Pith Number

pith:3ALPBNCA

pith:2025:3ALPBNCARBYBGKAAYA3NTA62JB

not attested not anchored not stored refs pending

"Pairs of Squares" Periodic Table

Leonid A. Levin

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.

arxiv:2506.11247 v8 · 2025-06-12 · physics.ed-ph · physics.chem-ph

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3ALPBNCARBYBGKAAYA3NTA62JB}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

This 'Pairs of Squares' rendering makes the Periodic Table very uniform and intuitive in contrast with its currently used presentations.

C2weakest 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.

C3one line summary

Proposes an alternative periodic table layout arranged in pairs of squares based on squared orbital counts at successive Madelung energy levels.

Receipt and verification

First computed	2026-06-05T01:15:14.438198Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d816f0b4408870132800c036d983da4868231f6549a5a19df0652b9835a1d114

Aliases

arxiv: 2506.11247 · arxiv_version: 2506.11247v8 · doi: 10.48550/arxiv.2506.11247 · pith_short_12: 3ALPBNCARBYB · pith_short_16: 3ALPBNCARBYBGKAA · pith_short_8: 3ALPBNCA

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3ALPBNCARBYBGKAAYA3NTA62JB \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d816f0b4408870132800c036d983da4868231f6549a5a19df0652b9835a1d114

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54ce48f4719a6bbc8a69784d85e973d957df125984b37845f7061bdde8918547",
    "cross_cats_sorted": [
      "physics.chem-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.ed-ph",
    "submitted_at": "2025-06-12T19:36:55Z",
    "title_canon_sha256": "341a44fc38bfe6b90896b41bb0f700005b28697b949445dd4680774003649d36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.11247",
    "kind": "arxiv",
    "version": 8
  }
}