{"paper":{"title":"Formal O(N3)-Scaling Second-Order Perturbation Theory by Block Tensor Decomposition: Implementation on MP2 and rPT2","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"physics.chem-ph","authors_text":"Peifeng Su, Wei Wu, Yueyang Zhang","submitted_at":"2026-05-27T17:08:11Z","abstract_excerpt":"Block tensor decomposition (BTD) and canonical polyadic decomposition (CPD) are combined into a unified $O(N^3)$-scaling framework for second-order perturbation theory (PT2), demonstrated on MP2 and renormalized PT2 (rPT2). BTD constructs the tensor hyper-contraction kernel at $O(N^3)$ via a dual-grid scheme; CPD factorizes the exchange channel through a block-based two-stage ALS. An asymmetric half-kernel design applies bare Coulomb to one vertex and coupling-constant-averaged screening to the other, capturing the SOSEX component of rPT2 without a frequency-dependent CPD. For MP2, BTD-CPD rep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.28750","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/2605.28750/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"}