Pith Number

pith:7OGSCD5L

pith:2026:7OGSCD5LFUCH4SGQXMKFUQ45YU

not attested not anchored not stored refs resolved

Shannon and R\'enyi entropies of molecular densities: insights into extensivity and the incomplete description of electron correlation

\'Angel Mart\'in Pend\'as, Diogo J. L. Rodrigues, Evelio Francisco

Electron-density entropies fail to capture static correlation and often violate extensivity.

arxiv:2604.18081 v1 · 2026-04-20 · quant-ph · physics.chem-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7OGSCD5LFUCH4SGQXMKFUQ45YU}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

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

electron-density-based measures are insufficient for capturing static correlation, suggesting that robust entropic descriptors should be constructed from higher-dimensional Hilbert-space objects.

C2weakest assumption

The Mulliken-like atomic partition combined with the infinite-separation asymptotic analysis correctly isolates and quantifies static correlation and extensivity properties of the underlying wavefunction.

C3one line summary

Shannon and Rényi entropies from molecular electron densities fail to encode static correlation and violate extensivity, indicating density-based descriptors are insufficient.

References

109 extracted · 6 resolved · 0 Pith anchors

[1] Shannon, C. E. A mathematical theory of communication.Bell System Tech- nical Journal27, 379–423 (1948) 1948

[2] Brillouin, L.Science and information theory(Courier Corporation, 2013) 2013

[3] Frieden, B. R., Luo, S. & Plastino, A. Physics and information.Physics Today 60, 14 (2007) 2007

[4] Jaynes, E. T. Information theory and statistical mechanics.Physical Review 106, 620–630 (1957) 1957

[5] Gatenby, R. A. & Frieden, B. R. Information theory in living systems, meth- ods, applications, and challenges.Bulletin of Mathematical Biology69, 635– 657 (2007) 2007

Receipt and verification

First computed	2026-05-21T01:05:19.293004Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb8d210fab2d047e48d0bb145a439dc522fa2c2dc1bc7699024c08710449cce4

Aliases

arxiv: 2604.18081 · arxiv_version: 2604.18081v1 · doi: 10.48550/arxiv.2604.18081 · pith_short_12: 7OGSCD5LFUCH · pith_short_16: 7OGSCD5LFUCH4SGQ · pith_short_8: 7OGSCD5L

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/7OGSCD5LFUCH4SGQXMKFUQ45YU \
  | 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: fb8d210fab2d047e48d0bb145a439dc522fa2c2dc1bc7699024c08710449cce4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "060411ab0f7a0326de6f9aa053e3cd5a166e54c53bc78216e5437be63bb778ba",
    "cross_cats_sorted": [
      "physics.chem-ph"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "quant-ph",
    "submitted_at": "2026-04-20T10:53:35Z",
    "title_canon_sha256": "8b6c9906fff280c75909f0eb859dee82739f429a6f5e4a63fcb56026b49b4d89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.18081",
    "kind": "arxiv",
    "version": 1
  }
}