Pith Number

pith:7NFUPEXH

pith:2010:7NFUPEXHDE4WQC25OOV7SLNGC7

not attested not anchored not stored refs pending

General, combinatorial formula for the density of states: insights into the energy equipartition principle and the theory of phase transitions

Agata Fronczak

arxiv:1009.5534 v2 · 2010-09-28 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7NFUPEXHDE4WQC25OOV7SLNGC7}

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	2026-05-18T03:55:21.952251Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fb4b4792e71939680b5d73abf92da617f477e403e7fd7022b7ac043deaf33dcc

Aliases

arxiv: 1009.5534 · arxiv_version: 1009.5534v2 · doi: 10.48550/arxiv.1009.5534 · pith_short_12: 7NFUPEXHDE4W · pith_short_16: 7NFUPEXHDE4WQC25 · pith_short_8: 7NFUPEXH

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/7NFUPEXHDE4WQC25OOV7SLNGC7 \
  | 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: fb4b4792e71939680b5d73abf92da617f477e403e7fd7022b7ac043deaf33dcc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cb475411e625e75e50ac3013ac96c8047c188ef419549ef7647553f132f8c51",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2010-09-28T11:24:32Z",
    "title_canon_sha256": "def20bff91779e77bef57904fb20f0b4f8b96d127d824d02df6c641eeddd9f53"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.5534",
    "kind": "arxiv",
    "version": 2
  }
}