15fbe288159981b79fb2ef9231857d","last_reissued_at":"2026-07-04T23:50:20.478943Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:50:20.478943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.10734","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":"2026-07-04T23:50:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A0qobiBXl5Sp4F2soA720/T1vEqzXTkWzPypC0mFQMsnVM+QilOfSDEjWRCDE3ztRq0iZtk6Ow8yMdcPd/Z0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T02:01:23.347066Z"},"content_sha256":"f640c528baf1d2eaaa4d7f613046f0f7bbc46cce681c68ce61abb457bbae42c9","schema_version":"1.0","event_id":"sha256:f640c528baf1d2eaaa4d7f613046f0f7bbc46cce681c68ce61abb457bbae42c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:YSCDYF2UPMSS4UOTZFKXVX3IO6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hierarchical Particle-Mesh: an FFT-accelerated Fast Multipole Method","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","astro-ph.GA"],"primary_cat":"physics.comp-ph","authors_text":"Nickolay Y. Gnedin","submitted_at":"2019-06-25T19:30:00Z","abstract_excerpt":"I describe a modification to the original Fast Multipole Method (FMM) of Greengard & Rokhlin that approximates the gravitation field of an FMM cell as a small uniform grid (a \"gridlet\") of effective masses. The effective masses on a gridlet are set from the requirement that the multipole moments of the FMM cells are reproduced exactly, hence preserving the accuracy of the gravitational field representation. The calculation of the gravitational field from a multipole expansion can then be computed for all multipole orders simultaneously, with a single Fast Fourier Transform, significantly reduc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10734","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1906.10734/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":"2026-07-04T23:50:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8jIkqeKMOIlzNwuYywj/hQkmLJYd7RJqW4I5hRxlYtJmNCQx32xuaXx9PAV+cZ3cBLsEZGCSVc8MbBFWWGuHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-02T02:01:23.347402Z"},"content_sha256":"4629c03f17691d34570c72fb75c2b98733159a86372bcfc09813e040c24b863c","schema_version":"1.0","event_id":"sha256:4629c03f17691d34570c72fb75c2b98733159a86372bcfc09813e040c24b863c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YSCDYF2UPMSS4UOTZFKXVX3IO6/bundle.json","state_url":"https://pith.science/pith/YSCDYF2UPMSS4UOTZFKXVX3IO6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YSCDYF2UPMSS4UOTZFKXVX3IO6/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":"2026-08-02T02:01:23Z","links":{"resolver":"https://pith.science/pith/YSCDYF2UPMSS4UOTZFKXVX3IO6","bundle":"https://pith.science/pith/YSCDYF2UPMSS4UOTZFKXVX3IO6/bundle.json","state":"https://pith.science/pith/YSCDYF2UPMSS4UOTZFKXVX3IO6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YSCDYF2UPMSS4UOTZFKXVX3IO6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:YSCDYF2UPMSS4UOTZFKXVX3IO6","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":"74af17046e7fb9e9e2692ab2da004ef49db6e7a2bd3b537108a03151bf8e8fb2","cross_cats_sorted":["astro-ph.CO","astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2019-06-25T19:30:00Z","title_canon_sha256":"6b071d08373166d774f193a96e4a8d22ef4a663182ac24a12d23238816f33f81"},"schema_version":"1.0","source":{"id":"1906.10734","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10734","created_at":"2026-07-04T23:50:20Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10734v1","created_at":"2026-07-04T23:50:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10734","created_at":"2026-07-04T23:50:20Z"},{"alias_kind":"pith_short_12","alias_value":"YSCDYF2UPMSS","created_at":"2026-07-04T23:50:20Z"},{"alias_kind":"pith_short_16","alias_value":"YSCDYF2UPMSS4UOT","created_at":"2026-07-04T23:50:20Z"},{"alias_kind":"pith_short_8","alias_value":"YSCDYF2U","created_at":"2026-07-04T23:50:20Z"}],"graph_snapshots":[{"event_id":"sha256:4629c03f17691d34570c72fb75c2b98733159a86372bcfc09813e040c24b863c","target":"graph","created_at":"2026-07-04T23:50:20Z","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/1906.10734/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"I describe a modification to the original Fast Multipole Method (FMM) of Greengard & Rokhlin that approximates the gravitation field of an FMM cell as a small uniform grid (a \"gridlet\") of effective masses. The effective masses on a gridlet are set from the requirement that the multipole moments of the FMM cells are reproduced exactly, hence preserving the accuracy of the gravitational field representation. The calculation of the gravitational field from a multipole expansion can then be computed for all multipole orders simultaneously, with a single Fast Fourier Transform, significantly reduc","authors_text":"Nickolay Y. Gnedin","cross_cats":["astro-ph.CO","astro-ph.GA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2019-06-25T19:30:00Z","title":"Hierarchical Particle-Mesh: an FFT-accelerated Fast Multipole Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10734","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:f640c528baf1d2eaaa4d7f613046f0f7bbc46cce681c68ce61abb457bbae42c9","target":"record","created_at":"2026-07-04T23:50:20Z","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":"74af17046e7fb9e9e2692ab2da004ef49db6e7a2bd3b537108a03151bf8e8fb2","cross_cats_sorted":["astro-ph.CO","astro-ph.GA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.comp-ph","submitted_at":"2019-06-25T19:30:00Z","title_canon_sha256":"6b071d08373166d774f193a96e4a8d22ef4a663182ac24a12d23238816f33f81"},"schema_version":"1.0","source":{"id":"1906.10734","kind":"arxiv","version":1}},"canonical_sha256":"c4843c17547b252e51d3c9557adf68778d15fbe288159981b79fb2ef9231857d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4843c17547b252e51d3c9557adf68778d15fbe288159981b79fb2ef9231857d","first_computed_at":"2026-07-04T23:50:20.478943Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:50:20.478943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"g7rIHUD8tc1Jl0F5poPsGbjF20UiBCq3xnKDQCW7lpj/wvdGfB9vnh7vTDtDVvplDKUkqAvgKxT5XT0MBNM/Ag==","signature_status":"signed_v1","signed_at":"2026-07-04T23:50:20.479394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.10734","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f640c528baf1d2eaaa4d7f613046f0f7bbc46cce681c68ce61abb457bbae42c9","sha256:4629c03f17691d34570c72fb75c2b98733159a86372bcfc09813e040c24b863c"],"state_sha256":"538605a9d3ef327b1005bf0e64682e46ddedac184a7ab50cb7406de8b94b3d9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hWdz2cBsoohCFhEFCAhF5Aoze0P4cADfgPRZUNeGTQs/jCGhDE0OteeEl1FI4lceRUzXot7hydNJJGhCy/jiBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-02T02:01:23.351587Z","bundle_sha256":"03ec2d8ea18c65d3cd43d98ddc8df95c3edb3b1fbe28746472875f3f543864a0"}}