{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:47HTALC3EL5U437FOU7HDYXYHS","short_pith_number":"pith:47HTALC3","canonical_record":{"source":{"id":"2202.02847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2022-02-06T20:38:12Z","cross_cats_sorted":[],"title_canon_sha256":"421a807d805e46ced7900a0ce0a79b33dd3e03c40c308b80501ab93ac671de1a","abstract_canon_sha256":"c5c9e4e03a58e2d5a3f0c8065616376bc4bf3c034203a7e5343d4af250d18344"},"schema_version":"1.0"},"canonical_sha256":"e7cf302c5b22fb4e6fe5753e71e2f83ca3df684fb33ac33a432e5de6af862723","source":{"kind":"arxiv","id":"2202.02847","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.02847","created_at":"2026-07-05T03:54:33Z"},{"alias_kind":"arxiv_version","alias_value":"2202.02847v1","created_at":"2026-07-05T03:54:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.02847","created_at":"2026-07-05T03:54:33Z"},{"alias_kind":"pith_short_12","alias_value":"47HTALC3EL5U","created_at":"2026-07-05T03:54:33Z"},{"alias_kind":"pith_short_16","alias_value":"47HTALC3EL5U437F","created_at":"2026-07-05T03:54:33Z"},{"alias_kind":"pith_short_8","alias_value":"47HTALC3","created_at":"2026-07-05T03:54:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:47HTALC3EL5U437FOU7HDYXYHS","target":"record","payload":{"canonical_record":{"source":{"id":"2202.02847","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2022-02-06T20:38:12Z","cross_cats_sorted":[],"title_canon_sha256":"421a807d805e46ced7900a0ce0a79b33dd3e03c40c308b80501ab93ac671de1a","abstract_canon_sha256":"c5c9e4e03a58e2d5a3f0c8065616376bc4bf3c034203a7e5343d4af250d18344"},"schema_version":"1.0"},"canonical_sha256":"e7cf302c5b22fb4e6fe5753e71e2f83ca3df684fb33ac33a432e5de6af862723","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:54:33.524840Z","signature_b64":"mVYizSmdCHf6Yx6v1GNsdTCUPqaEgPYjlurJTQF5EaJfDJRnnQqWfouDuggDXU2CCyTmJBcAh/JUdwxjmogeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7cf302c5b22fb4e6fe5753e71e2f83ca3df684fb33ac33a432e5de6af862723","last_reissued_at":"2026-07-05T03:54:33.524495Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:54:33.524495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2202.02847","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":"2026-07-05T03:54:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zSNvrkASU5Ia+hWXC0pzgJn60RRqveSKXWmmug2zdX64nJsbgzzj20jEEQEDHPVq9b5Ay2NiPc4l3X7KmGauCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T05:19:27.109420Z"},"content_sha256":"3cbca29d5ad202d94b07de9706e533fb8a45cf9d9215c568ed6f589be4463065","schema_version":"1.0","event_id":"sha256:3cbca29d5ad202d94b07de9706e533fb8a45cf9d9215c568ed6f589be4463065"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:47HTALC3EL5U437FOU7HDYXYHS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solidfmm: A highly optimised library of operations on the solid harmonics for use in fast multipole methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.MS","authors_text":"Matthias Kirchhart","submitted_at":"2022-02-06T20:38:12Z","abstract_excerpt":"We present solidfmm, a highly optimised C++ library for the solid harmonics as they are needed in fast multipole methods. The library provides efficient, vectorised implementations of the translation operations M2M, M2L, and L2L, and is available as free software. While asymptotically of complexity $O(P^3)$, for all practically relevant expansion orders, the translation operators display an empirical complexity of $O(P^2)$, outperforming the na\\\"ive implementation by orders of magnitude."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.02847","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/2202.02847/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":"2026-07-05T03:54:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bhEHneCU9WkLCzgxulsRcrqzyVNrMitxxRG1W1Cd0Bogn/dxsbK1DVb5IQcjw6gIX2fiD6cjOlThUse16r1LDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-09T05:19:27.109914Z"},"content_sha256":"9a906676ce89eae02011cedfbf63ef065ebf5e05b4bb5d68247604baa053d366","schema_version":"1.0","event_id":"sha256:9a906676ce89eae02011cedfbf63ef065ebf5e05b4bb5d68247604baa053d366"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/47HTALC3EL5U437FOU7HDYXYHS/bundle.json","state_url":"https://pith.science/pith/47HTALC3EL5U437FOU7HDYXYHS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/47HTALC3EL5U437FOU7HDYXYHS/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":"2026-07-09T05:19:27Z","links":{"resolver":"https://pith.science/pith/47HTALC3EL5U437FOU7HDYXYHS","bundle":"https://pith.science/pith/47HTALC3EL5U437FOU7HDYXYHS/bundle.json","state":"https://pith.science/pith/47HTALC3EL5U437FOU7HDYXYHS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/47HTALC3EL5U437FOU7HDYXYHS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:47HTALC3EL5U437FOU7HDYXYHS","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":"c5c9e4e03a58e2d5a3f0c8065616376bc4bf3c034203a7e5343d4af250d18344","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2022-02-06T20:38:12Z","title_canon_sha256":"421a807d805e46ced7900a0ce0a79b33dd3e03c40c308b80501ab93ac671de1a"},"schema_version":"1.0","source":{"id":"2202.02847","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2202.02847","created_at":"2026-07-05T03:54:33Z"},{"alias_kind":"arxiv_version","alias_value":"2202.02847v1","created_at":"2026-07-05T03:54:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2202.02847","created_at":"2026-07-05T03:54:33Z"},{"alias_kind":"pith_short_12","alias_value":"47HTALC3EL5U","created_at":"2026-07-05T03:54:33Z"},{"alias_kind":"pith_short_16","alias_value":"47HTALC3EL5U437F","created_at":"2026-07-05T03:54:33Z"},{"alias_kind":"pith_short_8","alias_value":"47HTALC3","created_at":"2026-07-05T03:54:33Z"}],"graph_snapshots":[{"event_id":"sha256:9a906676ce89eae02011cedfbf63ef065ebf5e05b4bb5d68247604baa053d366","target":"graph","created_at":"2026-07-05T03:54:33Z","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/2202.02847/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present solidfmm, a highly optimised C++ library for the solid harmonics as they are needed in fast multipole methods. The library provides efficient, vectorised implementations of the translation operations M2M, M2L, and L2L, and is available as free software. While asymptotically of complexity $O(P^3)$, for all practically relevant expansion orders, the translation operators display an empirical complexity of $O(P^2)$, outperforming the na\\\"ive implementation by orders of magnitude.","authors_text":"Matthias Kirchhart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2022-02-06T20:38:12Z","title":"Solidfmm: A highly optimised library of operations on the solid harmonics for use in fast multipole methods"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2202.02847","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":"sha256:3cbca29d5ad202d94b07de9706e533fb8a45cf9d9215c568ed6f589be4463065","target":"record","created_at":"2026-07-05T03:54:33Z","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":"c5c9e4e03a58e2d5a3f0c8065616376bc4bf3c034203a7e5343d4af250d18344","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.MS","submitted_at":"2022-02-06T20:38:12Z","title_canon_sha256":"421a807d805e46ced7900a0ce0a79b33dd3e03c40c308b80501ab93ac671de1a"},"schema_version":"1.0","source":{"id":"2202.02847","kind":"arxiv","version":1}},"canonical_sha256":"e7cf302c5b22fb4e6fe5753e71e2f83ca3df684fb33ac33a432e5de6af862723","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7cf302c5b22fb4e6fe5753e71e2f83ca3df684fb33ac33a432e5de6af862723","first_computed_at":"2026-07-05T03:54:33.524495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:54:33.524495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mVYizSmdCHf6Yx6v1GNsdTCUPqaEgPYjlurJTQF5EaJfDJRnnQqWfouDuggDXU2CCyTmJBcAh/JUdwxjmogeDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:54:33.524840Z","signed_message":"canonical_sha256_bytes"},"source_id":"2202.02847","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3cbca29d5ad202d94b07de9706e533fb8a45cf9d9215c568ed6f589be4463065","sha256:9a906676ce89eae02011cedfbf63ef065ebf5e05b4bb5d68247604baa053d366"],"state_sha256":"19194769acda33a420d749cbc1177fff0f64001976b811d8c7d1d0abe6dad153"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b6jLZ6A0mFnyhqa/WWoeLw7Pqq/p6fRVP+Wn6YRdDVt4+PCoSkqr01CPAgfVkTMdFVwyRGOz6ZWUZK1ox1zCAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-09T05:19:27.113601Z","bundle_sha256":"95595cf43c5da8e80864f84222a55a41e636ac5e424f0fd5bfa462b216528ffd"}}