{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WMU6EFO323NW22J7YON6NTXH4D","short_pith_number":"pith:WMU6EFO3","canonical_record":{"source":{"id":"1112.3376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2011-12-14T22:13:13Z","cross_cats_sorted":[],"title_canon_sha256":"3ae6c0a96a9cfb5d84c1bcadf2806052aa49a10552a8a15f16e76f74ff8f6190","abstract_canon_sha256":"95fa7e9cecff4b975867e8e9df3837030b60b90d356cb5f85cc435c1207bf73a"},"schema_version":"1.0"},"canonical_sha256":"b329e215dbd6db6d693fc39be6cee7e0c0f26c5f7121bfe01cfbe4455a0c183b","source":{"kind":"arxiv","id":"1112.3376","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3376","created_at":"2026-05-18T01:59:09Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3376v1","created_at":"2026-05-18T01:59:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3376","created_at":"2026-05-18T01:59:09Z"},{"alias_kind":"pith_short_12","alias_value":"WMU6EFO323NW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WMU6EFO323NW22J7","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WMU6EFO3","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WMU6EFO323NW22J7YON6NTXH4D","target":"record","payload":{"canonical_record":{"source":{"id":"1112.3376","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2011-12-14T22:13:13Z","cross_cats_sorted":[],"title_canon_sha256":"3ae6c0a96a9cfb5d84c1bcadf2806052aa49a10552a8a15f16e76f74ff8f6190","abstract_canon_sha256":"95fa7e9cecff4b975867e8e9df3837030b60b90d356cb5f85cc435c1207bf73a"},"schema_version":"1.0"},"canonical_sha256":"b329e215dbd6db6d693fc39be6cee7e0c0f26c5f7121bfe01cfbe4455a0c183b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:09.609083Z","signature_b64":"YdmzAKpIRlKc1Xg8OPpD65bsmJ+pxcupRE6RHjB2wJT5LdQz2SBQYmGrIcaviWXCbNurmDgEGXy346fgyfIEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b329e215dbd6db6d693fc39be6cee7e0c0f26c5f7121bfe01cfbe4455a0c183b","last_reissued_at":"2026-05-18T01:59:09.608289Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:09.608289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.3376","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":"2026-05-18T01:59:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OPMOOM8f2AMfCLrdSSyYL49hIHiK33vH7+2yfEHcUVTDdtjKkWV8F06rj4bdLyjfoLDls7oVkMLrE7QRPM3nAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:16:56.932354Z"},"content_sha256":"161b932a8af30315eef16d80b0ef9fbe070da0f085e758f3d569a97abf61857c","schema_version":"1.0","event_id":"sha256:161b932a8af30315eef16d80b0ef9fbe070da0f085e758f3d569a97abf61857c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WMU6EFO323NW22J7YON6NTXH4D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Physical Multipoles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.class-ph","authors_text":"Alexey Onufriev, Charles Baker, Ramu Anandakrishnan","submitted_at":"2011-12-14T22:13:13Z","abstract_excerpt":"Point multipole expansions are widely used to gain physical insight into complex distributions of charges and to reduce the cost of computing interactions between such distributions. However, practical applications that typically retain only a few leading terms may suffer from unacceptable loss of accuracy in the near-field. We propose an alternative approach for approximating electrostatic charge distributions, Optimal Physical Multipoles (OPMs), which optimally represent the original charge distribution with a set of point charges. By construction, approximation of electrostatic potential ba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3376","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":"2026-05-18T01:59:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HV/mT0R38fuYYltPvlppXAqfd7x6vvx/Sf0NtJzq0XGGFqJsVBuXmp5PXoQND8nnwXJIqwH9Id5rMTL/kj7NAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:16:56.932706Z"},"content_sha256":"681465c03c75cf558766f0ea128ada38fa78918323d23a77696f6bfdf0a18ead","schema_version":"1.0","event_id":"sha256:681465c03c75cf558766f0ea128ada38fa78918323d23a77696f6bfdf0a18ead"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WMU6EFO323NW22J7YON6NTXH4D/bundle.json","state_url":"https://pith.science/pith/WMU6EFO323NW22J7YON6NTXH4D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WMU6EFO323NW22J7YON6NTXH4D/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":"2026-05-28T13:16:56Z","links":{"resolver":"https://pith.science/pith/WMU6EFO323NW22J7YON6NTXH4D","bundle":"https://pith.science/pith/WMU6EFO323NW22J7YON6NTXH4D/bundle.json","state":"https://pith.science/pith/WMU6EFO323NW22J7YON6NTXH4D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WMU6EFO323NW22J7YON6NTXH4D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WMU6EFO323NW22J7YON6NTXH4D","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":"95fa7e9cecff4b975867e8e9df3837030b60b90d356cb5f85cc435c1207bf73a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2011-12-14T22:13:13Z","title_canon_sha256":"3ae6c0a96a9cfb5d84c1bcadf2806052aa49a10552a8a15f16e76f74ff8f6190"},"schema_version":"1.0","source":{"id":"1112.3376","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3376","created_at":"2026-05-18T01:59:09Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3376v1","created_at":"2026-05-18T01:59:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3376","created_at":"2026-05-18T01:59:09Z"},{"alias_kind":"pith_short_12","alias_value":"WMU6EFO323NW","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WMU6EFO323NW22J7","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WMU6EFO3","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:681465c03c75cf558766f0ea128ada38fa78918323d23a77696f6bfdf0a18ead","target":"graph","created_at":"2026-05-18T01:59:09Z","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":"Point multipole expansions are widely used to gain physical insight into complex distributions of charges and to reduce the cost of computing interactions between such distributions. However, practical applications that typically retain only a few leading terms may suffer from unacceptable loss of accuracy in the near-field. We propose an alternative approach for approximating electrostatic charge distributions, Optimal Physical Multipoles (OPMs), which optimally represent the original charge distribution with a set of point charges. By construction, approximation of electrostatic potential ba","authors_text":"Alexey Onufriev, Charles Baker, Ramu Anandakrishnan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2011-12-14T22:13:13Z","title":"Optimal Physical Multipoles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3376","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":"sha256:161b932a8af30315eef16d80b0ef9fbe070da0f085e758f3d569a97abf61857c","target":"record","created_at":"2026-05-18T01:59:09Z","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":"95fa7e9cecff4b975867e8e9df3837030b60b90d356cb5f85cc435c1207bf73a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.class-ph","submitted_at":"2011-12-14T22:13:13Z","title_canon_sha256":"3ae6c0a96a9cfb5d84c1bcadf2806052aa49a10552a8a15f16e76f74ff8f6190"},"schema_version":"1.0","source":{"id":"1112.3376","kind":"arxiv","version":1}},"canonical_sha256":"b329e215dbd6db6d693fc39be6cee7e0c0f26c5f7121bfe01cfbe4455a0c183b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b329e215dbd6db6d693fc39be6cee7e0c0f26c5f7121bfe01cfbe4455a0c183b","first_computed_at":"2026-05-18T01:59:09.608289Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:09.608289Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YdmzAKpIRlKc1Xg8OPpD65bsmJ+pxcupRE6RHjB2wJT5LdQz2SBQYmGrIcaviWXCbNurmDgEGXy346fgyfIEAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:09.609083Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3376","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:161b932a8af30315eef16d80b0ef9fbe070da0f085e758f3d569a97abf61857c","sha256:681465c03c75cf558766f0ea128ada38fa78918323d23a77696f6bfdf0a18ead"],"state_sha256":"baaa9f984cece2362df5d92dd6b54d1f72be54889fd3dcdb8d5054981757efe7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZYwikcas1k13BFJaeXoJdGep1vyhSVdM8QJkvJyTjNtMQb34F2mYK5QnbUfGyodpg2re0TEaeS9k1nVsqXlXDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:16:56.934678Z","bundle_sha256":"1887999dd2d64d0332b30b7b8efa546f2e46130e3d787c53d60da650249f3b55"}}