Pith Number

pith:6ADUAI4D

pith:2012:6ADUAI4DEG7HPXZFXSNJLYQ4YF

not attested not anchored not stored refs pending

The microscopic meaning of grand potential resulting from combinatorial approach to a general system of particles

Agata Fronczak

arxiv:1205.4986 v1 · 2012-05-21 · physics.gen-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{6ADUAI4DEG7HPXZFXSNJLYQ4YF}

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.

Receipt and verification

First computed	2026-05-18T03:41:58.613402Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f00740238321be77df25bc9a95e21cc15a08d0ef34e0708b21eaa362d89d9bc5

Aliases

arxiv: 1205.4986 · arxiv_version: 1205.4986v1 · doi: 10.48550/arxiv.1205.4986 · pith_short_12: 6ADUAI4DEG7H · pith_short_16: 6ADUAI4DEG7HPXZF · pith_short_8: 6ADUAI4D

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/6ADUAI4DEG7HPXZFXSNJLYQ4YF \
  | 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: f00740238321be77df25bc9a95e21cc15a08d0ef34e0708b21eaa362d89d9bc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f0a861f824a5a5482b2c6717ee245924f1eeac2de25d575e692c03136c6857a",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.gen-ph",
    "submitted_at": "2012-05-21T12:31:22Z",
    "title_canon_sha256": "f7c081bde31c77fec9442070bdefe535c93a18e17309611cf92fcd1ad77602f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.4986",
    "kind": "arxiv",
    "version": 1
  }
}