Pith Number

pith:6J6SVCUZ

pith:2026:6J6SVCUZNNM4ODIBENRI2KM5HZ

not attested not anchored not stored refs pending

A Density-Based Continuous Local Symmetry Measure

Devin A. Matthews, Duc Anh Lai

Local symmetry in molecules can be measured continuously from electron density localization.

arxiv:2603.22476 v2 · 2026-03-23 · physics.chem-ph

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\usepackage{pith}
\pithnumber{6J6SVCUZNNM4ODIBENRI2KM5HZ}

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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

We introduce a novel framework for evaluating local symmetry based on electron density localization, and present continuous symmetry representations for several representative molecules.

C2weakest assumption

That localizing electron density provides a valid and sufficient basis for defining and quantifying local symmetry without post-hoc adjustments or external benchmarks.

C3one line summary

A novel density-based continuous local symmetry measure is introduced that captures both global and local symmetry features in molecules along with related local chirality concepts.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-17T23:38:59.564719Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f27d2a8a996b59c70d0123628d299d3e60596dd089f20719bb78c4059a24f60d

Aliases

arxiv: 2603.22476 · arxiv_version: 2603.22476v2 · doi: 10.48550/arxiv.2603.22476 · pith_short_12: 6J6SVCUZNNM4 · pith_short_16: 6J6SVCUZNNM4ODIB · pith_short_8: 6J6SVCUZ

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/6J6SVCUZNNM4ODIBENRI2KM5HZ \
  | 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: f27d2a8a996b59c70d0123628d299d3e60596dd089f20719bb78c4059a24f60d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cd1d745d4fd8065b0e1db69b82b0cf95a8178f817c92fad71a8cd1309327fb31",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.chem-ph",
    "submitted_at": "2026-03-23T18:44:58Z",
    "title_canon_sha256": "9b7fc713a7424a76a94a377a63b7bffdbd361341dbbc8aff60dcb4e95310d036"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2603.22476",
    "kind": "arxiv",
    "version": 2
  }
}