Pith Number

pith:AJTAP2S4

pith:2010:AJTAP2S4FGE75CV76V2GTN37CJ

not attested not anchored not stored refs pending

A variational formula for the free energy of an interacting many-particle system

Andrea Collevecchio, Stefan Adams, Wolfgang K\"onig

arxiv:1003.1393 v3 · 2010-03-06 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{AJTAP2S4FGE75CV76V2GTN37CJ}

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	2026-05-18T04:23:56.921505Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

026607ea5c2989fe8abff57469b77f126ac50e2dc6af1e665aa16a5eb0d8d731

Aliases

arxiv: 1003.1393 · arxiv_version: 1003.1393v3 · doi: 10.48550/arxiv.1003.1393 · pith_short_12: AJTAP2S4FGE7 · pith_short_16: AJTAP2S4FGE75CV7 · pith_short_8: AJTAP2S4

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/AJTAP2S4FGE75CV76V2GTN37CJ \
  | 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: 026607ea5c2989fe8abff57469b77f126ac50e2dc6af1e665aa16a5eb0d8d731

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ce24c7ebf42e94f64d32c149708a25b9752829dd9c70239018f725d6b1f0f82",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-03-06T15:24:46Z",
    "title_canon_sha256": "9c74016fb17c6ae8b7c2dcab29f53a417f001a10a9edab9f761dbd0e08129e6f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.1393",
    "kind": "arxiv",
    "version": 3
  }
}