{"paper":{"title":"\"Pairs of Squares\" Periodic Table","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The 'Pairs of Squares' rendering organizes the Periodic Table according to perfect square counts of orbitals at Madelung energy levels, making it uniform and intuitive.","cross_cats":["physics.chem-ph"],"primary_cat":"physics.ed-ph","authors_text":"Leonid A. Levin","submitted_at":"2025-06-12T19:36:55Z","abstract_excerpt":"I present a new \"Pairs of Squares\" rendering of the Periodic Table. It takes advantage of the number of orbitals at each Madelung energy level being a whole square. This makes the table very uniform and intuitive in contrast with its currently used presentations."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"This 'Pairs of Squares' rendering makes the Periodic Table very uniform and intuitive in contrast with its currently used presentations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That basing the table layout on the mathematical property that orbital counts at Madelung levels are perfect squares will produce a meaningfully more uniform and intuitive arrangement than existing formats.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proposes an alternative periodic table layout arranged in pairs of squares based on squared orbital counts at successive Madelung energy levels.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The 'Pairs of Squares' rendering organizes the Periodic Table according to perfect square counts of orbitals at Madelung energy levels, making it uniform and intuitive.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"517294ca309c5facfd7595a0eb52a6f7cce0a454bc2a0d0a6084c821b9ad3ed8"},"source":{"id":"2506.11247","kind":"arxiv","version":8},"verdict":{"id":"c682756c-440a-47df-86c9-87458f28307f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T09:42:03.704867Z","strongest_claim":"This 'Pairs of Squares' rendering makes the Periodic Table very uniform and intuitive in contrast with its currently used presentations.","one_line_summary":"Proposes an alternative periodic table layout arranged in pairs of squares based on squared orbital counts at successive Madelung energy levels.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That basing the table layout on the mathematical property that orbital counts at Madelung levels are perfect squares will produce a meaningfully more uniform and intuitive arrangement than existing formats.","pith_extraction_headline":"The 'Pairs of Squares' rendering organizes the Periodic Table according to perfect square counts of orbitals at Madelung energy levels, making it uniform and intuitive."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.11247/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"}