{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YUMLMX4265QZVMLMUWTCNIVXM5","short_pith_number":"pith:YUMLMX42","canonical_record":{"source":{"id":"1405.2270","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-09T15:45:15Z","cross_cats_sorted":[],"title_canon_sha256":"2944034dc637418b276e99da8ff770642c3da1c6fdc91959186697784ef51e54","abstract_canon_sha256":"80da3a8a956791bed13822c09473342790c6f2d2102c0f59472a4249b02d792d"},"schema_version":"1.0"},"canonical_sha256":"c518b65f9af7619ab16ca5a626a2b76769dc179e85f49ba23197f40b8ae0c0b8","source":{"kind":"arxiv","id":"1405.2270","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2270","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2270v2","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2270","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"pith_short_12","alias_value":"YUMLMX4265QZ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YUMLMX4265QZVMLM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YUMLMX42","created_at":"2026-05-18T12:28:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YUMLMX4265QZVMLMUWTCNIVXM5","target":"record","payload":{"canonical_record":{"source":{"id":"1405.2270","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-09T15:45:15Z","cross_cats_sorted":[],"title_canon_sha256":"2944034dc637418b276e99da8ff770642c3da1c6fdc91959186697784ef51e54","abstract_canon_sha256":"80da3a8a956791bed13822c09473342790c6f2d2102c0f59472a4249b02d792d"},"schema_version":"1.0"},"canonical_sha256":"c518b65f9af7619ab16ca5a626a2b76769dc179e85f49ba23197f40b8ae0c0b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:15.690298Z","signature_b64":"M+C29IowMW5HrbvZXmv56xUSG2/HZtQDyF16l1nnHO44LZ1i2V3sHTQf9ioF0MgwqROHsReJamZIlIbpyOqWCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c518b65f9af7619ab16ca5a626a2b76769dc179e85f49ba23197f40b8ae0c0b8","last_reissued_at":"2026-05-18T01:43:15.689687Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:15.689687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.2270","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":"2026-05-18T01:43:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vsWYTRBiOhcOBTHnb1cJXD9ChltG8R5nicmoFxxqYy7nCgNuxsDHC32V8v5Wn9rZ4ASbaeLvL1qC7rIt9oCMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:08:33.290132Z"},"content_sha256":"0f1f14ed7c739358e6d77512a2262893ab1c1803ec92d665ca17967fbc3b8d66","schema_version":"1.0","event_id":"sha256:0f1f14ed7c739358e6d77512a2262893ab1c1803ec92d665ca17967fbc3b8d66"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YUMLMX4265QZVMLMUWTCNIVXM5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Boris N. Khoromskij, Venera Khoromskaia","submitted_at":"2014-05-09T15:45:15Z","abstract_excerpt":"We introduce and study a novel tensor approach for fast and accurate assembled summation of a large number of lattice-allocated potentials represented on 3D $N\\times N \\times N$ grid with the computational requirements only \\emph{weakly dependent} on the number of summed potentials. It is based on the assembled low-rank canonical tensor representations of the collected potentials using pointwise sums of shifted canonical vectors representing the single generating function, say the Newton kernel. For a sum of electrostatic potentials over $L\\times L \\times L$ lattice embedded in a box the requi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2270","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":"2026-05-18T01:43:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wboy49L0bLZRW4O3wOjDdBHwLT3s+xTo/MPrWBY2q9YMkYzdsX0AcldtcPekQxRP30DfRHL0f+xirYjOf0EmCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:08:33.290562Z"},"content_sha256":"87d0b5e83228072c97e92fe6796f1aef133dcbe0c0694dcdf0a837747eb15faa","schema_version":"1.0","event_id":"sha256:87d0b5e83228072c97e92fe6796f1aef133dcbe0c0694dcdf0a837747eb15faa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YUMLMX4265QZVMLMUWTCNIVXM5/bundle.json","state_url":"https://pith.science/pith/YUMLMX4265QZVMLMUWTCNIVXM5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YUMLMX4265QZVMLMUWTCNIVXM5/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":"2026-05-31T06:08:33Z","links":{"resolver":"https://pith.science/pith/YUMLMX4265QZVMLMUWTCNIVXM5","bundle":"https://pith.science/pith/YUMLMX4265QZVMLMUWTCNIVXM5/bundle.json","state":"https://pith.science/pith/YUMLMX4265QZVMLMUWTCNIVXM5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YUMLMX4265QZVMLMUWTCNIVXM5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YUMLMX4265QZVMLMUWTCNIVXM5","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":"80da3a8a956791bed13822c09473342790c6f2d2102c0f59472a4249b02d792d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-09T15:45:15Z","title_canon_sha256":"2944034dc637418b276e99da8ff770642c3da1c6fdc91959186697784ef51e54"},"schema_version":"1.0","source":{"id":"1405.2270","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2270","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2270v2","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2270","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"pith_short_12","alias_value":"YUMLMX4265QZ","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"YUMLMX4265QZVMLM","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"YUMLMX42","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:87d0b5e83228072c97e92fe6796f1aef133dcbe0c0694dcdf0a837747eb15faa","target":"graph","created_at":"2026-05-18T01:43:15Z","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":"We introduce and study a novel tensor approach for fast and accurate assembled summation of a large number of lattice-allocated potentials represented on 3D $N\\times N \\times N$ grid with the computational requirements only \\emph{weakly dependent} on the number of summed potentials. It is based on the assembled low-rank canonical tensor representations of the collected potentials using pointwise sums of shifted canonical vectors representing the single generating function, say the Newton kernel. For a sum of electrostatic potentials over $L\\times L \\times L$ lattice embedded in a box the requi","authors_text":"Boris N. Khoromskij, Venera Khoromskaia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-09T15:45:15Z","title":"Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2270","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":"sha256:0f1f14ed7c739358e6d77512a2262893ab1c1803ec92d665ca17967fbc3b8d66","target":"record","created_at":"2026-05-18T01:43:15Z","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":"80da3a8a956791bed13822c09473342790c6f2d2102c0f59472a4249b02d792d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2014-05-09T15:45:15Z","title_canon_sha256":"2944034dc637418b276e99da8ff770642c3da1c6fdc91959186697784ef51e54"},"schema_version":"1.0","source":{"id":"1405.2270","kind":"arxiv","version":2}},"canonical_sha256":"c518b65f9af7619ab16ca5a626a2b76769dc179e85f49ba23197f40b8ae0c0b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c518b65f9af7619ab16ca5a626a2b76769dc179e85f49ba23197f40b8ae0c0b8","first_computed_at":"2026-05-18T01:43:15.689687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:15.689687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M+C29IowMW5HrbvZXmv56xUSG2/HZtQDyF16l1nnHO44LZ1i2V3sHTQf9ioF0MgwqROHsReJamZIlIbpyOqWCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:15.690298Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2270","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f1f14ed7c739358e6d77512a2262893ab1c1803ec92d665ca17967fbc3b8d66","sha256:87d0b5e83228072c97e92fe6796f1aef133dcbe0c0694dcdf0a837747eb15faa"],"state_sha256":"d0baaa87969e296e3d12f8c6f20da4f0cfc6a45892d68e6ea4b28948e1cd152b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0AmeJ4/eqh9MouysDqIPCb2qBRiQ6yg3Ly1mUwLVECySSbjv8KHtxVLWqqIr7vcBqxQc7f4VHar+PqSi54XkBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:08:33.292839Z","bundle_sha256":"ad3ad4aa40073b22957ae8f30855393c2f43bd1ca5f3648012d7173ee3f840f6"}}